//------------------------------------------------------------------------------------- // DirectXCollision.inl -- C++ Collision Math library // // Copyright (c) Microsoft Corporation. All rights reserved. // Licensed under the MIT License. // // http://go.microsoft.com/fwlink/?LinkID=615560 //------------------------------------------------------------------------------------- #pragma once XMGLOBALCONST XMVECTORF32 g_BoxOffset[8] = { { { { -1.0f, -1.0f, 1.0f, 0.0f } } }, { { { 1.0f, -1.0f, 1.0f, 0.0f } } }, { { { 1.0f, 1.0f, 1.0f, 0.0f } } }, { { { -1.0f, 1.0f, 1.0f, 0.0f } } }, { { { -1.0f, -1.0f, -1.0f, 0.0f } } }, { { { 1.0f, -1.0f, -1.0f, 0.0f } } }, { { { 1.0f, 1.0f, -1.0f, 0.0f } } }, { { { -1.0f, 1.0f, -1.0f, 0.0f } } }, }; XMGLOBALCONST XMVECTORF32 g_RayEpsilon = { { { 1e-20f, 1e-20f, 1e-20f, 1e-20f } } }; XMGLOBALCONST XMVECTORF32 g_RayNegEpsilon = { { { -1e-20f, -1e-20f, -1e-20f, -1e-20f } } }; XMGLOBALCONST XMVECTORF32 g_FltMin = { { { -FLT_MAX, -FLT_MAX, -FLT_MAX, -FLT_MAX } } }; XMGLOBALCONST XMVECTORF32 g_FltMax = { { { FLT_MAX, FLT_MAX, FLT_MAX, FLT_MAX } } }; namespace Internal { //----------------------------------------------------------------------------- // Return true if any of the elements of a 3 vector are equal to 0xffffffff. // Slightly more efficient than using XMVector3EqualInt. //----------------------------------------------------------------------------- inline bool XMVector3AnyTrue(_In_ FXMVECTOR V) noexcept { // Duplicate the fourth element from the first element. XMVECTOR C = XMVectorSwizzle(V); return XMComparisonAnyTrue(XMVector4EqualIntR(C, XMVectorTrueInt())); } //----------------------------------------------------------------------------- // Return true if all of the elements of a 3 vector are equal to 0xffffffff. // Slightly more efficient than using XMVector3EqualInt. //----------------------------------------------------------------------------- inline bool XMVector3AllTrue(_In_ FXMVECTOR V) noexcept { // Duplicate the fourth element from the first element. XMVECTOR C = XMVectorSwizzle(V); return XMComparisonAllTrue(XMVector4EqualIntR(C, XMVectorTrueInt())); } #if defined(_PREFAST_) || !defined(NDEBUG) XMGLOBALCONST XMVECTORF32 g_UnitVectorEpsilon = { { { 1.0e-4f, 1.0e-4f, 1.0e-4f, 1.0e-4f } } }; XMGLOBALCONST XMVECTORF32 g_UnitQuaternionEpsilon = { { { 1.0e-4f, 1.0e-4f, 1.0e-4f, 1.0e-4f } } }; XMGLOBALCONST XMVECTORF32 g_UnitPlaneEpsilon = { { { 1.0e-4f, 1.0e-4f, 1.0e-4f, 1.0e-4f } } }; //----------------------------------------------------------------------------- // Return true if the vector is a unit vector (length == 1). //----------------------------------------------------------------------------- inline bool XMVector3IsUnit(_In_ FXMVECTOR V) noexcept { XMVECTOR Difference = XMVectorSubtract(XMVector3Length(V), XMVectorSplatOne()); return XMVector4Less(XMVectorAbs(Difference), g_UnitVectorEpsilon); } //----------------------------------------------------------------------------- // Return true if the quaterion is a unit quaternion. //----------------------------------------------------------------------------- inline bool XMQuaternionIsUnit(_In_ FXMVECTOR Q) noexcept { XMVECTOR Difference = XMVectorSubtract(XMVector4Length(Q), XMVectorSplatOne()); return XMVector4Less(XMVectorAbs(Difference), g_UnitQuaternionEpsilon); } //----------------------------------------------------------------------------- // Return true if the plane is a unit plane. //----------------------------------------------------------------------------- inline bool XMPlaneIsUnit(_In_ FXMVECTOR Plane) noexcept { XMVECTOR Difference = XMVectorSubtract(XMVector3Length(Plane), XMVectorSplatOne()); return XMVector4Less(XMVectorAbs(Difference), g_UnitPlaneEpsilon); } #endif // _PREFAST_ || !NDEBUG //----------------------------------------------------------------------------- inline XMVECTOR XMPlaneTransform(_In_ FXMVECTOR Plane, _In_ FXMVECTOR Rotation, _In_ FXMVECTOR Translation) noexcept { XMVECTOR vNormal = XMVector3Rotate(Plane, Rotation); XMVECTOR vD = XMVectorSubtract(XMVectorSplatW(Plane), XMVector3Dot(vNormal, Translation)); return XMVectorInsert<0, 0, 0, 0, 1>(vNormal, vD); } //----------------------------------------------------------------------------- // Return the point on the line segement (S1, S2) nearest the point P. //----------------------------------------------------------------------------- inline XMVECTOR PointOnLineSegmentNearestPoint(_In_ FXMVECTOR S1, _In_ FXMVECTOR S2, _In_ FXMVECTOR P) noexcept { XMVECTOR Dir = XMVectorSubtract(S2, S1); XMVECTOR Projection = XMVectorSubtract(XMVector3Dot(P, Dir), XMVector3Dot(S1, Dir)); XMVECTOR LengthSq = XMVector3Dot(Dir, Dir); XMVECTOR t = XMVectorMultiply(Projection, XMVectorReciprocal(LengthSq)); XMVECTOR Point = XMVectorMultiplyAdd(t, Dir, S1); // t < 0 XMVECTOR SelectS1 = XMVectorLess(Projection, XMVectorZero()); Point = XMVectorSelect(Point, S1, SelectS1); // t > 1 XMVECTOR SelectS2 = XMVectorGreater(Projection, LengthSq); Point = XMVectorSelect(Point, S2, SelectS2); return Point; } //----------------------------------------------------------------------------- // Test if the point (P) on the plane of the triangle is inside the triangle // (V0, V1, V2). //----------------------------------------------------------------------------- inline XMVECTOR XM_CALLCONV PointOnPlaneInsideTriangle(_In_ FXMVECTOR P, _In_ FXMVECTOR V0, _In_ FXMVECTOR V1, _In_ GXMVECTOR V2) noexcept { // Compute the triangle normal. XMVECTOR N = XMVector3Cross(XMVectorSubtract(V2, V0), XMVectorSubtract(V1, V0)); // Compute the cross products of the vector from the base of each edge to // the point with each edge vector. XMVECTOR C0 = XMVector3Cross(XMVectorSubtract(P, V0), XMVectorSubtract(V1, V0)); XMVECTOR C1 = XMVector3Cross(XMVectorSubtract(P, V1), XMVectorSubtract(V2, V1)); XMVECTOR C2 = XMVector3Cross(XMVectorSubtract(P, V2), XMVectorSubtract(V0, V2)); // If the cross product points in the same direction as the normal the the // point is inside the edge (it is zero if is on the edge). XMVECTOR Zero = XMVectorZero(); XMVECTOR Inside0 = XMVectorGreaterOrEqual(XMVector3Dot(C0, N), Zero); XMVECTOR Inside1 = XMVectorGreaterOrEqual(XMVector3Dot(C1, N), Zero); XMVECTOR Inside2 = XMVectorGreaterOrEqual(XMVector3Dot(C2, N), Zero); // If the point inside all of the edges it is inside. return XMVectorAndInt(XMVectorAndInt(Inside0, Inside1), Inside2); } //----------------------------------------------------------------------------- inline bool SolveCubic(_In_ float e, _In_ float f, _In_ float g, _Out_ float* t, _Out_ float* u, _Out_ float* v) noexcept { float p, q, h, rc, d, theta, costh3, sinth3; p = f - e * e / 3.0f; q = g - e * f / 3.0f + e * e * e * 2.0f / 27.0f; h = q * q / 4.0f + p * p * p / 27.0f; if (h > 0) { *t = *u = *v = 0.f; return false; // only one real root } if ((h == 0) && (q == 0)) // all the same root { *t = -e / 3; *u = -e / 3; *v = -e / 3; return true; } d = sqrtf(q * q / 4.0f - h); if (d < 0) rc = -powf(-d, 1.0f / 3.0f); else rc = powf(d, 1.0f / 3.0f); theta = XMScalarACos(-q / (2.0f * d)); costh3 = XMScalarCos(theta / 3.0f); sinth3 = sqrtf(3.0f) * XMScalarSin(theta / 3.0f); *t = 2.0f * rc * costh3 - e / 3.0f; *u = -rc * (costh3 + sinth3) - e / 3.0f; *v = -rc * (costh3 - sinth3) - e / 3.0f; return true; } //----------------------------------------------------------------------------- inline XMVECTOR CalculateEigenVector(_In_ float m11, _In_ float m12, _In_ float m13, _In_ float m22, _In_ float m23, _In_ float m33, _In_ float e) noexcept { float fTmp[3]; fTmp[0] = m12 * m23 - m13 * (m22 - e); fTmp[1] = m13 * m12 - m23 * (m11 - e); fTmp[2] = (m11 - e) * (m22 - e) - m12 * m12; XMVECTOR vTmp = XMLoadFloat3(reinterpret_cast(fTmp)); if (XMVector3Equal(vTmp, XMVectorZero())) // planar or linear { float f1, f2, f3; // we only have one equation - find a valid one if ((m11 - e != 0) || (m12 != 0) || (m13 != 0)) { f1 = m11 - e; f2 = m12; f3 = m13; } else if ((m12 != 0) || (m22 - e != 0) || (m23 != 0)) { f1 = m12; f2 = m22 - e; f3 = m23; } else if ((m13 != 0) || (m23 != 0) || (m33 - e != 0)) { f1 = m13; f2 = m23; f3 = m33 - e; } else { // error, we'll just make something up - we have NO context f1 = 1.0f; f2 = 0.0f; f3 = 0.0f; } if (f1 == 0) vTmp = XMVectorSetX(vTmp, 0.0f); else vTmp = XMVectorSetX(vTmp, 1.0f); if (f2 == 0) vTmp = XMVectorSetY(vTmp, 0.0f); else vTmp = XMVectorSetY(vTmp, 1.0f); if (f3 == 0) { vTmp = XMVectorSetZ(vTmp, 0.0f); // recalculate y to make equation work if (m12 != 0) vTmp = XMVectorSetY(vTmp, -f1 / f2); } else { vTmp = XMVectorSetZ(vTmp, (f2 - f1) / f3); } } if (XMVectorGetX(XMVector3LengthSq(vTmp)) > 1e-5f) { return XMVector3Normalize(vTmp); } else { // Multiply by a value large enough to make the vector non-zero. vTmp = XMVectorScale(vTmp, 1e5f); return XMVector3Normalize(vTmp); } } //----------------------------------------------------------------------------- inline bool CalculateEigenVectors(_In_ float m11, _In_ float m12, _In_ float m13, _In_ float m22, _In_ float m23, _In_ float m33, _In_ float e1, _In_ float e2, _In_ float e3, _Out_ XMVECTOR* pV1, _Out_ XMVECTOR* pV2, _Out_ XMVECTOR* pV3) noexcept { *pV1 = DirectX::Internal::CalculateEigenVector(m11, m12, m13, m22, m23, m33, e1); *pV2 = DirectX::Internal::CalculateEigenVector(m11, m12, m13, m22, m23, m33, e2); *pV3 = DirectX::Internal::CalculateEigenVector(m11, m12, m13, m22, m23, m33, e3); bool v1z = false; bool v2z = false; bool v3z = false; XMVECTOR Zero = XMVectorZero(); if (XMVector3Equal(*pV1, Zero)) v1z = true; if (XMVector3Equal(*pV2, Zero)) v2z = true; if (XMVector3Equal(*pV3, Zero)) v3z = true; bool e12 = (fabsf(XMVectorGetX(XMVector3Dot(*pV1, *pV2))) > 0.1f); // check for non-orthogonal vectors bool e13 = (fabsf(XMVectorGetX(XMVector3Dot(*pV1, *pV3))) > 0.1f); bool e23 = (fabsf(XMVectorGetX(XMVector3Dot(*pV2, *pV3))) > 0.1f); if ((v1z && v2z && v3z) || (e12 && e13 && e23) || (e12 && v3z) || (e13 && v2z) || (e23 && v1z)) // all eigenvectors are 0- any basis set { *pV1 = g_XMIdentityR0.v; *pV2 = g_XMIdentityR1.v; *pV3 = g_XMIdentityR2.v; return true; } if (v1z && v2z) { XMVECTOR vTmp = XMVector3Cross(g_XMIdentityR1, *pV3); if (XMVectorGetX(XMVector3LengthSq(vTmp)) < 1e-5f) { vTmp = XMVector3Cross(g_XMIdentityR0, *pV3); } *pV1 = XMVector3Normalize(vTmp); *pV2 = XMVector3Cross(*pV3, *pV1); return true; } if (v3z && v1z) { XMVECTOR vTmp = XMVector3Cross(g_XMIdentityR1, *pV2); if (XMVectorGetX(XMVector3LengthSq(vTmp)) < 1e-5f) { vTmp = XMVector3Cross(g_XMIdentityR0, *pV2); } *pV3 = XMVector3Normalize(vTmp); *pV1 = XMVector3Cross(*pV2, *pV3); return true; } if (v2z && v3z) { XMVECTOR vTmp = XMVector3Cross(g_XMIdentityR1, *pV1); if (XMVectorGetX(XMVector3LengthSq(vTmp)) < 1e-5f) { vTmp = XMVector3Cross(g_XMIdentityR0, *pV1); } *pV2 = XMVector3Normalize(vTmp); *pV3 = XMVector3Cross(*pV1, *pV2); return true; } if ((v1z) || e12) { *pV1 = XMVector3Cross(*pV2, *pV3); return true; } if ((v2z) || e23) { *pV2 = XMVector3Cross(*pV3, *pV1); return true; } if ((v3z) || e13) { *pV3 = XMVector3Cross(*pV1, *pV2); return true; } return true; } //----------------------------------------------------------------------------- inline bool CalculateEigenVectorsFromCovarianceMatrix(_In_ float Cxx, _In_ float Cyy, _In_ float Czz, _In_ float Cxy, _In_ float Cxz, _In_ float Cyz, _Out_ XMVECTOR* pV1, _Out_ XMVECTOR* pV2, _Out_ XMVECTOR* pV3) noexcept { // Calculate the eigenvalues by solving a cubic equation. float e = -(Cxx + Cyy + Czz); float f = Cxx * Cyy + Cyy * Czz + Czz * Cxx - Cxy * Cxy - Cxz * Cxz - Cyz * Cyz; float g = Cxy * Cxy * Czz + Cxz * Cxz * Cyy + Cyz * Cyz * Cxx - Cxy * Cyz * Cxz * 2.0f - Cxx * Cyy * Czz; float ev1, ev2, ev3; if (!DirectX::Internal::SolveCubic(e, f, g, &ev1, &ev2, &ev3)) { // set them to arbitrary orthonormal basis set *pV1 = g_XMIdentityR0.v; *pV2 = g_XMIdentityR1.v; *pV3 = g_XMIdentityR2.v; return false; } return DirectX::Internal::CalculateEigenVectors(Cxx, Cxy, Cxz, Cyy, Cyz, Czz, ev1, ev2, ev3, pV1, pV2, pV3); } //----------------------------------------------------------------------------- inline void XM_CALLCONV FastIntersectTrianglePlane( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2, GXMVECTOR Plane, XMVECTOR& Outside, XMVECTOR& Inside) noexcept { // Plane0 XMVECTOR Dist0 = XMVector4Dot(V0, Plane); XMVECTOR Dist1 = XMVector4Dot(V1, Plane); XMVECTOR Dist2 = XMVector4Dot(V2, Plane); XMVECTOR MinDist = XMVectorMin(Dist0, Dist1); MinDist = XMVectorMin(MinDist, Dist2); XMVECTOR MaxDist = XMVectorMax(Dist0, Dist1); MaxDist = XMVectorMax(MaxDist, Dist2); XMVECTOR Zero = XMVectorZero(); // Outside the plane? Outside = XMVectorGreater(MinDist, Zero); // Fully inside the plane? Inside = XMVectorLess(MaxDist, Zero); } //----------------------------------------------------------------------------- inline void FastIntersectSpherePlane(_In_ FXMVECTOR Center, _In_ FXMVECTOR Radius, _In_ FXMVECTOR Plane, _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside) noexcept { XMVECTOR Dist = XMVector4Dot(Center, Plane); // Outside the plane? Outside = XMVectorGreater(Dist, Radius); // Fully inside the plane? Inside = XMVectorLess(Dist, XMVectorNegate(Radius)); } //----------------------------------------------------------------------------- inline void FastIntersectAxisAlignedBoxPlane(_In_ FXMVECTOR Center, _In_ FXMVECTOR Extents, _In_ FXMVECTOR Plane, _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside) noexcept { // Compute the distance to the center of the box. XMVECTOR Dist = XMVector4Dot(Center, Plane); // Project the axes of the box onto the normal of the plane. Half the // length of the projection (sometime called the "radius") is equal to // h(u) * abs(n dot b(u))) + h(v) * abs(n dot b(v)) + h(w) * abs(n dot b(w)) // where h(i) are extents of the box, n is the plane normal, and b(i) are the // axes of the box. In this case b(i) = [(1,0,0), (0,1,0), (0,0,1)]. XMVECTOR Radius = XMVector3Dot(Extents, XMVectorAbs(Plane)); // Outside the plane? Outside = XMVectorGreater(Dist, Radius); // Fully inside the plane? Inside = XMVectorLess(Dist, XMVectorNegate(Radius)); } //----------------------------------------------------------------------------- inline void XM_CALLCONV FastIntersectOrientedBoxPlane( _In_ FXMVECTOR Center, _In_ FXMVECTOR Extents, _In_ FXMVECTOR Axis0, _In_ GXMVECTOR Axis1, _In_ HXMVECTOR Axis2, _In_ HXMVECTOR Plane, _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside) noexcept { // Compute the distance to the center of the box. XMVECTOR Dist = XMVector4Dot(Center, Plane); // Project the axes of the box onto the normal of the plane. Half the // length of the projection (sometime called the "radius") is equal to // h(u) * abs(n dot b(u))) + h(v) * abs(n dot b(v)) + h(w) * abs(n dot b(w)) // where h(i) are extents of the box, n is the plane normal, and b(i) are the // axes of the box. XMVECTOR Radius = XMVector3Dot(Plane, Axis0); Radius = XMVectorInsert<0, 0, 1, 0, 0>(Radius, XMVector3Dot(Plane, Axis1)); Radius = XMVectorInsert<0, 0, 0, 1, 0>(Radius, XMVector3Dot(Plane, Axis2)); Radius = XMVector3Dot(Extents, XMVectorAbs(Radius)); // Outside the plane? Outside = XMVectorGreater(Dist, Radius); // Fully inside the plane? Inside = XMVectorLess(Dist, XMVectorNegate(Radius)); } //----------------------------------------------------------------------------- inline void XM_CALLCONV FastIntersectFrustumPlane( _In_ FXMVECTOR Point0, _In_ FXMVECTOR Point1, _In_ FXMVECTOR Point2, _In_ GXMVECTOR Point3, _In_ HXMVECTOR Point4, _In_ HXMVECTOR Point5, _In_ CXMVECTOR Point6, _In_ CXMVECTOR Point7, _In_ CXMVECTOR Plane, _Out_ XMVECTOR& Outside, _Out_ XMVECTOR& Inside) noexcept { // Find the min/max projection of the frustum onto the plane normal. XMVECTOR Min, Max, Dist; Min = Max = XMVector3Dot(Plane, Point0); Dist = XMVector3Dot(Plane, Point1); Min = XMVectorMin(Min, Dist); Max = XMVectorMax(Max, Dist); Dist = XMVector3Dot(Plane, Point2); Min = XMVectorMin(Min, Dist); Max = XMVectorMax(Max, Dist); Dist = XMVector3Dot(Plane, Point3); Min = XMVectorMin(Min, Dist); Max = XMVectorMax(Max, Dist); Dist = XMVector3Dot(Plane, Point4); Min = XMVectorMin(Min, Dist); Max = XMVectorMax(Max, Dist); Dist = XMVector3Dot(Plane, Point5); Min = XMVectorMin(Min, Dist); Max = XMVectorMax(Max, Dist); Dist = XMVector3Dot(Plane, Point6); Min = XMVectorMin(Min, Dist); Max = XMVectorMax(Max, Dist); Dist = XMVector3Dot(Plane, Point7); Min = XMVectorMin(Min, Dist); Max = XMVectorMax(Max, Dist); XMVECTOR PlaneDist = XMVectorNegate(XMVectorSplatW(Plane)); // Outside the plane? Outside = XMVectorGreater(Min, PlaneDist); // Fully inside the plane? Inside = XMVectorLess(Max, PlaneDist); } } // namespace Internal /**************************************************************************** * * BoundingSphere * ****************************************************************************/ //----------------------------------------------------------------------------- // Transform a sphere by an angle preserving transform. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void XM_CALLCONV BoundingSphere::Transform(BoundingSphere& Out, FXMMATRIX M) const noexcept { // Load the center of the sphere. XMVECTOR vCenter = XMLoadFloat3(&Center); // Transform the center of the sphere. XMVECTOR C = XMVector3Transform(vCenter, M); XMVECTOR dX = XMVector3Dot(M.r[0], M.r[0]); XMVECTOR dY = XMVector3Dot(M.r[1], M.r[1]); XMVECTOR dZ = XMVector3Dot(M.r[2], M.r[2]); XMVECTOR d = XMVectorMax(dX, XMVectorMax(dY, dZ)); // Store the center sphere. XMStoreFloat3(&Out.Center, C); // Scale the radius of the pshere. float Scale = sqrtf(XMVectorGetX(d)); Out.Radius = Radius * Scale; } _Use_decl_annotations_ inline void XM_CALLCONV BoundingSphere::Transform(BoundingSphere& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation) const noexcept { // Load the center of the sphere. XMVECTOR vCenter = XMLoadFloat3(&Center); // Transform the center of the sphere. vCenter = XMVectorAdd(XMVector3Rotate(XMVectorScale(vCenter, Scale), Rotation), Translation); // Store the center sphere. XMStoreFloat3(&Out.Center, vCenter); // Scale the radius of the pshere. Out.Radius = Radius * Scale; } //----------------------------------------------------------------------------- // Point in sphere test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingSphere::Contains(FXMVECTOR Point) const noexcept { XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); XMVECTOR DistanceSquared = XMVector3LengthSq(XMVectorSubtract(Point, vCenter)); XMVECTOR RadiusSquared = XMVectorMultiply(vRadius, vRadius); return XMVector3LessOrEqual(DistanceSquared, RadiusSquared) ? CONTAINS : DISJOINT; } //----------------------------------------------------------------------------- // Triangle in sphere test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingSphere::Contains(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { if (!Intersects(V0, V1, V2)) return DISJOINT; XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); XMVECTOR RadiusSquared = XMVectorMultiply(vRadius, vRadius); XMVECTOR DistanceSquared = XMVector3LengthSq(XMVectorSubtract(V0, vCenter)); XMVECTOR Inside = XMVectorLessOrEqual(DistanceSquared, RadiusSquared); DistanceSquared = XMVector3LengthSq(XMVectorSubtract(V1, vCenter)); Inside = XMVectorAndInt(Inside, XMVectorLessOrEqual(DistanceSquared, RadiusSquared)); DistanceSquared = XMVector3LengthSq(XMVectorSubtract(V2, vCenter)); Inside = XMVectorAndInt(Inside, XMVectorLessOrEqual(DistanceSquared, RadiusSquared)); return (XMVector3EqualInt(Inside, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Sphere in sphere test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingSphere::Contains(const BoundingSphere& sh) const noexcept { XMVECTOR Center1 = XMLoadFloat3(&Center); float r1 = Radius; XMVECTOR Center2 = XMLoadFloat3(&sh.Center); float r2 = sh.Radius; XMVECTOR V = XMVectorSubtract(Center2, Center1); XMVECTOR Dist = XMVector3Length(V); float d = XMVectorGetX(Dist); return (r1 + r2 >= d) ? ((r1 - r2 >= d) ? CONTAINS : INTERSECTS) : DISJOINT; } //----------------------------------------------------------------------------- // Axis-aligned box in sphere test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingSphere::Contains(const BoundingBox& box) const noexcept { if (!box.Intersects(*this)) return DISJOINT; XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); XMVECTOR RadiusSq = XMVectorMultiply(vRadius, vRadius); XMVECTOR boxCenter = XMLoadFloat3(&box.Center); XMVECTOR boxExtents = XMLoadFloat3(&box.Extents); XMVECTOR InsideAll = XMVectorTrueInt(); XMVECTOR offset = XMVectorSubtract(boxCenter, vCenter); for (size_t i = 0; i < BoundingBox::CORNER_COUNT; ++i) { XMVECTOR C = XMVectorMultiplyAdd(boxExtents, g_BoxOffset[i], offset); XMVECTOR d = XMVector3LengthSq(C); InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(d, RadiusSq)); } return (XMVector3EqualInt(InsideAll, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Oriented box in sphere test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingSphere::Contains(const BoundingOrientedBox& box) const noexcept { if (!box.Intersects(*this)) return DISJOINT; XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); XMVECTOR RadiusSq = XMVectorMultiply(vRadius, vRadius); XMVECTOR boxCenter = XMLoadFloat3(&box.Center); XMVECTOR boxExtents = XMLoadFloat3(&box.Extents); XMVECTOR boxOrientation = XMLoadFloat4(&box.Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(boxOrientation)); XMVECTOR InsideAll = XMVectorTrueInt(); for (size_t i = 0; i < BoundingOrientedBox::CORNER_COUNT; ++i) { XMVECTOR C = XMVectorAdd(XMVector3Rotate(XMVectorMultiply(boxExtents, g_BoxOffset[i]), boxOrientation), boxCenter); XMVECTOR d = XMVector3LengthSq(XMVectorSubtract(vCenter, C)); InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(d, RadiusSq)); } return (XMVector3EqualInt(InsideAll, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Frustum in sphere test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingSphere::Contains(const BoundingFrustum& fr) const noexcept { if (!fr.Intersects(*this)) return DISJOINT; XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); XMVECTOR RadiusSq = XMVectorMultiply(vRadius, vRadius); XMVECTOR vOrigin = XMLoadFloat3(&fr.Origin); XMVECTOR vOrientation = XMLoadFloat4(&fr.Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Build the corners of the frustum. XMVECTOR vRightTop = XMVectorSet(fr.RightSlope, fr.TopSlope, 1.0f, 0.0f); XMVECTOR vRightBottom = XMVectorSet(fr.RightSlope, fr.BottomSlope, 1.0f, 0.0f); XMVECTOR vLeftTop = XMVectorSet(fr.LeftSlope, fr.TopSlope, 1.0f, 0.0f); XMVECTOR vLeftBottom = XMVectorSet(fr.LeftSlope, fr.BottomSlope, 1.0f, 0.0f); XMVECTOR vNear = XMVectorReplicatePtr(&fr.Near); XMVECTOR vFar = XMVectorReplicatePtr(&fr.Far); XMVECTOR Corners[BoundingFrustum::CORNER_COUNT]; Corners[0] = XMVectorMultiply(vRightTop, vNear); Corners[1] = XMVectorMultiply(vRightBottom, vNear); Corners[2] = XMVectorMultiply(vLeftTop, vNear); Corners[3] = XMVectorMultiply(vLeftBottom, vNear); Corners[4] = XMVectorMultiply(vRightTop, vFar); Corners[5] = XMVectorMultiply(vRightBottom, vFar); Corners[6] = XMVectorMultiply(vLeftTop, vFar); Corners[7] = XMVectorMultiply(vLeftBottom, vFar); XMVECTOR InsideAll = XMVectorTrueInt(); for (size_t i = 0; i < BoundingFrustum::CORNER_COUNT; ++i) { XMVECTOR C = XMVectorAdd(XMVector3Rotate(Corners[i], vOrientation), vOrigin); XMVECTOR d = XMVector3LengthSq(XMVectorSubtract(vCenter, C)); InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(d, RadiusSq)); } return (XMVector3EqualInt(InsideAll, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Sphere vs. sphere test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingSphere::Intersects(const BoundingSphere& sh) const noexcept { // Load A. XMVECTOR vCenterA = XMLoadFloat3(&Center); XMVECTOR vRadiusA = XMVectorReplicatePtr(&Radius); // Load B. XMVECTOR vCenterB = XMLoadFloat3(&sh.Center); XMVECTOR vRadiusB = XMVectorReplicatePtr(&sh.Radius); // Distance squared between centers. XMVECTOR Delta = XMVectorSubtract(vCenterB, vCenterA); XMVECTOR DistanceSquared = XMVector3LengthSq(Delta); // Sum of the radii squared. XMVECTOR RadiusSquared = XMVectorAdd(vRadiusA, vRadiusB); RadiusSquared = XMVectorMultiply(RadiusSquared, RadiusSquared); return XMVector3LessOrEqual(DistanceSquared, RadiusSquared); } //----------------------------------------------------------------------------- // Box vs. sphere test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingSphere::Intersects(const BoundingBox& box) const noexcept { return box.Intersects(*this); } _Use_decl_annotations_ inline bool BoundingSphere::Intersects(const BoundingOrientedBox& box) const noexcept { return box.Intersects(*this); } //----------------------------------------------------------------------------- // Frustum vs. sphere test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingSphere::Intersects(const BoundingFrustum& fr) const noexcept { return fr.Intersects(*this); } //----------------------------------------------------------------------------- // Triangle vs sphere test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingSphere::Intersects(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { // Load the sphere. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); // Compute the plane of the triangle (has to be normalized). XMVECTOR N = XMVector3Normalize(XMVector3Cross(XMVectorSubtract(V1, V0), XMVectorSubtract(V2, V0))); // Assert that the triangle is not degenerate. assert(!XMVector3Equal(N, XMVectorZero())); // Find the nearest feature on the triangle to the sphere. XMVECTOR Dist = XMVector3Dot(XMVectorSubtract(vCenter, V0), N); // If the center of the sphere is farther from the plane of the triangle than // the radius of the sphere, then there cannot be an intersection. XMVECTOR NoIntersection = XMVectorLess(Dist, XMVectorNegate(vRadius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Dist, vRadius)); // Project the center of the sphere onto the plane of the triangle. XMVECTOR Point = XMVectorNegativeMultiplySubtract(N, Dist, vCenter); // Is it inside all the edges? If so we intersect because the distance // to the plane is less than the radius. XMVECTOR Intersection = DirectX::Internal::PointOnPlaneInsideTriangle(Point, V0, V1, V2); // Find the nearest point on each edge. XMVECTOR RadiusSq = XMVectorMultiply(vRadius, vRadius); // Edge 0,1 Point = DirectX::Internal::PointOnLineSegmentNearestPoint(V0, V1, vCenter); // If the distance to the center of the sphere to the point is less than // the radius of the sphere then it must intersect. Intersection = XMVectorOrInt(Intersection, XMVectorLessOrEqual(XMVector3LengthSq(XMVectorSubtract(vCenter, Point)), RadiusSq)); // Edge 1,2 Point = DirectX::Internal::PointOnLineSegmentNearestPoint(V1, V2, vCenter); // If the distance to the center of the sphere to the point is less than // the radius of the sphere then it must intersect. Intersection = XMVectorOrInt(Intersection, XMVectorLessOrEqual(XMVector3LengthSq(XMVectorSubtract(vCenter, Point)), RadiusSq)); // Edge 2,0 Point = DirectX::Internal::PointOnLineSegmentNearestPoint(V2, V0, vCenter); // If the distance to the center of the sphere to the point is less than // the radius of the sphere then it must intersect. Intersection = XMVectorOrInt(Intersection, XMVectorLessOrEqual(XMVector3LengthSq(XMVectorSubtract(vCenter, Point)), RadiusSq)); return XMVector4EqualInt(XMVectorAndCInt(Intersection, NoIntersection), XMVectorTrueInt()); } //----------------------------------------------------------------------------- // Sphere-plane intersection //----------------------------------------------------------------------------- _Use_decl_annotations_ inline PlaneIntersectionType XM_CALLCONV BoundingSphere::Intersects(FXMVECTOR Plane) const noexcept { assert(DirectX::Internal::XMPlaneIsUnit(Plane)); // Load the sphere. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); // Set w of the center to one so we can dot4 with a plane. vCenter = XMVectorInsert<0, 0, 0, 0, 1>(vCenter, XMVectorSplatOne()); XMVECTOR Outside, Inside; DirectX::Internal::FastIntersectSpherePlane(vCenter, vRadius, Plane, Outside, Inside); // If the sphere is outside any plane it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return FRONT; // If the sphere is inside all planes it is inside. if (XMVector4EqualInt(Inside, XMVectorTrueInt())) return BACK; // The sphere is not inside all planes or outside a plane it intersects. return INTERSECTING; } //----------------------------------------------------------------------------- // Compute the intersection of a ray (Origin, Direction) with a sphere. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingSphere::Intersects(FXMVECTOR Origin, FXMVECTOR Direction, float& Dist) const noexcept { assert(DirectX::Internal::XMVector3IsUnit(Direction)); XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); // l is the vector from the ray origin to the center of the sphere. XMVECTOR l = XMVectorSubtract(vCenter, Origin); // s is the projection of the l onto the ray direction. XMVECTOR s = XMVector3Dot(l, Direction); XMVECTOR l2 = XMVector3Dot(l, l); XMVECTOR r2 = XMVectorMultiply(vRadius, vRadius); // m2 is squared distance from the center of the sphere to the projection. XMVECTOR m2 = XMVectorNegativeMultiplySubtract(s, s, l2); XMVECTOR NoIntersection; // If the ray origin is outside the sphere and the center of the sphere is // behind the ray origin there is no intersection. NoIntersection = XMVectorAndInt(XMVectorLess(s, XMVectorZero()), XMVectorGreater(l2, r2)); // If the squared distance from the center of the sphere to the projection // is greater than the radius squared the ray will miss the sphere. NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(m2, r2)); // The ray hits the sphere, compute the nearest intersection point. XMVECTOR q = XMVectorSqrt(XMVectorSubtract(r2, m2)); XMVECTOR t1 = XMVectorSubtract(s, q); XMVECTOR t2 = XMVectorAdd(s, q); XMVECTOR OriginInside = XMVectorLessOrEqual(l2, r2); XMVECTOR t = XMVectorSelect(t1, t2, OriginInside); if (XMVector4NotEqualInt(NoIntersection, XMVectorTrueInt())) { // Store the x-component to *pDist. XMStoreFloat(&Dist, t); return true; } Dist = 0.f; return false; } //----------------------------------------------------------------------------- // Test a sphere vs 6 planes (typically forming a frustum). //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingSphere::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2, GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5) const noexcept { // Load the sphere. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vRadius = XMVectorReplicatePtr(&Radius); // Set w of the center to one so we can dot4 with a plane. vCenter = XMVectorInsert<0, 0, 0, 0, 1>(vCenter, XMVectorSplatOne()); XMVECTOR Outside, Inside; // Test against each plane. DirectX::Internal::FastIntersectSpherePlane(vCenter, vRadius, Plane0, Outside, Inside); XMVECTOR AnyOutside = Outside; XMVECTOR AllInside = Inside; DirectX::Internal::FastIntersectSpherePlane(vCenter, vRadius, Plane1, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectSpherePlane(vCenter, vRadius, Plane2, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectSpherePlane(vCenter, vRadius, Plane3, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectSpherePlane(vCenter, vRadius, Plane4, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectSpherePlane(vCenter, vRadius, Plane5, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); // If the sphere is outside any plane it is outside. if (XMVector4EqualInt(AnyOutside, XMVectorTrueInt())) return DISJOINT; // If the sphere is inside all planes it is inside. if (XMVector4EqualInt(AllInside, XMVectorTrueInt())) return CONTAINS; // The sphere is not inside all planes or outside a plane, it may intersect. return INTERSECTS; } //----------------------------------------------------------------------------- // Creates a bounding sphere that contains two other bounding spheres //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingSphere::CreateMerged(BoundingSphere& Out, const BoundingSphere& S1, const BoundingSphere& S2) noexcept { XMVECTOR Center1 = XMLoadFloat3(&S1.Center); float r1 = S1.Radius; XMVECTOR Center2 = XMLoadFloat3(&S2.Center); float r2 = S2.Radius; XMVECTOR V = XMVectorSubtract(Center2, Center1); XMVECTOR Dist = XMVector3Length(V); float d = XMVectorGetX(Dist); if (r1 + r2 >= d) { if (r1 - r2 >= d) { Out = S1; return; } else if (r2 - r1 >= d) { Out = S2; return; } } XMVECTOR N = XMVectorDivide(V, Dist); float t1 = XMMin(-r1, d - r2); float t2 = XMMax(r1, d + r2); float t_5 = (t2 - t1) * 0.5f; XMVECTOR NCenter = XMVectorAdd(Center1, XMVectorMultiply(N, XMVectorReplicate(t_5 + t1))); XMStoreFloat3(&Out.Center, NCenter); Out.Radius = t_5; } //----------------------------------------------------------------------------- // Create sphere enscribing bounding box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingSphere::CreateFromBoundingBox(BoundingSphere& Out, const BoundingBox& box) noexcept { Out.Center = box.Center; XMVECTOR vExtents = XMLoadFloat3(&box.Extents); Out.Radius = XMVectorGetX(XMVector3Length(vExtents)); } _Use_decl_annotations_ inline void BoundingSphere::CreateFromBoundingBox(BoundingSphere& Out, const BoundingOrientedBox& box) noexcept { // Bounding box orientation is irrelevant because a sphere is rotationally invariant Out.Center = box.Center; XMVECTOR vExtents = XMLoadFloat3(&box.Extents); Out.Radius = XMVectorGetX(XMVector3Length(vExtents)); } //----------------------------------------------------------------------------- // Find the approximate smallest enclosing bounding sphere for a set of // points. Exact computation of the smallest enclosing bounding sphere is // possible but is slower and requires a more complex algorithm. // The algorithm is based on Jack Ritter, "An Efficient Bounding Sphere", // Graphics Gems. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingSphere::CreateFromPoints(BoundingSphere& Out, size_t Count, const XMFLOAT3* pPoints, size_t Stride) noexcept { assert(Count > 0); assert(pPoints); // Find the points with minimum and maximum x, y, and z XMVECTOR MinX, MaxX, MinY, MaxY, MinZ, MaxZ; MinX = MaxX = MinY = MaxY = MinZ = MaxZ = XMLoadFloat3(pPoints); for (size_t i = 1; i < Count; ++i) { XMVECTOR Point = XMLoadFloat3(reinterpret_cast(reinterpret_cast(pPoints) + i * Stride)); float px = XMVectorGetX(Point); float py = XMVectorGetY(Point); float pz = XMVectorGetZ(Point); if (px < XMVectorGetX(MinX)) MinX = Point; if (px > XMVectorGetX(MaxX)) MaxX = Point; if (py < XMVectorGetY(MinY)) MinY = Point; if (py > XMVectorGetY(MaxY)) MaxY = Point; if (pz < XMVectorGetZ(MinZ)) MinZ = Point; if (pz > XMVectorGetZ(MaxZ)) MaxZ = Point; } // Use the min/max pair that are farthest apart to form the initial sphere. XMVECTOR DeltaX = XMVectorSubtract(MaxX, MinX); XMVECTOR DistX = XMVector3Length(DeltaX); XMVECTOR DeltaY = XMVectorSubtract(MaxY, MinY); XMVECTOR DistY = XMVector3Length(DeltaY); XMVECTOR DeltaZ = XMVectorSubtract(MaxZ, MinZ); XMVECTOR DistZ = XMVector3Length(DeltaZ); XMVECTOR vCenter; XMVECTOR vRadius; if (XMVector3Greater(DistX, DistY)) { if (XMVector3Greater(DistX, DistZ)) { // Use min/max x. vCenter = XMVectorLerp(MaxX, MinX, 0.5f); vRadius = XMVectorScale(DistX, 0.5f); } else { // Use min/max z. vCenter = XMVectorLerp(MaxZ, MinZ, 0.5f); vRadius = XMVectorScale(DistZ, 0.5f); } } else // Y >= X { if (XMVector3Greater(DistY, DistZ)) { // Use min/max y. vCenter = XMVectorLerp(MaxY, MinY, 0.5f); vRadius = XMVectorScale(DistY, 0.5f); } else { // Use min/max z. vCenter = XMVectorLerp(MaxZ, MinZ, 0.5f); vRadius = XMVectorScale(DistZ, 0.5f); } } // Add any points not inside the sphere. for (size_t i = 0; i < Count; ++i) { XMVECTOR Point = XMLoadFloat3(reinterpret_cast(reinterpret_cast(pPoints) + i * Stride)); XMVECTOR Delta = XMVectorSubtract(Point, vCenter); XMVECTOR Dist = XMVector3Length(Delta); if (XMVector3Greater(Dist, vRadius)) { // Adjust sphere to include the new point. vRadius = XMVectorScale(XMVectorAdd(vRadius, Dist), 0.5f); vCenter = XMVectorAdd(vCenter, XMVectorMultiply(XMVectorSubtract(XMVectorReplicate(1.0f), XMVectorDivide(vRadius, Dist)), Delta)); } } XMStoreFloat3(&Out.Center, vCenter); XMStoreFloat(&Out.Radius, vRadius); } //----------------------------------------------------------------------------- // Create sphere containing frustum //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingSphere::CreateFromFrustum(BoundingSphere& Out, const BoundingFrustum& fr) noexcept { XMFLOAT3 Corners[BoundingFrustum::CORNER_COUNT]; fr.GetCorners(Corners); CreateFromPoints(Out, BoundingFrustum::CORNER_COUNT, Corners, sizeof(XMFLOAT3)); } /**************************************************************************** * * BoundingBox * ****************************************************************************/ //----------------------------------------------------------------------------- // Transform an axis aligned box by an angle preserving transform. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void XM_CALLCONV BoundingBox::Transform(BoundingBox& Out, FXMMATRIX M) const noexcept { // Load center and extents. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); // Compute and transform the corners and find new min/max bounds. XMVECTOR Corner = XMVectorMultiplyAdd(vExtents, g_BoxOffset[0], vCenter); Corner = XMVector3Transform(Corner, M); XMVECTOR Min, Max; Min = Max = Corner; for (size_t i = 1; i < CORNER_COUNT; ++i) { Corner = XMVectorMultiplyAdd(vExtents, g_BoxOffset[i], vCenter); Corner = XMVector3Transform(Corner, M); Min = XMVectorMin(Min, Corner); Max = XMVectorMax(Max, Corner); } // Store center and extents. XMStoreFloat3(&Out.Center, XMVectorScale(XMVectorAdd(Min, Max), 0.5f)); XMStoreFloat3(&Out.Extents, XMVectorScale(XMVectorSubtract(Max, Min), 0.5f)); } _Use_decl_annotations_ inline void XM_CALLCONV BoundingBox::Transform(BoundingBox& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation) const noexcept { assert(DirectX::Internal::XMQuaternionIsUnit(Rotation)); // Load center and extents. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR VectorScale = XMVectorReplicate(Scale); // Compute and transform the corners and find new min/max bounds. XMVECTOR Corner = XMVectorMultiplyAdd(vExtents, g_BoxOffset[0], vCenter); Corner = XMVectorAdd(XMVector3Rotate(XMVectorMultiply(Corner, VectorScale), Rotation), Translation); XMVECTOR Min, Max; Min = Max = Corner; for (size_t i = 1; i < CORNER_COUNT; ++i) { Corner = XMVectorMultiplyAdd(vExtents, g_BoxOffset[i], vCenter); Corner = XMVectorAdd(XMVector3Rotate(XMVectorMultiply(Corner, VectorScale), Rotation), Translation); Min = XMVectorMin(Min, Corner); Max = XMVectorMax(Max, Corner); } // Store center and extents. XMStoreFloat3(&Out.Center, XMVectorScale(XMVectorAdd(Min, Max), 0.5f)); XMStoreFloat3(&Out.Extents, XMVectorScale(XMVectorSubtract(Max, Min), 0.5f)); } //----------------------------------------------------------------------------- // Get the corner points of the box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingBox::GetCorners(XMFLOAT3* Corners) const noexcept { assert(Corners != nullptr); // Load the box XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); for (size_t i = 0; i < CORNER_COUNT; ++i) { XMVECTOR C = XMVectorMultiplyAdd(vExtents, g_BoxOffset[i], vCenter); XMStoreFloat3(&Corners[i], C); } } //----------------------------------------------------------------------------- // Point in axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingBox::Contains(FXMVECTOR Point) const noexcept { XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); return XMVector3InBounds(XMVectorSubtract(Point, vCenter), vExtents) ? CONTAINS : DISJOINT; } //----------------------------------------------------------------------------- // Triangle in axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingBox::Contains(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { if (!Intersects(V0, V1, V2)) return DISJOINT; XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR d = XMVectorAbs(XMVectorSubtract(V0, vCenter)); XMVECTOR Inside = XMVectorLessOrEqual(d, vExtents); d = XMVectorAbs(XMVectorSubtract(V1, vCenter)); Inside = XMVectorAndInt(Inside, XMVectorLessOrEqual(d, vExtents)); d = XMVectorAbs(XMVectorSubtract(V2, vCenter)); Inside = XMVectorAndInt(Inside, XMVectorLessOrEqual(d, vExtents)); return (XMVector3EqualInt(Inside, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Sphere in axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingBox::Contains(const BoundingSphere& sh) const noexcept { XMVECTOR SphereCenter = XMLoadFloat3(&sh.Center); XMVECTOR SphereRadius = XMVectorReplicatePtr(&sh.Radius); XMVECTOR BoxCenter = XMLoadFloat3(&Center); XMVECTOR BoxExtents = XMLoadFloat3(&Extents); XMVECTOR BoxMin = XMVectorSubtract(BoxCenter, BoxExtents); XMVECTOR BoxMax = XMVectorAdd(BoxCenter, BoxExtents); // Find the distance to the nearest point on the box. // for each i in (x, y, z) // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2 // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2 XMVECTOR d = XMVectorZero(); // Compute d for each dimension. XMVECTOR LessThanMin = XMVectorLess(SphereCenter, BoxMin); XMVECTOR GreaterThanMax = XMVectorGreater(SphereCenter, BoxMax); XMVECTOR MinDelta = XMVectorSubtract(SphereCenter, BoxMin); XMVECTOR MaxDelta = XMVectorSubtract(SphereCenter, BoxMax); // Choose value for each dimension based on the comparison. d = XMVectorSelect(d, MinDelta, LessThanMin); d = XMVectorSelect(d, MaxDelta, GreaterThanMax); // Use a dot-product to square them and sum them together. XMVECTOR d2 = XMVector3Dot(d, d); if (XMVector3Greater(d2, XMVectorMultiply(SphereRadius, SphereRadius))) return DISJOINT; XMVECTOR InsideAll = XMVectorLessOrEqual(XMVectorAdd(BoxMin, SphereRadius), SphereCenter); InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(SphereCenter, XMVectorSubtract(BoxMax, SphereRadius))); InsideAll = XMVectorAndInt(InsideAll, XMVectorGreater(XMVectorSubtract(BoxMax, BoxMin), SphereRadius)); return (XMVector3EqualInt(InsideAll, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Axis-aligned box in axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingBox::Contains(const BoundingBox& box) const noexcept { XMVECTOR CenterA = XMLoadFloat3(&Center); XMVECTOR ExtentsA = XMLoadFloat3(&Extents); XMVECTOR CenterB = XMLoadFloat3(&box.Center); XMVECTOR ExtentsB = XMLoadFloat3(&box.Extents); XMVECTOR MinA = XMVectorSubtract(CenterA, ExtentsA); XMVECTOR MaxA = XMVectorAdd(CenterA, ExtentsA); XMVECTOR MinB = XMVectorSubtract(CenterB, ExtentsB); XMVECTOR MaxB = XMVectorAdd(CenterB, ExtentsB); // for each i in (x, y, z) if a_min(i) > b_max(i) or b_min(i) > a_max(i) then return false XMVECTOR Disjoint = XMVectorOrInt(XMVectorGreater(MinA, MaxB), XMVectorGreater(MinB, MaxA)); if (DirectX::Internal::XMVector3AnyTrue(Disjoint)) return DISJOINT; // for each i in (x, y, z) if a_min(i) <= b_min(i) and b_max(i) <= a_max(i) then A contains B XMVECTOR Inside = XMVectorAndInt(XMVectorLessOrEqual(MinA, MinB), XMVectorLessOrEqual(MaxB, MaxA)); return DirectX::Internal::XMVector3AllTrue(Inside) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Oriented box in axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingBox::Contains(const BoundingOrientedBox& box) const noexcept { if (!box.Intersects(*this)) return DISJOINT; XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); // Subtract off the AABB center to remove a subtract below XMVECTOR oCenter = XMVectorSubtract(XMLoadFloat3(&box.Center), vCenter); XMVECTOR oExtents = XMLoadFloat3(&box.Extents); XMVECTOR oOrientation = XMLoadFloat4(&box.Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(oOrientation)); XMVECTOR Inside = XMVectorTrueInt(); for (size_t i = 0; i < BoundingOrientedBox::CORNER_COUNT; ++i) { XMVECTOR C = XMVectorAdd(XMVector3Rotate(XMVectorMultiply(oExtents, g_BoxOffset[i]), oOrientation), oCenter); XMVECTOR d = XMVectorAbs(C); Inside = XMVectorAndInt(Inside, XMVectorLessOrEqual(d, vExtents)); } return (XMVector3EqualInt(Inside, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Frustum in axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingBox::Contains(const BoundingFrustum& fr) const noexcept { if (!fr.Intersects(*this)) return DISJOINT; XMFLOAT3 Corners[BoundingFrustum::CORNER_COUNT]; fr.GetCorners(Corners); XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR Inside = XMVectorTrueInt(); for (size_t i = 0; i < BoundingFrustum::CORNER_COUNT; ++i) { XMVECTOR Point = XMLoadFloat3(&Corners[i]); XMVECTOR d = XMVectorAbs(XMVectorSubtract(Point, vCenter)); Inside = XMVectorAndInt(Inside, XMVectorLessOrEqual(d, vExtents)); } return (XMVector3EqualInt(Inside, XMVectorTrueInt())) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Sphere vs axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingBox::Intersects(const BoundingSphere& sh) const noexcept { XMVECTOR SphereCenter = XMLoadFloat3(&sh.Center); XMVECTOR SphereRadius = XMVectorReplicatePtr(&sh.Radius); XMVECTOR BoxCenter = XMLoadFloat3(&Center); XMVECTOR BoxExtents = XMLoadFloat3(&Extents); XMVECTOR BoxMin = XMVectorSubtract(BoxCenter, BoxExtents); XMVECTOR BoxMax = XMVectorAdd(BoxCenter, BoxExtents); // Find the distance to the nearest point on the box. // for each i in (x, y, z) // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2 // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2 XMVECTOR d = XMVectorZero(); // Compute d for each dimension. XMVECTOR LessThanMin = XMVectorLess(SphereCenter, BoxMin); XMVECTOR GreaterThanMax = XMVectorGreater(SphereCenter, BoxMax); XMVECTOR MinDelta = XMVectorSubtract(SphereCenter, BoxMin); XMVECTOR MaxDelta = XMVectorSubtract(SphereCenter, BoxMax); // Choose value for each dimension based on the comparison. d = XMVectorSelect(d, MinDelta, LessThanMin); d = XMVectorSelect(d, MaxDelta, GreaterThanMax); // Use a dot-product to square them and sum them together. XMVECTOR d2 = XMVector3Dot(d, d); return XMVector3LessOrEqual(d2, XMVectorMultiply(SphereRadius, SphereRadius)); } //----------------------------------------------------------------------------- // Axis-aligned box vs. axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingBox::Intersects(const BoundingBox& box) const noexcept { XMVECTOR CenterA = XMLoadFloat3(&Center); XMVECTOR ExtentsA = XMLoadFloat3(&Extents); XMVECTOR CenterB = XMLoadFloat3(&box.Center); XMVECTOR ExtentsB = XMLoadFloat3(&box.Extents); XMVECTOR MinA = XMVectorSubtract(CenterA, ExtentsA); XMVECTOR MaxA = XMVectorAdd(CenterA, ExtentsA); XMVECTOR MinB = XMVectorSubtract(CenterB, ExtentsB); XMVECTOR MaxB = XMVectorAdd(CenterB, ExtentsB); // for each i in (x, y, z) if a_min(i) > b_max(i) or b_min(i) > a_max(i) then return false XMVECTOR Disjoint = XMVectorOrInt(XMVectorGreater(MinA, MaxB), XMVectorGreater(MinB, MaxA)); return !DirectX::Internal::XMVector3AnyTrue(Disjoint); } //----------------------------------------------------------------------------- // Oriented box vs. axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingBox::Intersects(const BoundingOrientedBox& box) const noexcept { return box.Intersects(*this); } //----------------------------------------------------------------------------- // Frustum vs. axis-aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingBox::Intersects(const BoundingFrustum& fr) const noexcept { return fr.Intersects(*this); } //----------------------------------------------------------------------------- // Triangle vs. axis aligned box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingBox::Intersects(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { XMVECTOR Zero = XMVectorZero(); // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR BoxMin = XMVectorSubtract(vCenter, vExtents); XMVECTOR BoxMax = XMVectorAdd(vCenter, vExtents); // Test the axes of the box (in effect test the AAB against the minimal AAB // around the triangle). XMVECTOR TriMin = XMVectorMin(XMVectorMin(V0, V1), V2); XMVECTOR TriMax = XMVectorMax(XMVectorMax(V0, V1), V2); // for each i in (x, y, z) if a_min(i) > b_max(i) or b_min(i) > a_max(i) then disjoint XMVECTOR Disjoint = XMVectorOrInt(XMVectorGreater(TriMin, BoxMax), XMVectorGreater(BoxMin, TriMax)); if (DirectX::Internal::XMVector3AnyTrue(Disjoint)) return false; // Test the plane of the triangle. XMVECTOR Normal = XMVector3Cross(XMVectorSubtract(V1, V0), XMVectorSubtract(V2, V0)); XMVECTOR Dist = XMVector3Dot(Normal, V0); // Assert that the triangle is not degenerate. assert(!XMVector3Equal(Normal, Zero)); // for each i in (x, y, z) if n(i) >= 0 then v_min(i)=b_min(i), v_max(i)=b_max(i) // else v_min(i)=b_max(i), v_max(i)=b_min(i) XMVECTOR NormalSelect = XMVectorGreater(Normal, Zero); XMVECTOR V_Min = XMVectorSelect(BoxMax, BoxMin, NormalSelect); XMVECTOR V_Max = XMVectorSelect(BoxMin, BoxMax, NormalSelect); // if n dot v_min + d > 0 || n dot v_max + d < 0 then disjoint XMVECTOR MinDist = XMVector3Dot(V_Min, Normal); XMVECTOR MaxDist = XMVector3Dot(V_Max, Normal); XMVECTOR NoIntersection = XMVectorGreater(MinDist, Dist); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(MaxDist, Dist)); // Move the box center to zero to simplify the following tests. XMVECTOR TV0 = XMVectorSubtract(V0, vCenter); XMVECTOR TV1 = XMVectorSubtract(V1, vCenter); XMVECTOR TV2 = XMVectorSubtract(V2, vCenter); // Test the edge/edge axes (3*3). XMVECTOR e0 = XMVectorSubtract(TV1, TV0); XMVECTOR e1 = XMVectorSubtract(TV2, TV1); XMVECTOR e2 = XMVectorSubtract(TV0, TV2); // Make w zero. e0 = XMVectorInsert<0, 0, 0, 0, 1>(e0, Zero); e1 = XMVectorInsert<0, 0, 0, 0, 1>(e1, Zero); e2 = XMVectorInsert<0, 0, 0, 0, 1>(e2, Zero); XMVECTOR Axis; XMVECTOR p0, p1, p2; XMVECTOR Min, Max; XMVECTOR Radius; // Axis == (1,0,0) x e0 = (0, -e0.z, e0.y) Axis = XMVectorPermute(e0, XMVectorNegate(e0)); p0 = XMVector3Dot(TV0, Axis); // p1 = XMVector3Dot( V1, Axis ); // p1 = p0; p2 = XMVector3Dot(TV2, Axis); Min = XMVectorMin(p0, p2); Max = XMVectorMax(p0, p2); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (1,0,0) x e1 = (0, -e1.z, e1.y) Axis = XMVectorPermute(e1, XMVectorNegate(e1)); p0 = XMVector3Dot(TV0, Axis); p1 = XMVector3Dot(TV1, Axis); // p2 = XMVector3Dot( V2, Axis ); // p2 = p1; Min = XMVectorMin(p0, p1); Max = XMVectorMax(p0, p1); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (1,0,0) x e2 = (0, -e2.z, e2.y) Axis = XMVectorPermute(e2, XMVectorNegate(e2)); p0 = XMVector3Dot(TV0, Axis); p1 = XMVector3Dot(TV1, Axis); // p2 = XMVector3Dot( V2, Axis ); // p2 = p0; Min = XMVectorMin(p0, p1); Max = XMVectorMax(p0, p1); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (0,1,0) x e0 = (e0.z, 0, -e0.x) Axis = XMVectorPermute(e0, XMVectorNegate(e0)); p0 = XMVector3Dot(TV0, Axis); // p1 = XMVector3Dot( V1, Axis ); // p1 = p0; p2 = XMVector3Dot(TV2, Axis); Min = XMVectorMin(p0, p2); Max = XMVectorMax(p0, p2); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (0,1,0) x e1 = (e1.z, 0, -e1.x) Axis = XMVectorPermute(e1, XMVectorNegate(e1)); p0 = XMVector3Dot(TV0, Axis); p1 = XMVector3Dot(TV1, Axis); // p2 = XMVector3Dot( V2, Axis ); // p2 = p1; Min = XMVectorMin(p0, p1); Max = XMVectorMax(p0, p1); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (0,0,1) x e2 = (e2.z, 0, -e2.x) Axis = XMVectorPermute(e2, XMVectorNegate(e2)); p0 = XMVector3Dot(TV0, Axis); p1 = XMVector3Dot(TV1, Axis); // p2 = XMVector3Dot( V2, Axis ); // p2 = p0; Min = XMVectorMin(p0, p1); Max = XMVectorMax(p0, p1); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (0,0,1) x e0 = (-e0.y, e0.x, 0) Axis = XMVectorPermute(e0, XMVectorNegate(e0)); p0 = XMVector3Dot(TV0, Axis); // p1 = XMVector3Dot( V1, Axis ); // p1 = p0; p2 = XMVector3Dot(TV2, Axis); Min = XMVectorMin(p0, p2); Max = XMVectorMax(p0, p2); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (0,0,1) x e1 = (-e1.y, e1.x, 0) Axis = XMVectorPermute(e1, XMVectorNegate(e1)); p0 = XMVector3Dot(TV0, Axis); p1 = XMVector3Dot(TV1, Axis); // p2 = XMVector3Dot( V2, Axis ); // p2 = p1; Min = XMVectorMin(p0, p1); Max = XMVectorMax(p0, p1); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); // Axis == (0,0,1) x e2 = (-e2.y, e2.x, 0) Axis = XMVectorPermute(e2, XMVectorNegate(e2)); p0 = XMVector3Dot(TV0, Axis); p1 = XMVector3Dot(TV1, Axis); // p2 = XMVector3Dot( V2, Axis ); // p2 = p0; Min = XMVectorMin(p0, p1); Max = XMVectorMax(p0, p1); Radius = XMVector3Dot(vExtents, XMVectorAbs(Axis)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(Min, Radius)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(Max, XMVectorNegate(Radius))); return XMVector4NotEqualInt(NoIntersection, XMVectorTrueInt()); } //----------------------------------------------------------------------------- _Use_decl_annotations_ inline PlaneIntersectionType XM_CALLCONV BoundingBox::Intersects(FXMVECTOR Plane) const noexcept { assert(DirectX::Internal::XMPlaneIsUnit(Plane)); // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); // Set w of the center to one so we can dot4 with a plane. vCenter = XMVectorInsert<0, 0, 0, 0, 1>(vCenter, XMVectorSplatOne()); XMVECTOR Outside, Inside; DirectX::Internal::FastIntersectAxisAlignedBoxPlane(vCenter, vExtents, Plane, Outside, Inside); // If the box is outside any plane it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return FRONT; // If the box is inside all planes it is inside. if (XMVector4EqualInt(Inside, XMVectorTrueInt())) return BACK; // The box is not inside all planes or outside a plane it intersects. return INTERSECTING; } //----------------------------------------------------------------------------- // Compute the intersection of a ray (Origin, Direction) with an axis aligned // box using the slabs method. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingBox::Intersects(FXMVECTOR Origin, FXMVECTOR Direction, float& Dist) const noexcept { assert(DirectX::Internal::XMVector3IsUnit(Direction)); // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); // Adjust ray origin to be relative to center of the box. XMVECTOR TOrigin = XMVectorSubtract(vCenter, Origin); // Compute the dot product againt each axis of the box. // Since the axii are (1,0,0), (0,1,0), (0,0,1) no computation is necessary. XMVECTOR AxisDotOrigin = TOrigin; XMVECTOR AxisDotDirection = Direction; // if (fabs(AxisDotDirection) <= Epsilon) the ray is nearly parallel to the slab. XMVECTOR IsParallel = XMVectorLessOrEqual(XMVectorAbs(AxisDotDirection), g_RayEpsilon); // Test against all three axii simultaneously. XMVECTOR InverseAxisDotDirection = XMVectorReciprocal(AxisDotDirection); XMVECTOR t1 = XMVectorMultiply(XMVectorSubtract(AxisDotOrigin, vExtents), InverseAxisDotDirection); XMVECTOR t2 = XMVectorMultiply(XMVectorAdd(AxisDotOrigin, vExtents), InverseAxisDotDirection); // Compute the max of min(t1,t2) and the min of max(t1,t2) ensuring we don't // use the results from any directions parallel to the slab. XMVECTOR t_min = XMVectorSelect(XMVectorMin(t1, t2), g_FltMin, IsParallel); XMVECTOR t_max = XMVectorSelect(XMVectorMax(t1, t2), g_FltMax, IsParallel); // t_min.x = maximum( t_min.x, t_min.y, t_min.z ); // t_max.x = minimum( t_max.x, t_max.y, t_max.z ); t_min = XMVectorMax(t_min, XMVectorSplatY(t_min)); // x = max(x,y) t_min = XMVectorMax(t_min, XMVectorSplatZ(t_min)); // x = max(max(x,y),z) t_max = XMVectorMin(t_max, XMVectorSplatY(t_max)); // x = min(x,y) t_max = XMVectorMin(t_max, XMVectorSplatZ(t_max)); // x = min(min(x,y),z) // if ( t_min > t_max ) return false; XMVECTOR NoIntersection = XMVectorGreater(XMVectorSplatX(t_min), XMVectorSplatX(t_max)); // if ( t_max < 0.0f ) return false; NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(XMVectorSplatX(t_max), XMVectorZero())); // if (IsParallel && (-Extents > AxisDotOrigin || Extents < AxisDotOrigin)) return false; XMVECTOR ParallelOverlap = XMVectorInBounds(AxisDotOrigin, vExtents); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorAndCInt(IsParallel, ParallelOverlap)); if (!DirectX::Internal::XMVector3AnyTrue(NoIntersection)) { // Store the x-component to *pDist XMStoreFloat(&Dist, t_min); return true; } Dist = 0.f; return false; } //----------------------------------------------------------------------------- // Test an axis alinged box vs 6 planes (typically forming a frustum). //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingBox::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2, GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5) const noexcept { // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); // Set w of the center to one so we can dot4 with a plane. vCenter = XMVectorInsert<0, 0, 0, 0, 1>(vCenter, XMVectorSplatOne()); XMVECTOR Outside, Inside; // Test against each plane. DirectX::Internal::FastIntersectAxisAlignedBoxPlane(vCenter, vExtents, Plane0, Outside, Inside); XMVECTOR AnyOutside = Outside; XMVECTOR AllInside = Inside; DirectX::Internal::FastIntersectAxisAlignedBoxPlane(vCenter, vExtents, Plane1, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectAxisAlignedBoxPlane(vCenter, vExtents, Plane2, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectAxisAlignedBoxPlane(vCenter, vExtents, Plane3, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectAxisAlignedBoxPlane(vCenter, vExtents, Plane4, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectAxisAlignedBoxPlane(vCenter, vExtents, Plane5, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); // If the box is outside any plane it is outside. if (XMVector4EqualInt(AnyOutside, XMVectorTrueInt())) return DISJOINT; // If the box is inside all planes it is inside. if (XMVector4EqualInt(AllInside, XMVectorTrueInt())) return CONTAINS; // The box is not inside all planes or outside a plane, it may intersect. return INTERSECTS; } //----------------------------------------------------------------------------- // Create axis-aligned box that contains two other bounding boxes //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingBox::CreateMerged(BoundingBox& Out, const BoundingBox& b1, const BoundingBox& b2) noexcept { XMVECTOR b1Center = XMLoadFloat3(&b1.Center); XMVECTOR b1Extents = XMLoadFloat3(&b1.Extents); XMVECTOR b2Center = XMLoadFloat3(&b2.Center); XMVECTOR b2Extents = XMLoadFloat3(&b2.Extents); XMVECTOR Min = XMVectorSubtract(b1Center, b1Extents); Min = XMVectorMin(Min, XMVectorSubtract(b2Center, b2Extents)); XMVECTOR Max = XMVectorAdd(b1Center, b1Extents); Max = XMVectorMax(Max, XMVectorAdd(b2Center, b2Extents)); assert(XMVector3LessOrEqual(Min, Max)); XMStoreFloat3(&Out.Center, XMVectorScale(XMVectorAdd(Min, Max), 0.5f)); XMStoreFloat3(&Out.Extents, XMVectorScale(XMVectorSubtract(Max, Min), 0.5f)); } //----------------------------------------------------------------------------- // Create axis-aligned box that contains a bounding sphere //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingBox::CreateFromSphere(BoundingBox& Out, const BoundingSphere& sh) noexcept { XMVECTOR spCenter = XMLoadFloat3(&sh.Center); XMVECTOR shRadius = XMVectorReplicatePtr(&sh.Radius); XMVECTOR Min = XMVectorSubtract(spCenter, shRadius); XMVECTOR Max = XMVectorAdd(spCenter, shRadius); assert(XMVector3LessOrEqual(Min, Max)); XMStoreFloat3(&Out.Center, XMVectorScale(XMVectorAdd(Min, Max), 0.5f)); XMStoreFloat3(&Out.Extents, XMVectorScale(XMVectorSubtract(Max, Min), 0.5f)); } //----------------------------------------------------------------------------- // Create axis-aligned box from min/max points //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void XM_CALLCONV BoundingBox::CreateFromPoints(BoundingBox& Out, FXMVECTOR pt1, FXMVECTOR pt2) noexcept { XMVECTOR Min = XMVectorMin(pt1, pt2); XMVECTOR Max = XMVectorMax(pt1, pt2); // Store center and extents. XMStoreFloat3(&Out.Center, XMVectorScale(XMVectorAdd(Min, Max), 0.5f)); XMStoreFloat3(&Out.Extents, XMVectorScale(XMVectorSubtract(Max, Min), 0.5f)); } //----------------------------------------------------------------------------- // Find the minimum axis aligned bounding box containing a set of points. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingBox::CreateFromPoints(BoundingBox& Out, size_t Count, const XMFLOAT3* pPoints, size_t Stride) noexcept { assert(Count > 0); assert(pPoints); // Find the minimum and maximum x, y, and z XMVECTOR vMin, vMax; vMin = vMax = XMLoadFloat3(pPoints); for (size_t i = 1; i < Count; ++i) { XMVECTOR Point = XMLoadFloat3(reinterpret_cast(reinterpret_cast(pPoints) + i * Stride)); vMin = XMVectorMin(vMin, Point); vMax = XMVectorMax(vMax, Point); } // Store center and extents. XMStoreFloat3(&Out.Center, XMVectorScale(XMVectorAdd(vMin, vMax), 0.5f)); XMStoreFloat3(&Out.Extents, XMVectorScale(XMVectorSubtract(vMax, vMin), 0.5f)); } /**************************************************************************** * * BoundingOrientedBox * ****************************************************************************/ //----------------------------------------------------------------------------- // Transform an oriented box by an angle preserving transform. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void XM_CALLCONV BoundingOrientedBox::Transform(BoundingOrientedBox& Out, FXMMATRIX M) const noexcept { // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Composite the box rotation and the transform rotation. XMMATRIX nM; nM.r[0] = XMVector3Normalize(M.r[0]); nM.r[1] = XMVector3Normalize(M.r[1]); nM.r[2] = XMVector3Normalize(M.r[2]); nM.r[3] = g_XMIdentityR3; XMVECTOR Rotation = XMQuaternionRotationMatrix(nM); vOrientation = XMQuaternionMultiply(vOrientation, Rotation); // Transform the center. vCenter = XMVector3Transform(vCenter, M); // Scale the box extents. XMVECTOR dX = XMVector3Length(M.r[0]); XMVECTOR dY = XMVector3Length(M.r[1]); XMVECTOR dZ = XMVector3Length(M.r[2]); XMVECTOR VectorScale = XMVectorSelect(dY, dX, g_XMSelect1000); VectorScale = XMVectorSelect(dZ, VectorScale, g_XMSelect1100); vExtents = XMVectorMultiply(vExtents, VectorScale); // Store the box. XMStoreFloat3(&Out.Center, vCenter); XMStoreFloat3(&Out.Extents, vExtents); XMStoreFloat4(&Out.Orientation, vOrientation); } _Use_decl_annotations_ inline void XM_CALLCONV BoundingOrientedBox::Transform(BoundingOrientedBox& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation) const noexcept { assert(DirectX::Internal::XMQuaternionIsUnit(Rotation)); // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Composite the box rotation and the transform rotation. vOrientation = XMQuaternionMultiply(vOrientation, Rotation); // Transform the center. XMVECTOR VectorScale = XMVectorReplicate(Scale); vCenter = XMVectorAdd(XMVector3Rotate(XMVectorMultiply(vCenter, VectorScale), Rotation), Translation); // Scale the box extents. vExtents = XMVectorMultiply(vExtents, VectorScale); // Store the box. XMStoreFloat3(&Out.Center, vCenter); XMStoreFloat3(&Out.Extents, vExtents); XMStoreFloat4(&Out.Orientation, vOrientation); } //----------------------------------------------------------------------------- // Get the corner points of the box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingOrientedBox::GetCorners(XMFLOAT3* Corners) const noexcept { assert(Corners != nullptr); // Load the box XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); for (size_t i = 0; i < CORNER_COUNT; ++i) { XMVECTOR C = XMVectorAdd(XMVector3Rotate(XMVectorMultiply(vExtents, g_BoxOffset[i]), vOrientation), vCenter); XMStoreFloat3(&Corners[i], C); } } //----------------------------------------------------------------------------- // Point in oriented box test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingOrientedBox::Contains(FXMVECTOR Point) const noexcept { XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Transform the point to be local to the box. XMVECTOR TPoint = XMVector3InverseRotate(XMVectorSubtract(Point, vCenter), vOrientation); return XMVector3InBounds(TPoint, vExtents) ? CONTAINS : DISJOINT; } //----------------------------------------------------------------------------- // Triangle in oriented bounding box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingOrientedBox::Contains(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { // Load the box center & orientation. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Transform the triangle vertices into the space of the box. XMVECTOR TV0 = XMVector3InverseRotate(XMVectorSubtract(V0, vCenter), vOrientation); XMVECTOR TV1 = XMVector3InverseRotate(XMVectorSubtract(V1, vCenter), vOrientation); XMVECTOR TV2 = XMVector3InverseRotate(XMVectorSubtract(V2, vCenter), vOrientation); BoundingBox box; box.Center = XMFLOAT3(0.0f, 0.0f, 0.0f); box.Extents = Extents; // Use the triangle vs axis aligned box intersection routine. return box.Contains(TV0, TV1, TV2); } //----------------------------------------------------------------------------- // Sphere in oriented bounding box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingOrientedBox::Contains(const BoundingSphere& sh) const noexcept { XMVECTOR SphereCenter = XMLoadFloat3(&sh.Center); XMVECTOR SphereRadius = XMVectorReplicatePtr(&sh.Radius); XMVECTOR BoxCenter = XMLoadFloat3(&Center); XMVECTOR BoxExtents = XMLoadFloat3(&Extents); XMVECTOR BoxOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(BoxOrientation)); // Transform the center of the sphere to be local to the box. // BoxMin = -BoxExtents // BoxMax = +BoxExtents SphereCenter = XMVector3InverseRotate(XMVectorSubtract(SphereCenter, BoxCenter), BoxOrientation); // Find the distance to the nearest point on the box. // for each i in (x, y, z) // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2 // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2 XMVECTOR d = XMVectorZero(); // Compute d for each dimension. XMVECTOR LessThanMin = XMVectorLess(SphereCenter, XMVectorNegate(BoxExtents)); XMVECTOR GreaterThanMax = XMVectorGreater(SphereCenter, BoxExtents); XMVECTOR MinDelta = XMVectorAdd(SphereCenter, BoxExtents); XMVECTOR MaxDelta = XMVectorSubtract(SphereCenter, BoxExtents); // Choose value for each dimension based on the comparison. d = XMVectorSelect(d, MinDelta, LessThanMin); d = XMVectorSelect(d, MaxDelta, GreaterThanMax); // Use a dot-product to square them and sum them together. XMVECTOR d2 = XMVector3Dot(d, d); XMVECTOR SphereRadiusSq = XMVectorMultiply(SphereRadius, SphereRadius); if (XMVector4Greater(d2, SphereRadiusSq)) return DISJOINT; // See if we are completely inside the box XMVECTOR SMin = XMVectorSubtract(SphereCenter, SphereRadius); XMVECTOR SMax = XMVectorAdd(SphereCenter, SphereRadius); return (XMVector3InBounds(SMin, BoxExtents) && XMVector3InBounds(SMax, BoxExtents)) ? CONTAINS : INTERSECTS; } //----------------------------------------------------------------------------- // Axis aligned box vs. oriented box. Constructs an oriented box and uses // the oriented box vs. oriented box test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingOrientedBox::Contains(const BoundingBox& box) const noexcept { // Make the axis aligned box oriented and do an OBB vs OBB test. BoundingOrientedBox obox(box.Center, box.Extents, XMFLOAT4(0.f, 0.f, 0.f, 1.f)); return Contains(obox); } //----------------------------------------------------------------------------- // Oriented bounding box in oriented bounding box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingOrientedBox::Contains(const BoundingOrientedBox& box) const noexcept { if (!Intersects(box)) return DISJOINT; // Load the boxes XMVECTOR aCenter = XMLoadFloat3(&Center); XMVECTOR aExtents = XMLoadFloat3(&Extents); XMVECTOR aOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(aOrientation)); XMVECTOR bCenter = XMLoadFloat3(&box.Center); XMVECTOR bExtents = XMLoadFloat3(&box.Extents); XMVECTOR bOrientation = XMLoadFloat4(&box.Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(bOrientation)); XMVECTOR offset = XMVectorSubtract(bCenter, aCenter); for (size_t i = 0; i < CORNER_COUNT; ++i) { // Cb = rotate( bExtents * corneroffset[i], bOrientation ) + bcenter // Ca = invrotate( Cb - aCenter, aOrientation ) XMVECTOR C = XMVectorAdd(XMVector3Rotate(XMVectorMultiply(bExtents, g_BoxOffset[i]), bOrientation), offset); C = XMVector3InverseRotate(C, aOrientation); if (!XMVector3InBounds(C, aExtents)) return INTERSECTS; } return CONTAINS; } //----------------------------------------------------------------------------- // Frustum in oriented bounding box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingOrientedBox::Contains(const BoundingFrustum& fr) const noexcept { if (!fr.Intersects(*this)) return DISJOINT; XMFLOAT3 Corners[BoundingFrustum::CORNER_COUNT]; fr.GetCorners(Corners); // Load the box XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); for (size_t i = 0; i < BoundingFrustum::CORNER_COUNT; ++i) { XMVECTOR C = XMVector3InverseRotate(XMVectorSubtract(XMLoadFloat3(&Corners[i]), vCenter), vOrientation); if (!XMVector3InBounds(C, vExtents)) return INTERSECTS; } return CONTAINS; } //----------------------------------------------------------------------------- // Sphere vs. oriented box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingOrientedBox::Intersects(const BoundingSphere& sh) const noexcept { XMVECTOR SphereCenter = XMLoadFloat3(&sh.Center); XMVECTOR SphereRadius = XMVectorReplicatePtr(&sh.Radius); XMVECTOR BoxCenter = XMLoadFloat3(&Center); XMVECTOR BoxExtents = XMLoadFloat3(&Extents); XMVECTOR BoxOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(BoxOrientation)); // Transform the center of the sphere to be local to the box. // BoxMin = -BoxExtents // BoxMax = +BoxExtents SphereCenter = XMVector3InverseRotate(XMVectorSubtract(SphereCenter, BoxCenter), BoxOrientation); // Find the distance to the nearest point on the box. // for each i in (x, y, z) // if (SphereCenter(i) < BoxMin(i)) d2 += (SphereCenter(i) - BoxMin(i)) ^ 2 // else if (SphereCenter(i) > BoxMax(i)) d2 += (SphereCenter(i) - BoxMax(i)) ^ 2 XMVECTOR d = XMVectorZero(); // Compute d for each dimension. XMVECTOR LessThanMin = XMVectorLess(SphereCenter, XMVectorNegate(BoxExtents)); XMVECTOR GreaterThanMax = XMVectorGreater(SphereCenter, BoxExtents); XMVECTOR MinDelta = XMVectorAdd(SphereCenter, BoxExtents); XMVECTOR MaxDelta = XMVectorSubtract(SphereCenter, BoxExtents); // Choose value for each dimension based on the comparison. d = XMVectorSelect(d, MinDelta, LessThanMin); d = XMVectorSelect(d, MaxDelta, GreaterThanMax); // Use a dot-product to square them and sum them together. XMVECTOR d2 = XMVector3Dot(d, d); return XMVector4LessOrEqual(d2, XMVectorMultiply(SphereRadius, SphereRadius)) ? true : false; } //----------------------------------------------------------------------------- // Axis aligned box vs. oriented box. Constructs an oriented box and uses // the oriented box vs. oriented box test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingOrientedBox::Intersects(const BoundingBox& box) const noexcept { // Make the axis aligned box oriented and do an OBB vs OBB test. BoundingOrientedBox obox(box.Center, box.Extents, XMFLOAT4(0.f, 0.f, 0.f, 1.f)); return Intersects(obox); } //----------------------------------------------------------------------------- // Fast oriented box / oriented box intersection test using the separating axis // theorem. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingOrientedBox::Intersects(const BoundingOrientedBox& box) const noexcept { // Build the 3x3 rotation matrix that defines the orientation of B relative to A. XMVECTOR A_quat = XMLoadFloat4(&Orientation); XMVECTOR B_quat = XMLoadFloat4(&box.Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(A_quat)); assert(DirectX::Internal::XMQuaternionIsUnit(B_quat)); XMVECTOR Q = XMQuaternionMultiply(A_quat, XMQuaternionConjugate(B_quat)); XMMATRIX R = XMMatrixRotationQuaternion(Q); // Compute the translation of B relative to A. XMVECTOR A_cent = XMLoadFloat3(&Center); XMVECTOR B_cent = XMLoadFloat3(&box.Center); XMVECTOR t = XMVector3InverseRotate(XMVectorSubtract(B_cent, A_cent), A_quat); // // h(A) = extents of A. // h(B) = extents of B. // // a(u) = axes of A = (1,0,0), (0,1,0), (0,0,1) // b(u) = axes of B relative to A = (r00,r10,r20), (r01,r11,r21), (r02,r12,r22) // // For each possible separating axis l: // d(A) = sum (for i = u,v,w) h(A)(i) * abs( a(i) dot l ) // d(B) = sum (for i = u,v,w) h(B)(i) * abs( b(i) dot l ) // if abs( t dot l ) > d(A) + d(B) then disjoint // // Load extents of A and B. XMVECTOR h_A = XMLoadFloat3(&Extents); XMVECTOR h_B = XMLoadFloat3(&box.Extents); // Rows. Note R[0,1,2]X.w = 0. XMVECTOR R0X = R.r[0]; XMVECTOR R1X = R.r[1]; XMVECTOR R2X = R.r[2]; R = XMMatrixTranspose(R); // Columns. Note RX[0,1,2].w = 0. XMVECTOR RX0 = R.r[0]; XMVECTOR RX1 = R.r[1]; XMVECTOR RX2 = R.r[2]; // Absolute value of rows. XMVECTOR AR0X = XMVectorAbs(R0X); XMVECTOR AR1X = XMVectorAbs(R1X); XMVECTOR AR2X = XMVectorAbs(R2X); // Absolute value of columns. XMVECTOR ARX0 = XMVectorAbs(RX0); XMVECTOR ARX1 = XMVectorAbs(RX1); XMVECTOR ARX2 = XMVectorAbs(RX2); // Test each of the 15 possible seperating axii. XMVECTOR d, d_A, d_B; // l = a(u) = (1, 0, 0) // t dot l = t.x // d(A) = h(A).x // d(B) = h(B) dot abs(r00, r01, r02) d = XMVectorSplatX(t); d_A = XMVectorSplatX(h_A); d_B = XMVector3Dot(h_B, AR0X); XMVECTOR NoIntersection = XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B)); // l = a(v) = (0, 1, 0) // t dot l = t.y // d(A) = h(A).y // d(B) = h(B) dot abs(r10, r11, r12) d = XMVectorSplatY(t); d_A = XMVectorSplatY(h_A); d_B = XMVector3Dot(h_B, AR1X); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(w) = (0, 0, 1) // t dot l = t.z // d(A) = h(A).z // d(B) = h(B) dot abs(r20, r21, r22) d = XMVectorSplatZ(t); d_A = XMVectorSplatZ(h_A); d_B = XMVector3Dot(h_B, AR2X); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = b(u) = (r00, r10, r20) // d(A) = h(A) dot abs(r00, r10, r20) // d(B) = h(B).x d = XMVector3Dot(t, RX0); d_A = XMVector3Dot(h_A, ARX0); d_B = XMVectorSplatX(h_B); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = b(v) = (r01, r11, r21) // d(A) = h(A) dot abs(r01, r11, r21) // d(B) = h(B).y d = XMVector3Dot(t, RX1); d_A = XMVector3Dot(h_A, ARX1); d_B = XMVectorSplatY(h_B); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = b(w) = (r02, r12, r22) // d(A) = h(A) dot abs(r02, r12, r22) // d(B) = h(B).z d = XMVector3Dot(t, RX2); d_A = XMVector3Dot(h_A, ARX2); d_B = XMVectorSplatZ(h_B); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(u) x b(u) = (0, -r20, r10) // d(A) = h(A) dot abs(0, r20, r10) // d(B) = h(B) dot abs(0, r02, r01) d = XMVector3Dot(t, XMVectorPermute(RX0, XMVectorNegate(RX0))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX0)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR0X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(u) x b(v) = (0, -r21, r11) // d(A) = h(A) dot abs(0, r21, r11) // d(B) = h(B) dot abs(r02, 0, r00) d = XMVector3Dot(t, XMVectorPermute(RX1, XMVectorNegate(RX1))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX1)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR0X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(u) x b(w) = (0, -r22, r12) // d(A) = h(A) dot abs(0, r22, r12) // d(B) = h(B) dot abs(r01, r00, 0) d = XMVector3Dot(t, XMVectorPermute(RX2, XMVectorNegate(RX2))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX2)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR0X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(v) x b(u) = (r20, 0, -r00) // d(A) = h(A) dot abs(r20, 0, r00) // d(B) = h(B) dot abs(0, r12, r11) d = XMVector3Dot(t, XMVectorPermute(RX0, XMVectorNegate(RX0))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX0)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR1X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(v) x b(v) = (r21, 0, -r01) // d(A) = h(A) dot abs(r21, 0, r01) // d(B) = h(B) dot abs(r12, 0, r10) d = XMVector3Dot(t, XMVectorPermute(RX1, XMVectorNegate(RX1))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX1)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR1X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(v) x b(w) = (r22, 0, -r02) // d(A) = h(A) dot abs(r22, 0, r02) // d(B) = h(B) dot abs(r11, r10, 0) d = XMVector3Dot(t, XMVectorPermute(RX2, XMVectorNegate(RX2))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX2)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR1X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(w) x b(u) = (-r10, r00, 0) // d(A) = h(A) dot abs(r10, r00, 0) // d(B) = h(B) dot abs(0, r22, r21) d = XMVector3Dot(t, XMVectorPermute(RX0, XMVectorNegate(RX0))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX0)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR2X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(w) x b(v) = (-r11, r01, 0) // d(A) = h(A) dot abs(r11, r01, 0) // d(B) = h(B) dot abs(r22, 0, r20) d = XMVector3Dot(t, XMVectorPermute(RX1, XMVectorNegate(RX1))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX1)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR2X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // l = a(w) x b(w) = (-r12, r02, 0) // d(A) = h(A) dot abs(r12, r02, 0) // d(B) = h(B) dot abs(r21, r20, 0) d = XMVector3Dot(t, XMVectorPermute(RX2, XMVectorNegate(RX2))); d_A = XMVector3Dot(h_A, XMVectorSwizzle(ARX2)); d_B = XMVector3Dot(h_B, XMVectorSwizzle(AR2X)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAbs(d), XMVectorAdd(d_A, d_B))); // No seperating axis found, boxes must intersect. return XMVector4NotEqualInt(NoIntersection, XMVectorTrueInt()) ? true : false; } //----------------------------------------------------------------------------- // Frustum vs. oriented box test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingOrientedBox::Intersects(const BoundingFrustum& fr) const noexcept { return fr.Intersects(*this); } //----------------------------------------------------------------------------- // Triangle vs. oriented box test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingOrientedBox::Intersects(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { // Load the box center & orientation. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Transform the triangle vertices into the space of the box. XMVECTOR TV0 = XMVector3InverseRotate(XMVectorSubtract(V0, vCenter), vOrientation); XMVECTOR TV1 = XMVector3InverseRotate(XMVectorSubtract(V1, vCenter), vOrientation); XMVECTOR TV2 = XMVector3InverseRotate(XMVectorSubtract(V2, vCenter), vOrientation); BoundingBox box; box.Center = XMFLOAT3(0.0f, 0.0f, 0.0f); box.Extents = Extents; // Use the triangle vs axis aligned box intersection routine. return box.Intersects(TV0, TV1, TV2); } //----------------------------------------------------------------------------- _Use_decl_annotations_ inline PlaneIntersectionType XM_CALLCONV BoundingOrientedBox::Intersects(FXMVECTOR Plane) const noexcept { assert(DirectX::Internal::XMPlaneIsUnit(Plane)); // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR BoxOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(BoxOrientation)); // Set w of the center to one so we can dot4 with a plane. vCenter = XMVectorInsert<0, 0, 0, 0, 1>(vCenter, XMVectorSplatOne()); // Build the 3x3 rotation matrix that defines the box axes. XMMATRIX R = XMMatrixRotationQuaternion(BoxOrientation); XMVECTOR Outside, Inside; DirectX::Internal::FastIntersectOrientedBoxPlane(vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane, Outside, Inside); // If the box is outside any plane it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return FRONT; // If the box is inside all planes it is inside. if (XMVector4EqualInt(Inside, XMVectorTrueInt())) return BACK; // The box is not inside all planes or outside a plane it intersects. return INTERSECTING; } //----------------------------------------------------------------------------- // Compute the intersection of a ray (Origin, Direction) with an oriented box // using the slabs method. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingOrientedBox::Intersects(FXMVECTOR Origin, FXMVECTOR Direction, float& Dist) const noexcept { assert(DirectX::Internal::XMVector3IsUnit(Direction)); static const XMVECTORU32 SelectY = { { { XM_SELECT_0, XM_SELECT_1, XM_SELECT_0, XM_SELECT_0 } } }; static const XMVECTORU32 SelectZ = { { { XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0 } } }; // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Get the boxes normalized side directions. XMMATRIX R = XMMatrixRotationQuaternion(vOrientation); // Adjust ray origin to be relative to center of the box. XMVECTOR TOrigin = XMVectorSubtract(vCenter, Origin); // Compute the dot product againt each axis of the box. XMVECTOR AxisDotOrigin = XMVector3Dot(R.r[0], TOrigin); AxisDotOrigin = XMVectorSelect(AxisDotOrigin, XMVector3Dot(R.r[1], TOrigin), SelectY); AxisDotOrigin = XMVectorSelect(AxisDotOrigin, XMVector3Dot(R.r[2], TOrigin), SelectZ); XMVECTOR AxisDotDirection = XMVector3Dot(R.r[0], Direction); AxisDotDirection = XMVectorSelect(AxisDotDirection, XMVector3Dot(R.r[1], Direction), SelectY); AxisDotDirection = XMVectorSelect(AxisDotDirection, XMVector3Dot(R.r[2], Direction), SelectZ); // if (fabs(AxisDotDirection) <= Epsilon) the ray is nearly parallel to the slab. XMVECTOR IsParallel = XMVectorLessOrEqual(XMVectorAbs(AxisDotDirection), g_RayEpsilon); // Test against all three axes simultaneously. XMVECTOR InverseAxisDotDirection = XMVectorReciprocal(AxisDotDirection); XMVECTOR t1 = XMVectorMultiply(XMVectorSubtract(AxisDotOrigin, vExtents), InverseAxisDotDirection); XMVECTOR t2 = XMVectorMultiply(XMVectorAdd(AxisDotOrigin, vExtents), InverseAxisDotDirection); // Compute the max of min(t1,t2) and the min of max(t1,t2) ensuring we don't // use the results from any directions parallel to the slab. XMVECTOR t_min = XMVectorSelect(XMVectorMin(t1, t2), g_FltMin, IsParallel); XMVECTOR t_max = XMVectorSelect(XMVectorMax(t1, t2), g_FltMax, IsParallel); // t_min.x = maximum( t_min.x, t_min.y, t_min.z ); // t_max.x = minimum( t_max.x, t_max.y, t_max.z ); t_min = XMVectorMax(t_min, XMVectorSplatY(t_min)); // x = max(x,y) t_min = XMVectorMax(t_min, XMVectorSplatZ(t_min)); // x = max(max(x,y),z) t_max = XMVectorMin(t_max, XMVectorSplatY(t_max)); // x = min(x,y) t_max = XMVectorMin(t_max, XMVectorSplatZ(t_max)); // x = min(min(x,y),z) // if ( t_min > t_max ) return false; XMVECTOR NoIntersection = XMVectorGreater(XMVectorSplatX(t_min), XMVectorSplatX(t_max)); // if ( t_max < 0.0f ) return false; NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(XMVectorSplatX(t_max), XMVectorZero())); // if (IsParallel && (-Extents > AxisDotOrigin || Extents < AxisDotOrigin)) return false; XMVECTOR ParallelOverlap = XMVectorInBounds(AxisDotOrigin, vExtents); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorAndCInt(IsParallel, ParallelOverlap)); if (!DirectX::Internal::XMVector3AnyTrue(NoIntersection)) { // Store the x-component to *pDist XMStoreFloat(&Dist, t_min); return true; } Dist = 0.f; return false; } //----------------------------------------------------------------------------- // Test an oriented box vs 6 planes (typically forming a frustum). //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingOrientedBox::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2, GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5) const noexcept { // Load the box. XMVECTOR vCenter = XMLoadFloat3(&Center); XMVECTOR vExtents = XMLoadFloat3(&Extents); XMVECTOR BoxOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(BoxOrientation)); // Set w of the center to one so we can dot4 with a plane. vCenter = XMVectorInsert<0, 0, 0, 0, 1>(vCenter, XMVectorSplatOne()); // Build the 3x3 rotation matrix that defines the box axes. XMMATRIX R = XMMatrixRotationQuaternion(BoxOrientation); XMVECTOR Outside, Inside; // Test against each plane. DirectX::Internal::FastIntersectOrientedBoxPlane(vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane0, Outside, Inside); XMVECTOR AnyOutside = Outside; XMVECTOR AllInside = Inside; DirectX::Internal::FastIntersectOrientedBoxPlane(vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane1, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectOrientedBoxPlane(vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane2, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectOrientedBoxPlane(vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane3, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectOrientedBoxPlane(vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane4, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectOrientedBoxPlane(vCenter, vExtents, R.r[0], R.r[1], R.r[2], Plane5, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); // If the box is outside any plane it is outside. if (XMVector4EqualInt(AnyOutside, XMVectorTrueInt())) return DISJOINT; // If the box is inside all planes it is inside. if (XMVector4EqualInt(AllInside, XMVectorTrueInt())) return CONTAINS; // The box is not inside all planes or outside a plane, it may intersect. return INTERSECTS; } //----------------------------------------------------------------------------- // Create oriented bounding box from axis-aligned bounding box //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingOrientedBox::CreateFromBoundingBox(BoundingOrientedBox& Out, const BoundingBox& box) noexcept { Out.Center = box.Center; Out.Extents = box.Extents; Out.Orientation = XMFLOAT4(0.f, 0.f, 0.f, 1.f); } //----------------------------------------------------------------------------- // Find the approximate minimum oriented bounding box containing a set of // points. Exact computation of minimum oriented bounding box is possible but // is slower and requires a more complex algorithm. // The algorithm works by computing the inertia tensor of the points and then // using the eigenvectors of the intertia tensor as the axes of the box. // Computing the intertia tensor of the convex hull of the points will usually // result in better bounding box but the computation is more complex. // Exact computation of the minimum oriented bounding box is possible but the // best know algorithm is O(N^3) and is significanly more complex to implement. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingOrientedBox::CreateFromPoints(BoundingOrientedBox& Out, size_t Count, const XMFLOAT3* pPoints, size_t Stride) noexcept { assert(Count > 0); assert(pPoints != nullptr); XMVECTOR CenterOfMass = XMVectorZero(); // Compute the center of mass and inertia tensor of the points. for (size_t i = 0; i < Count; ++i) { XMVECTOR Point = XMLoadFloat3(reinterpret_cast(reinterpret_cast(pPoints) + i * Stride)); CenterOfMass = XMVectorAdd(CenterOfMass, Point); } CenterOfMass = XMVectorMultiply(CenterOfMass, XMVectorReciprocal(XMVectorReplicate(float(Count)))); // Compute the inertia tensor of the points around the center of mass. // Using the center of mass is not strictly necessary, but will hopefully // improve the stability of finding the eigenvectors. XMVECTOR XX_YY_ZZ = XMVectorZero(); XMVECTOR XY_XZ_YZ = XMVectorZero(); for (size_t i = 0; i < Count; ++i) { XMVECTOR Point = XMVectorSubtract(XMLoadFloat3(reinterpret_cast(reinterpret_cast(pPoints) + i * Stride)), CenterOfMass); XX_YY_ZZ = XMVectorAdd(XX_YY_ZZ, XMVectorMultiply(Point, Point)); XMVECTOR XXY = XMVectorSwizzle(Point); XMVECTOR YZZ = XMVectorSwizzle(Point); XY_XZ_YZ = XMVectorAdd(XY_XZ_YZ, XMVectorMultiply(XXY, YZZ)); } XMVECTOR v1, v2, v3; // Compute the eigenvectors of the inertia tensor. DirectX::Internal::CalculateEigenVectorsFromCovarianceMatrix(XMVectorGetX(XX_YY_ZZ), XMVectorGetY(XX_YY_ZZ), XMVectorGetZ(XX_YY_ZZ), XMVectorGetX(XY_XZ_YZ), XMVectorGetY(XY_XZ_YZ), XMVectorGetZ(XY_XZ_YZ), &v1, &v2, &v3); // Put them in a matrix. XMMATRIX R; R.r[0] = XMVectorSetW(v1, 0.f); R.r[1] = XMVectorSetW(v2, 0.f); R.r[2] = XMVectorSetW(v3, 0.f); R.r[3] = g_XMIdentityR3.v; // Multiply by -1 to convert the matrix into a right handed coordinate // system (Det ~= 1) in case the eigenvectors form a left handed // coordinate system (Det ~= -1) because XMQuaternionRotationMatrix only // works on right handed matrices. XMVECTOR Det = XMMatrixDeterminant(R); if (XMVector4Less(Det, XMVectorZero())) { R.r[0] = XMVectorMultiply(R.r[0], g_XMNegativeOne.v); R.r[1] = XMVectorMultiply(R.r[1], g_XMNegativeOne.v); R.r[2] = XMVectorMultiply(R.r[2], g_XMNegativeOne.v); } // Get the rotation quaternion from the matrix. XMVECTOR vOrientation = XMQuaternionRotationMatrix(R); // Make sure it is normal (in case the vectors are slightly non-orthogonal). vOrientation = XMQuaternionNormalize(vOrientation); // Rebuild the rotation matrix from the quaternion. R = XMMatrixRotationQuaternion(vOrientation); // Build the rotation into the rotated space. XMMATRIX InverseR = XMMatrixTranspose(R); // Find the minimum OBB using the eigenvectors as the axes. XMVECTOR vMin, vMax; vMin = vMax = XMVector3TransformNormal(XMLoadFloat3(pPoints), InverseR); for (size_t i = 1; i < Count; ++i) { XMVECTOR Point = XMVector3TransformNormal(XMLoadFloat3(reinterpret_cast(reinterpret_cast(pPoints) + i * Stride)), InverseR); vMin = XMVectorMin(vMin, Point); vMax = XMVectorMax(vMax, Point); } // Rotate the center into world space. XMVECTOR vCenter = XMVectorScale(XMVectorAdd(vMin, vMax), 0.5f); vCenter = XMVector3TransformNormal(vCenter, R); // Store center, extents, and orientation. XMStoreFloat3(&Out.Center, vCenter); XMStoreFloat3(&Out.Extents, XMVectorScale(XMVectorSubtract(vMax, vMin), 0.5f)); XMStoreFloat4(&Out.Orientation, vOrientation); } /**************************************************************************** * * BoundingFrustum * ****************************************************************************/ _Use_decl_annotations_ inline BoundingFrustum::BoundingFrustum(CXMMATRIX Projection, bool rhcoords) noexcept { CreateFromMatrix(*this, Projection, rhcoords); } //----------------------------------------------------------------------------- // Transform a frustum by an angle preserving transform. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void XM_CALLCONV BoundingFrustum::Transform(BoundingFrustum& Out, FXMMATRIX M) const noexcept { // Load the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Composite the frustum rotation and the transform rotation XMMATRIX nM; nM.r[0] = XMVector3Normalize(M.r[0]); nM.r[1] = XMVector3Normalize(M.r[1]); nM.r[2] = XMVector3Normalize(M.r[2]); nM.r[3] = g_XMIdentityR3; XMVECTOR Rotation = XMQuaternionRotationMatrix(nM); vOrientation = XMQuaternionMultiply(vOrientation, Rotation); // Transform the center. vOrigin = XMVector3Transform(vOrigin, M); // Store the frustum. XMStoreFloat3(&Out.Origin, vOrigin); XMStoreFloat4(&Out.Orientation, vOrientation); // Scale the near and far distances (the slopes remain the same). XMVECTOR dX = XMVector3Dot(M.r[0], M.r[0]); XMVECTOR dY = XMVector3Dot(M.r[1], M.r[1]); XMVECTOR dZ = XMVector3Dot(M.r[2], M.r[2]); XMVECTOR d = XMVectorMax(dX, XMVectorMax(dY, dZ)); float Scale = sqrtf(XMVectorGetX(d)); Out.Near = Near * Scale; Out.Far = Far * Scale; // Copy the slopes. Out.RightSlope = RightSlope; Out.LeftSlope = LeftSlope; Out.TopSlope = TopSlope; Out.BottomSlope = BottomSlope; } _Use_decl_annotations_ inline void XM_CALLCONV BoundingFrustum::Transform(BoundingFrustum& Out, float Scale, FXMVECTOR Rotation, FXMVECTOR Translation) const noexcept { assert(DirectX::Internal::XMQuaternionIsUnit(Rotation)); // Load the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Composite the frustum rotation and the transform rotation. vOrientation = XMQuaternionMultiply(vOrientation, Rotation); // Transform the origin. vOrigin = XMVectorAdd(XMVector3Rotate(XMVectorScale(vOrigin, Scale), Rotation), Translation); // Store the frustum. XMStoreFloat3(&Out.Origin, vOrigin); XMStoreFloat4(&Out.Orientation, vOrientation); // Scale the near and far distances (the slopes remain the same). Out.Near = Near * Scale; Out.Far = Far * Scale; // Copy the slopes. Out.RightSlope = RightSlope; Out.LeftSlope = LeftSlope; Out.TopSlope = TopSlope; Out.BottomSlope = BottomSlope; } //----------------------------------------------------------------------------- // Get the corner points of the frustum //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingFrustum::GetCorners(XMFLOAT3* Corners) const noexcept { assert(Corners != nullptr); // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Build the corners of the frustum. XMVECTOR vRightTop = XMVectorSet(RightSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vRightBottom = XMVectorSet(RightSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vLeftTop = XMVectorSet(LeftSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vLeftBottom = XMVectorSet(LeftSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vNear = XMVectorReplicatePtr(&Near); XMVECTOR vFar = XMVectorReplicatePtr(&Far); // Returns 8 corners position of bounding frustum. // Near Far // 0----1 4----5 // | | | | // | | | | // 3----2 7----6 XMVECTOR vCorners[CORNER_COUNT]; vCorners[0] = XMVectorMultiply(vLeftTop, vNear); vCorners[1] = XMVectorMultiply(vRightTop, vNear); vCorners[2] = XMVectorMultiply(vRightBottom, vNear); vCorners[3] = XMVectorMultiply(vLeftBottom, vNear); vCorners[4] = XMVectorMultiply(vLeftTop, vFar); vCorners[5] = XMVectorMultiply(vRightTop, vFar); vCorners[6] = XMVectorMultiply(vRightBottom, vFar); vCorners[7] = XMVectorMultiply(vLeftBottom, vFar); for (size_t i = 0; i < CORNER_COUNT; ++i) { XMVECTOR C = XMVectorAdd(XMVector3Rotate(vCorners[i], vOrientation), vOrigin); XMStoreFloat3(&Corners[i], C); } } //----------------------------------------------------------------------------- // Point in frustum test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingFrustum::Contains(FXMVECTOR Point) const noexcept { // Build frustum planes. XMVECTOR Planes[6]; Planes[0] = XMVectorSet(0.0f, 0.0f, -1.0f, Near); Planes[1] = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); Planes[2] = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); Planes[3] = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); Planes[4] = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); Planes[5] = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); // Load origin and orientation. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Transform point into local space of frustum. XMVECTOR TPoint = XMVector3InverseRotate(XMVectorSubtract(Point, vOrigin), vOrientation); // Set w to one. TPoint = XMVectorInsert<0, 0, 0, 0, 1>(TPoint, XMVectorSplatOne()); XMVECTOR Zero = XMVectorZero(); XMVECTOR Outside = Zero; // Test point against each plane of the frustum. for (size_t i = 0; i < 6; ++i) { XMVECTOR Dot = XMVector4Dot(TPoint, Planes[i]); Outside = XMVectorOrInt(Outside, XMVectorGreater(Dot, Zero)); } return XMVector4NotEqualInt(Outside, XMVectorTrueInt()) ? CONTAINS : DISJOINT; } //----------------------------------------------------------------------------- // Triangle vs frustum test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingFrustum::Contains(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Create 6 planes (do it inline to encourage use of registers) XMVECTOR NearPlane = XMVectorSet(0.0f, 0.0f, -1.0f, Near); NearPlane = DirectX::Internal::XMPlaneTransform(NearPlane, vOrientation, vOrigin); NearPlane = XMPlaneNormalize(NearPlane); XMVECTOR FarPlane = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); FarPlane = DirectX::Internal::XMPlaneTransform(FarPlane, vOrientation, vOrigin); FarPlane = XMPlaneNormalize(FarPlane); XMVECTOR RightPlane = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); RightPlane = DirectX::Internal::XMPlaneTransform(RightPlane, vOrientation, vOrigin); RightPlane = XMPlaneNormalize(RightPlane); XMVECTOR LeftPlane = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); LeftPlane = DirectX::Internal::XMPlaneTransform(LeftPlane, vOrientation, vOrigin); LeftPlane = XMPlaneNormalize(LeftPlane); XMVECTOR TopPlane = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); TopPlane = DirectX::Internal::XMPlaneTransform(TopPlane, vOrientation, vOrigin); TopPlane = XMPlaneNormalize(TopPlane); XMVECTOR BottomPlane = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); BottomPlane = DirectX::Internal::XMPlaneTransform(BottomPlane, vOrientation, vOrigin); BottomPlane = XMPlaneNormalize(BottomPlane); return TriangleTests::ContainedBy(V0, V1, V2, NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane); } //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingFrustum::Contains(const BoundingSphere& sh) const noexcept { // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Create 6 planes (do it inline to encourage use of registers) XMVECTOR NearPlane = XMVectorSet(0.0f, 0.0f, -1.0f, Near); NearPlane = DirectX::Internal::XMPlaneTransform(NearPlane, vOrientation, vOrigin); NearPlane = XMPlaneNormalize(NearPlane); XMVECTOR FarPlane = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); FarPlane = DirectX::Internal::XMPlaneTransform(FarPlane, vOrientation, vOrigin); FarPlane = XMPlaneNormalize(FarPlane); XMVECTOR RightPlane = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); RightPlane = DirectX::Internal::XMPlaneTransform(RightPlane, vOrientation, vOrigin); RightPlane = XMPlaneNormalize(RightPlane); XMVECTOR LeftPlane = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); LeftPlane = DirectX::Internal::XMPlaneTransform(LeftPlane, vOrientation, vOrigin); LeftPlane = XMPlaneNormalize(LeftPlane); XMVECTOR TopPlane = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); TopPlane = DirectX::Internal::XMPlaneTransform(TopPlane, vOrientation, vOrigin); TopPlane = XMPlaneNormalize(TopPlane); XMVECTOR BottomPlane = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); BottomPlane = DirectX::Internal::XMPlaneTransform(BottomPlane, vOrientation, vOrigin); BottomPlane = XMPlaneNormalize(BottomPlane); return sh.ContainedBy(NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane); } //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingFrustum::Contains(const BoundingBox& box) const noexcept { // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Create 6 planes (do it inline to encourage use of registers) XMVECTOR NearPlane = XMVectorSet(0.0f, 0.0f, -1.0f, Near); NearPlane = DirectX::Internal::XMPlaneTransform(NearPlane, vOrientation, vOrigin); NearPlane = XMPlaneNormalize(NearPlane); XMVECTOR FarPlane = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); FarPlane = DirectX::Internal::XMPlaneTransform(FarPlane, vOrientation, vOrigin); FarPlane = XMPlaneNormalize(FarPlane); XMVECTOR RightPlane = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); RightPlane = DirectX::Internal::XMPlaneTransform(RightPlane, vOrientation, vOrigin); RightPlane = XMPlaneNormalize(RightPlane); XMVECTOR LeftPlane = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); LeftPlane = DirectX::Internal::XMPlaneTransform(LeftPlane, vOrientation, vOrigin); LeftPlane = XMPlaneNormalize(LeftPlane); XMVECTOR TopPlane = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); TopPlane = DirectX::Internal::XMPlaneTransform(TopPlane, vOrientation, vOrigin); TopPlane = XMPlaneNormalize(TopPlane); XMVECTOR BottomPlane = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); BottomPlane = DirectX::Internal::XMPlaneTransform(BottomPlane, vOrientation, vOrigin); BottomPlane = XMPlaneNormalize(BottomPlane); return box.ContainedBy(NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane); } //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingFrustum::Contains(const BoundingOrientedBox& box) const noexcept { // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Create 6 planes (do it inline to encourage use of registers) XMVECTOR NearPlane = XMVectorSet(0.0f, 0.0f, -1.0f, Near); NearPlane = DirectX::Internal::XMPlaneTransform(NearPlane, vOrientation, vOrigin); NearPlane = XMPlaneNormalize(NearPlane); XMVECTOR FarPlane = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); FarPlane = DirectX::Internal::XMPlaneTransform(FarPlane, vOrientation, vOrigin); FarPlane = XMPlaneNormalize(FarPlane); XMVECTOR RightPlane = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); RightPlane = DirectX::Internal::XMPlaneTransform(RightPlane, vOrientation, vOrigin); RightPlane = XMPlaneNormalize(RightPlane); XMVECTOR LeftPlane = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); LeftPlane = DirectX::Internal::XMPlaneTransform(LeftPlane, vOrientation, vOrigin); LeftPlane = XMPlaneNormalize(LeftPlane); XMVECTOR TopPlane = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); TopPlane = DirectX::Internal::XMPlaneTransform(TopPlane, vOrientation, vOrigin); TopPlane = XMPlaneNormalize(TopPlane); XMVECTOR BottomPlane = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); BottomPlane = DirectX::Internal::XMPlaneTransform(BottomPlane, vOrientation, vOrigin); BottomPlane = XMPlaneNormalize(BottomPlane); return box.ContainedBy(NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane); } //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType BoundingFrustum::Contains(const BoundingFrustum& fr) const noexcept { // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); // Create 6 planes (do it inline to encourage use of registers) XMVECTOR NearPlane = XMVectorSet(0.0f, 0.0f, -1.0f, Near); NearPlane = DirectX::Internal::XMPlaneTransform(NearPlane, vOrientation, vOrigin); NearPlane = XMPlaneNormalize(NearPlane); XMVECTOR FarPlane = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); FarPlane = DirectX::Internal::XMPlaneTransform(FarPlane, vOrientation, vOrigin); FarPlane = XMPlaneNormalize(FarPlane); XMVECTOR RightPlane = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); RightPlane = DirectX::Internal::XMPlaneTransform(RightPlane, vOrientation, vOrigin); RightPlane = XMPlaneNormalize(RightPlane); XMVECTOR LeftPlane = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); LeftPlane = DirectX::Internal::XMPlaneTransform(LeftPlane, vOrientation, vOrigin); LeftPlane = XMPlaneNormalize(LeftPlane); XMVECTOR TopPlane = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); TopPlane = DirectX::Internal::XMPlaneTransform(TopPlane, vOrientation, vOrigin); TopPlane = XMPlaneNormalize(TopPlane); XMVECTOR BottomPlane = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); BottomPlane = DirectX::Internal::XMPlaneTransform(BottomPlane, vOrientation, vOrigin); BottomPlane = XMPlaneNormalize(BottomPlane); return fr.ContainedBy(NearPlane, FarPlane, RightPlane, LeftPlane, TopPlane, BottomPlane); } //----------------------------------------------------------------------------- // Exact sphere vs frustum test. The algorithm first checks the sphere against // the planes of the frustum, then if the plane checks were indeterminate finds // the nearest feature (plane, line, point) on the frustum to the center of the // sphere and compares the distance to the nearest feature to the radius of the // sphere //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingFrustum::Intersects(const BoundingSphere& sh) const noexcept { XMVECTOR Zero = XMVectorZero(); // Build the frustum planes. XMVECTOR Planes[6]; Planes[0] = XMVectorSet(0.0f, 0.0f, -1.0f, Near); Planes[1] = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); Planes[2] = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); Planes[3] = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); Planes[4] = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); Planes[5] = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); // Normalize the planes so we can compare to the sphere radius. Planes[2] = XMVector3Normalize(Planes[2]); Planes[3] = XMVector3Normalize(Planes[3]); Planes[4] = XMVector3Normalize(Planes[4]); Planes[5] = XMVector3Normalize(Planes[5]); // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Load the sphere. XMVECTOR vCenter = XMLoadFloat3(&sh.Center); XMVECTOR vRadius = XMVectorReplicatePtr(&sh.Radius); // Transform the center of the sphere into the local space of frustum. vCenter = XMVector3InverseRotate(XMVectorSubtract(vCenter, vOrigin), vOrientation); // Set w of the center to one so we can dot4 with the plane. vCenter = XMVectorInsert<0, 0, 0, 0, 1>(vCenter, XMVectorSplatOne()); // Check against each plane of the frustum. XMVECTOR Outside = XMVectorFalseInt(); XMVECTOR InsideAll = XMVectorTrueInt(); XMVECTOR CenterInsideAll = XMVectorTrueInt(); XMVECTOR Dist[6]; for (size_t i = 0; i < 6; ++i) { Dist[i] = XMVector4Dot(vCenter, Planes[i]); // Outside the plane? Outside = XMVectorOrInt(Outside, XMVectorGreater(Dist[i], vRadius)); // Fully inside the plane? InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(Dist[i], XMVectorNegate(vRadius))); // Check if the center is inside the plane. CenterInsideAll = XMVectorAndInt(CenterInsideAll, XMVectorLessOrEqual(Dist[i], Zero)); } // If the sphere is outside any of the planes it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // If the sphere is inside all planes it is fully inside. if (XMVector4EqualInt(InsideAll, XMVectorTrueInt())) return true; // If the center of the sphere is inside all planes and the sphere intersects // one or more planes then it must intersect. if (XMVector4EqualInt(CenterInsideAll, XMVectorTrueInt())) return true; // The sphere may be outside the frustum or intersecting the frustum. // Find the nearest feature (face, edge, or corner) on the frustum // to the sphere. // The faces adjacent to each face are: static const size_t adjacent_faces[6][4] = { { 2, 3, 4, 5 }, // 0 { 2, 3, 4, 5 }, // 1 { 0, 1, 4, 5 }, // 2 { 0, 1, 4, 5 }, // 3 { 0, 1, 2, 3 }, // 4 { 0, 1, 2, 3 } }; // 5 XMVECTOR Intersects = XMVectorFalseInt(); // Check to see if the nearest feature is one of the planes. for (size_t i = 0; i < 6; ++i) { // Find the nearest point on the plane to the center of the sphere. XMVECTOR Point = XMVectorNegativeMultiplySubtract(Planes[i], Dist[i], vCenter); // Set w of the point to one. Point = XMVectorInsert<0, 0, 0, 0, 1>(Point, XMVectorSplatOne()); // If the point is inside the face (inside the adjacent planes) then // this plane is the nearest feature. XMVECTOR InsideFace = XMVectorTrueInt(); for (size_t j = 0; j < 4; j++) { size_t plane_index = adjacent_faces[i][j]; InsideFace = XMVectorAndInt(InsideFace, XMVectorLessOrEqual(XMVector4Dot(Point, Planes[plane_index]), Zero)); } // Since we have already checked distance from the plane we know that the // sphere must intersect if this plane is the nearest feature. Intersects = XMVectorOrInt(Intersects, XMVectorAndInt(XMVectorGreater(Dist[i], Zero), InsideFace)); } if (XMVector4EqualInt(Intersects, XMVectorTrueInt())) return true; // Build the corners of the frustum. XMVECTOR vRightTop = XMVectorSet(RightSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vRightBottom = XMVectorSet(RightSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vLeftTop = XMVectorSet(LeftSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vLeftBottom = XMVectorSet(LeftSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vNear = XMVectorReplicatePtr(&Near); XMVECTOR vFar = XMVectorReplicatePtr(&Far); XMVECTOR Corners[CORNER_COUNT]; Corners[0] = XMVectorMultiply(vRightTop, vNear); Corners[1] = XMVectorMultiply(vRightBottom, vNear); Corners[2] = XMVectorMultiply(vLeftTop, vNear); Corners[3] = XMVectorMultiply(vLeftBottom, vNear); Corners[4] = XMVectorMultiply(vRightTop, vFar); Corners[5] = XMVectorMultiply(vRightBottom, vFar); Corners[6] = XMVectorMultiply(vLeftTop, vFar); Corners[7] = XMVectorMultiply(vLeftBottom, vFar); // The Edges are: static const size_t edges[12][2] = { { 0, 1 }, { 2, 3 }, { 0, 2 }, { 1, 3 }, // Near plane { 4, 5 }, { 6, 7 }, { 4, 6 }, { 5, 7 }, // Far plane { 0, 4 }, { 1, 5 }, { 2, 6 }, { 3, 7 }, }; // Near to far XMVECTOR RadiusSq = XMVectorMultiply(vRadius, vRadius); // Check to see if the nearest feature is one of the edges (or corners). for (size_t i = 0; i < 12; ++i) { size_t ei0 = edges[i][0]; size_t ei1 = edges[i][1]; // Find the nearest point on the edge to the center of the sphere. // The corners of the frustum are included as the endpoints of the edges. XMVECTOR Point = DirectX::Internal::PointOnLineSegmentNearestPoint(Corners[ei0], Corners[ei1], vCenter); XMVECTOR Delta = XMVectorSubtract(vCenter, Point); XMVECTOR DistSq = XMVector3Dot(Delta, Delta); // If the distance to the center of the sphere to the point is less than // the radius of the sphere then it must intersect. Intersects = XMVectorOrInt(Intersects, XMVectorLessOrEqual(DistSq, RadiusSq)); } if (XMVector4EqualInt(Intersects, XMVectorTrueInt())) return true; // The sphere must be outside the frustum. return false; } //----------------------------------------------------------------------------- // Exact axis aligned box vs frustum test. Constructs an oriented box and uses // the oriented box vs frustum test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingFrustum::Intersects(const BoundingBox& box) const noexcept { // Make the axis aligned box oriented and do an OBB vs frustum test. BoundingOrientedBox obox(box.Center, box.Extents, XMFLOAT4(0.f, 0.f, 0.f, 1.f)); return Intersects(obox); } //----------------------------------------------------------------------------- // Exact oriented box vs frustum test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingFrustum::Intersects(const BoundingOrientedBox& box) const noexcept { static const XMVECTORU32 SelectY = { { { XM_SELECT_0, XM_SELECT_1, XM_SELECT_0, XM_SELECT_0 } } }; static const XMVECTORU32 SelectZ = { { { XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0 } } }; XMVECTOR Zero = XMVectorZero(); // Build the frustum planes. XMVECTOR Planes[6]; Planes[0] = XMVectorSet(0.0f, 0.0f, -1.0f, Near); Planes[1] = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); Planes[2] = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); Planes[3] = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); Planes[4] = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); Planes[5] = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR FrustumOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(FrustumOrientation)); // Load the box. XMVECTOR Center = XMLoadFloat3(&box.Center); XMVECTOR Extents = XMLoadFloat3(&box.Extents); XMVECTOR BoxOrientation = XMLoadFloat4(&box.Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(BoxOrientation)); // Transform the oriented box into the space of the frustum in order to // minimize the number of transforms we have to do. Center = XMVector3InverseRotate(XMVectorSubtract(Center, vOrigin), FrustumOrientation); BoxOrientation = XMQuaternionMultiply(BoxOrientation, XMQuaternionConjugate(FrustumOrientation)); // Set w of the center to one so we can dot4 with the plane. Center = XMVectorInsert<0, 0, 0, 0, 1>(Center, XMVectorSplatOne()); // Build the 3x3 rotation matrix that defines the box axes. XMMATRIX R = XMMatrixRotationQuaternion(BoxOrientation); // Check against each plane of the frustum. XMVECTOR Outside = XMVectorFalseInt(); XMVECTOR InsideAll = XMVectorTrueInt(); XMVECTOR CenterInsideAll = XMVectorTrueInt(); for (size_t i = 0; i < 6; ++i) { // Compute the distance to the center of the box. XMVECTOR Dist = XMVector4Dot(Center, Planes[i]); // Project the axes of the box onto the normal of the plane. Half the // length of the projection (sometime called the "radius") is equal to // h(u) * abs(n dot b(u))) + h(v) * abs(n dot b(v)) + h(w) * abs(n dot b(w)) // where h(i) are extents of the box, n is the plane normal, and b(i) are the // axes of the box. XMVECTOR Radius = XMVector3Dot(Planes[i], R.r[0]); Radius = XMVectorSelect(Radius, XMVector3Dot(Planes[i], R.r[1]), SelectY); Radius = XMVectorSelect(Radius, XMVector3Dot(Planes[i], R.r[2]), SelectZ); Radius = XMVector3Dot(Extents, XMVectorAbs(Radius)); // Outside the plane? Outside = XMVectorOrInt(Outside, XMVectorGreater(Dist, Radius)); // Fully inside the plane? InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(Dist, XMVectorNegate(Radius))); // Check if the center is inside the plane. CenterInsideAll = XMVectorAndInt(CenterInsideAll, XMVectorLessOrEqual(Dist, Zero)); } // If the box is outside any of the planes it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // If the box is inside all planes it is fully inside. if (XMVector4EqualInt(InsideAll, XMVectorTrueInt())) return true; // If the center of the box is inside all planes and the box intersects // one or more planes then it must intersect. if (XMVector4EqualInt(CenterInsideAll, XMVectorTrueInt())) return true; // Build the corners of the frustum. XMVECTOR vRightTop = XMVectorSet(RightSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vRightBottom = XMVectorSet(RightSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vLeftTop = XMVectorSet(LeftSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vLeftBottom = XMVectorSet(LeftSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vNear = XMVectorReplicatePtr(&Near); XMVECTOR vFar = XMVectorReplicatePtr(&Far); XMVECTOR Corners[CORNER_COUNT]; Corners[0] = XMVectorMultiply(vRightTop, vNear); Corners[1] = XMVectorMultiply(vRightBottom, vNear); Corners[2] = XMVectorMultiply(vLeftTop, vNear); Corners[3] = XMVectorMultiply(vLeftBottom, vNear); Corners[4] = XMVectorMultiply(vRightTop, vFar); Corners[5] = XMVectorMultiply(vRightBottom, vFar); Corners[6] = XMVectorMultiply(vLeftTop, vFar); Corners[7] = XMVectorMultiply(vLeftBottom, vFar); // Test against box axes (3) { // Find the min/max values of the projection of the frustum onto each axis. XMVECTOR FrustumMin, FrustumMax; FrustumMin = XMVector3Dot(Corners[0], R.r[0]); FrustumMin = XMVectorSelect(FrustumMin, XMVector3Dot(Corners[0], R.r[1]), SelectY); FrustumMin = XMVectorSelect(FrustumMin, XMVector3Dot(Corners[0], R.r[2]), SelectZ); FrustumMax = FrustumMin; for (size_t i = 1; i < BoundingOrientedBox::CORNER_COUNT; ++i) { XMVECTOR Temp = XMVector3Dot(Corners[i], R.r[0]); Temp = XMVectorSelect(Temp, XMVector3Dot(Corners[i], R.r[1]), SelectY); Temp = XMVectorSelect(Temp, XMVector3Dot(Corners[i], R.r[2]), SelectZ); FrustumMin = XMVectorMin(FrustumMin, Temp); FrustumMax = XMVectorMax(FrustumMax, Temp); } // Project the center of the box onto the axes. XMVECTOR BoxDist = XMVector3Dot(Center, R.r[0]); BoxDist = XMVectorSelect(BoxDist, XMVector3Dot(Center, R.r[1]), SelectY); BoxDist = XMVectorSelect(BoxDist, XMVector3Dot(Center, R.r[2]), SelectZ); // The projection of the box onto the axis is just its Center and Extents. // if (min > box_max || max < box_min) reject; XMVECTOR Result = XMVectorOrInt(XMVectorGreater(FrustumMin, XMVectorAdd(BoxDist, Extents)), XMVectorLess(FrustumMax, XMVectorSubtract(BoxDist, Extents))); if (DirectX::Internal::XMVector3AnyTrue(Result)) return false; } // Test against edge/edge axes (3*6). XMVECTOR FrustumEdgeAxis[6]; FrustumEdgeAxis[0] = vRightTop; FrustumEdgeAxis[1] = vRightBottom; FrustumEdgeAxis[2] = vLeftTop; FrustumEdgeAxis[3] = vLeftBottom; FrustumEdgeAxis[4] = XMVectorSubtract(vRightTop, vLeftTop); FrustumEdgeAxis[5] = XMVectorSubtract(vLeftBottom, vLeftTop); for (size_t i = 0; i < 3; ++i) { for (size_t j = 0; j < 6; j++) { // Compute the axis we are going to test. XMVECTOR Axis = XMVector3Cross(R.r[i], FrustumEdgeAxis[j]); // Find the min/max values of the projection of the frustum onto the axis. XMVECTOR FrustumMin, FrustumMax; FrustumMin = FrustumMax = XMVector3Dot(Axis, Corners[0]); for (size_t k = 1; k < CORNER_COUNT; k++) { XMVECTOR Temp = XMVector3Dot(Axis, Corners[k]); FrustumMin = XMVectorMin(FrustumMin, Temp); FrustumMax = XMVectorMax(FrustumMax, Temp); } // Project the center of the box onto the axis. XMVECTOR Dist = XMVector3Dot(Center, Axis); // Project the axes of the box onto the axis to find the "radius" of the box. XMVECTOR Radius = XMVector3Dot(Axis, R.r[0]); Radius = XMVectorSelect(Radius, XMVector3Dot(Axis, R.r[1]), SelectY); Radius = XMVectorSelect(Radius, XMVector3Dot(Axis, R.r[2]), SelectZ); Radius = XMVector3Dot(Extents, XMVectorAbs(Radius)); // if (center > max + radius || center < min - radius) reject; Outside = XMVectorOrInt(Outside, XMVectorGreater(Dist, XMVectorAdd(FrustumMax, Radius))); Outside = XMVectorOrInt(Outside, XMVectorLess(Dist, XMVectorSubtract(FrustumMin, Radius))); } } if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // If we did not find a separating plane then the box must intersect the frustum. return true; } //----------------------------------------------------------------------------- // Exact frustum vs frustum test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool BoundingFrustum::Intersects(const BoundingFrustum& fr) const noexcept { // Load origin and orientation of frustum B. XMVECTOR OriginB = XMLoadFloat3(&Origin); XMVECTOR OrientationB = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(OrientationB)); // Build the planes of frustum B. XMVECTOR AxisB[6]; AxisB[0] = XMVectorSet(0.0f, 0.0f, -1.0f, 0.0f); AxisB[1] = XMVectorSet(0.0f, 0.0f, 1.0f, 0.0f); AxisB[2] = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); AxisB[3] = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); AxisB[4] = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); AxisB[5] = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); XMVECTOR PlaneDistB[6]; PlaneDistB[0] = XMVectorNegate(XMVectorReplicatePtr(&Near)); PlaneDistB[1] = XMVectorReplicatePtr(&Far); PlaneDistB[2] = XMVectorZero(); PlaneDistB[3] = XMVectorZero(); PlaneDistB[4] = XMVectorZero(); PlaneDistB[5] = XMVectorZero(); // Load origin and orientation of frustum A. XMVECTOR OriginA = XMLoadFloat3(&fr.Origin); XMVECTOR OrientationA = XMLoadFloat4(&fr.Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(OrientationA)); // Transform frustum A into the space of the frustum B in order to // minimize the number of transforms we have to do. OriginA = XMVector3InverseRotate(XMVectorSubtract(OriginA, OriginB), OrientationB); OrientationA = XMQuaternionMultiply(OrientationA, XMQuaternionConjugate(OrientationB)); // Build the corners of frustum A (in the local space of B). XMVECTOR RightTopA = XMVectorSet(fr.RightSlope, fr.TopSlope, 1.0f, 0.0f); XMVECTOR RightBottomA = XMVectorSet(fr.RightSlope, fr.BottomSlope, 1.0f, 0.0f); XMVECTOR LeftTopA = XMVectorSet(fr.LeftSlope, fr.TopSlope, 1.0f, 0.0f); XMVECTOR LeftBottomA = XMVectorSet(fr.LeftSlope, fr.BottomSlope, 1.0f, 0.0f); XMVECTOR NearA = XMVectorReplicatePtr(&fr.Near); XMVECTOR FarA = XMVectorReplicatePtr(&fr.Far); RightTopA = XMVector3Rotate(RightTopA, OrientationA); RightBottomA = XMVector3Rotate(RightBottomA, OrientationA); LeftTopA = XMVector3Rotate(LeftTopA, OrientationA); LeftBottomA = XMVector3Rotate(LeftBottomA, OrientationA); XMVECTOR CornersA[CORNER_COUNT]; CornersA[0] = XMVectorMultiplyAdd(RightTopA, NearA, OriginA); CornersA[1] = XMVectorMultiplyAdd(RightBottomA, NearA, OriginA); CornersA[2] = XMVectorMultiplyAdd(LeftTopA, NearA, OriginA); CornersA[3] = XMVectorMultiplyAdd(LeftBottomA, NearA, OriginA); CornersA[4] = XMVectorMultiplyAdd(RightTopA, FarA, OriginA); CornersA[5] = XMVectorMultiplyAdd(RightBottomA, FarA, OriginA); CornersA[6] = XMVectorMultiplyAdd(LeftTopA, FarA, OriginA); CornersA[7] = XMVectorMultiplyAdd(LeftBottomA, FarA, OriginA); // Check frustum A against each plane of frustum B. XMVECTOR Outside = XMVectorFalseInt(); XMVECTOR InsideAll = XMVectorTrueInt(); for (size_t i = 0; i < 6; ++i) { // Find the min/max projection of the frustum onto the plane normal. XMVECTOR Min, Max; Min = Max = XMVector3Dot(AxisB[i], CornersA[0]); for (size_t j = 1; j < CORNER_COUNT; j++) { XMVECTOR Temp = XMVector3Dot(AxisB[i], CornersA[j]); Min = XMVectorMin(Min, Temp); Max = XMVectorMax(Max, Temp); } // Outside the plane? Outside = XMVectorOrInt(Outside, XMVectorGreater(Min, PlaneDistB[i])); // Fully inside the plane? InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(Max, PlaneDistB[i])); } // If the frustum A is outside any of the planes of frustum B it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // If frustum A is inside all planes of frustum B it is fully inside. if (XMVector4EqualInt(InsideAll, XMVectorTrueInt())) return true; // Build the corners of frustum B. XMVECTOR RightTopB = XMVectorSet(RightSlope, TopSlope, 1.0f, 0.0f); XMVECTOR RightBottomB = XMVectorSet(RightSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR LeftTopB = XMVectorSet(LeftSlope, TopSlope, 1.0f, 0.0f); XMVECTOR LeftBottomB = XMVectorSet(LeftSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR NearB = XMVectorReplicatePtr(&Near); XMVECTOR FarB = XMVectorReplicatePtr(&Far); XMVECTOR CornersB[BoundingFrustum::CORNER_COUNT]; CornersB[0] = XMVectorMultiply(RightTopB, NearB); CornersB[1] = XMVectorMultiply(RightBottomB, NearB); CornersB[2] = XMVectorMultiply(LeftTopB, NearB); CornersB[3] = XMVectorMultiply(LeftBottomB, NearB); CornersB[4] = XMVectorMultiply(RightTopB, FarB); CornersB[5] = XMVectorMultiply(RightBottomB, FarB); CornersB[6] = XMVectorMultiply(LeftTopB, FarB); CornersB[7] = XMVectorMultiply(LeftBottomB, FarB); // Build the planes of frustum A (in the local space of B). XMVECTOR AxisA[6]; XMVECTOR PlaneDistA[6]; AxisA[0] = XMVectorSet(0.0f, 0.0f, -1.0f, 0.0f); AxisA[1] = XMVectorSet(0.0f, 0.0f, 1.0f, 0.0f); AxisA[2] = XMVectorSet(1.0f, 0.0f, -fr.RightSlope, 0.0f); AxisA[3] = XMVectorSet(-1.0f, 0.0f, fr.LeftSlope, 0.0f); AxisA[4] = XMVectorSet(0.0f, 1.0f, -fr.TopSlope, 0.0f); AxisA[5] = XMVectorSet(0.0f, -1.0f, fr.BottomSlope, 0.0f); AxisA[0] = XMVector3Rotate(AxisA[0], OrientationA); AxisA[1] = XMVectorNegate(AxisA[0]); AxisA[2] = XMVector3Rotate(AxisA[2], OrientationA); AxisA[3] = XMVector3Rotate(AxisA[3], OrientationA); AxisA[4] = XMVector3Rotate(AxisA[4], OrientationA); AxisA[5] = XMVector3Rotate(AxisA[5], OrientationA); PlaneDistA[0] = XMVector3Dot(AxisA[0], CornersA[0]); // Re-use corner on near plane. PlaneDistA[1] = XMVector3Dot(AxisA[1], CornersA[4]); // Re-use corner on far plane. PlaneDistA[2] = XMVector3Dot(AxisA[2], OriginA); PlaneDistA[3] = XMVector3Dot(AxisA[3], OriginA); PlaneDistA[4] = XMVector3Dot(AxisA[4], OriginA); PlaneDistA[5] = XMVector3Dot(AxisA[5], OriginA); // Check each axis of frustum A for a seperating plane (5). for (size_t i = 0; i < 6; ++i) { // Find the minimum projection of the frustum onto the plane normal. XMVECTOR Min; Min = XMVector3Dot(AxisA[i], CornersB[0]); for (size_t j = 1; j < CORNER_COUNT; j++) { XMVECTOR Temp = XMVector3Dot(AxisA[i], CornersB[j]); Min = XMVectorMin(Min, Temp); } // Outside the plane? Outside = XMVectorOrInt(Outside, XMVectorGreater(Min, PlaneDistA[i])); } // If the frustum B is outside any of the planes of frustum A it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // Check edge/edge axes (6 * 6). XMVECTOR FrustumEdgeAxisA[6]; FrustumEdgeAxisA[0] = RightTopA; FrustumEdgeAxisA[1] = RightBottomA; FrustumEdgeAxisA[2] = LeftTopA; FrustumEdgeAxisA[3] = LeftBottomA; FrustumEdgeAxisA[4] = XMVectorSubtract(RightTopA, LeftTopA); FrustumEdgeAxisA[5] = XMVectorSubtract(LeftBottomA, LeftTopA); XMVECTOR FrustumEdgeAxisB[6]; FrustumEdgeAxisB[0] = RightTopB; FrustumEdgeAxisB[1] = RightBottomB; FrustumEdgeAxisB[2] = LeftTopB; FrustumEdgeAxisB[3] = LeftBottomB; FrustumEdgeAxisB[4] = XMVectorSubtract(RightTopB, LeftTopB); FrustumEdgeAxisB[5] = XMVectorSubtract(LeftBottomB, LeftTopB); for (size_t i = 0; i < 6; ++i) { for (size_t j = 0; j < 6; j++) { // Compute the axis we are going to test. XMVECTOR Axis = XMVector3Cross(FrustumEdgeAxisA[i], FrustumEdgeAxisB[j]); // Find the min/max values of the projection of both frustums onto the axis. XMVECTOR MinA, MaxA; XMVECTOR MinB, MaxB; MinA = MaxA = XMVector3Dot(Axis, CornersA[0]); MinB = MaxB = XMVector3Dot(Axis, CornersB[0]); for (size_t k = 1; k < CORNER_COUNT; k++) { XMVECTOR TempA = XMVector3Dot(Axis, CornersA[k]); MinA = XMVectorMin(MinA, TempA); MaxA = XMVectorMax(MaxA, TempA); XMVECTOR TempB = XMVector3Dot(Axis, CornersB[k]); MinB = XMVectorMin(MinB, TempB); MaxB = XMVectorMax(MaxB, TempB); } // if (MinA > MaxB || MinB > MaxA) reject Outside = XMVectorOrInt(Outside, XMVectorGreater(MinA, MaxB)); Outside = XMVectorOrInt(Outside, XMVectorGreater(MinB, MaxA)); } } // If there is a seperating plane, then the frustums do not intersect. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // If we did not find a separating plane then the frustums intersect. return true; } //----------------------------------------------------------------------------- // Triangle vs frustum test. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingFrustum::Intersects(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2) const noexcept { // Build the frustum planes (NOTE: D is negated from the usual). XMVECTOR Planes[6]; Planes[0] = XMVectorSet(0.0f, 0.0f, -1.0f, -Near); Planes[1] = XMVectorSet(0.0f, 0.0f, 1.0f, Far); Planes[2] = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); Planes[3] = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); Planes[4] = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); Planes[5] = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Transform triangle into the local space of frustum. XMVECTOR TV0 = XMVector3InverseRotate(XMVectorSubtract(V0, vOrigin), vOrientation); XMVECTOR TV1 = XMVector3InverseRotate(XMVectorSubtract(V1, vOrigin), vOrientation); XMVECTOR TV2 = XMVector3InverseRotate(XMVectorSubtract(V2, vOrigin), vOrientation); // Test each vertex of the triangle against the frustum planes. XMVECTOR Outside = XMVectorFalseInt(); XMVECTOR InsideAll = XMVectorTrueInt(); for (size_t i = 0; i < 6; ++i) { XMVECTOR Dist0 = XMVector3Dot(TV0, Planes[i]); XMVECTOR Dist1 = XMVector3Dot(TV1, Planes[i]); XMVECTOR Dist2 = XMVector3Dot(TV2, Planes[i]); XMVECTOR MinDist = XMVectorMin(Dist0, Dist1); MinDist = XMVectorMin(MinDist, Dist2); XMVECTOR MaxDist = XMVectorMax(Dist0, Dist1); MaxDist = XMVectorMax(MaxDist, Dist2); XMVECTOR PlaneDist = XMVectorSplatW(Planes[i]); // Outside the plane? Outside = XMVectorOrInt(Outside, XMVectorGreater(MinDist, PlaneDist)); // Fully inside the plane? InsideAll = XMVectorAndInt(InsideAll, XMVectorLessOrEqual(MaxDist, PlaneDist)); } // If the triangle is outside any of the planes it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // If the triangle is inside all planes it is fully inside. if (XMVector4EqualInt(InsideAll, XMVectorTrueInt())) return true; // Build the corners of the frustum. XMVECTOR vRightTop = XMVectorSet(RightSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vRightBottom = XMVectorSet(RightSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vLeftTop = XMVectorSet(LeftSlope, TopSlope, 1.0f, 0.0f); XMVECTOR vLeftBottom = XMVectorSet(LeftSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vNear = XMVectorReplicatePtr(&Near); XMVECTOR vFar = XMVectorReplicatePtr(&Far); XMVECTOR Corners[CORNER_COUNT]; Corners[0] = XMVectorMultiply(vRightTop, vNear); Corners[1] = XMVectorMultiply(vRightBottom, vNear); Corners[2] = XMVectorMultiply(vLeftTop, vNear); Corners[3] = XMVectorMultiply(vLeftBottom, vNear); Corners[4] = XMVectorMultiply(vRightTop, vFar); Corners[5] = XMVectorMultiply(vRightBottom, vFar); Corners[6] = XMVectorMultiply(vLeftTop, vFar); Corners[7] = XMVectorMultiply(vLeftBottom, vFar); // Test the plane of the triangle. XMVECTOR Normal = XMVector3Cross(XMVectorSubtract(V1, V0), XMVectorSubtract(V2, V0)); XMVECTOR Dist = XMVector3Dot(Normal, V0); XMVECTOR MinDist, MaxDist; MinDist = MaxDist = XMVector3Dot(Corners[0], Normal); for (size_t i = 1; i < CORNER_COUNT; ++i) { XMVECTOR Temp = XMVector3Dot(Corners[i], Normal); MinDist = XMVectorMin(MinDist, Temp); MaxDist = XMVectorMax(MaxDist, Temp); } Outside = XMVectorOrInt(XMVectorGreater(MinDist, Dist), XMVectorLess(MaxDist, Dist)); if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // Check the edge/edge axes (3*6). XMVECTOR TriangleEdgeAxis[3]; TriangleEdgeAxis[0] = XMVectorSubtract(V1, V0); TriangleEdgeAxis[1] = XMVectorSubtract(V2, V1); TriangleEdgeAxis[2] = XMVectorSubtract(V0, V2); XMVECTOR FrustumEdgeAxis[6]; FrustumEdgeAxis[0] = vRightTop; FrustumEdgeAxis[1] = vRightBottom; FrustumEdgeAxis[2] = vLeftTop; FrustumEdgeAxis[3] = vLeftBottom; FrustumEdgeAxis[4] = XMVectorSubtract(vRightTop, vLeftTop); FrustumEdgeAxis[5] = XMVectorSubtract(vLeftBottom, vLeftTop); for (size_t i = 0; i < 3; ++i) { for (size_t j = 0; j < 6; j++) { // Compute the axis we are going to test. XMVECTOR Axis = XMVector3Cross(TriangleEdgeAxis[i], FrustumEdgeAxis[j]); // Find the min/max of the projection of the triangle onto the axis. XMVECTOR MinA, MaxA; XMVECTOR Dist0 = XMVector3Dot(V0, Axis); XMVECTOR Dist1 = XMVector3Dot(V1, Axis); XMVECTOR Dist2 = XMVector3Dot(V2, Axis); MinA = XMVectorMin(Dist0, Dist1); MinA = XMVectorMin(MinA, Dist2); MaxA = XMVectorMax(Dist0, Dist1); MaxA = XMVectorMax(MaxA, Dist2); // Find the min/max of the projection of the frustum onto the axis. XMVECTOR MinB, MaxB; MinB = MaxB = XMVector3Dot(Axis, Corners[0]); for (size_t k = 1; k < CORNER_COUNT; k++) { XMVECTOR Temp = XMVector3Dot(Axis, Corners[k]); MinB = XMVectorMin(MinB, Temp); MaxB = XMVectorMax(MaxB, Temp); } // if (MinA > MaxB || MinB > MaxA) reject; Outside = XMVectorOrInt(Outside, XMVectorGreater(MinA, MaxB)); Outside = XMVectorOrInt(Outside, XMVectorGreater(MinB, MaxA)); } } if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return false; // If we did not find a separating plane then the triangle must intersect the frustum. return true; } //----------------------------------------------------------------------------- _Use_decl_annotations_ inline PlaneIntersectionType XM_CALLCONV BoundingFrustum::Intersects(FXMVECTOR Plane) const noexcept { assert(DirectX::Internal::XMPlaneIsUnit(Plane)); // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Set w of the origin to one so we can dot4 with a plane. vOrigin = XMVectorInsert<0, 0, 0, 0, 1>(vOrigin, XMVectorSplatOne()); // Build the corners of the frustum (in world space). XMVECTOR RightTop = XMVectorSet(RightSlope, TopSlope, 1.0f, 0.0f); XMVECTOR RightBottom = XMVectorSet(RightSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR LeftTop = XMVectorSet(LeftSlope, TopSlope, 1.0f, 0.0f); XMVECTOR LeftBottom = XMVectorSet(LeftSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vNear = XMVectorReplicatePtr(&Near); XMVECTOR vFar = XMVectorReplicatePtr(&Far); RightTop = XMVector3Rotate(RightTop, vOrientation); RightBottom = XMVector3Rotate(RightBottom, vOrientation); LeftTop = XMVector3Rotate(LeftTop, vOrientation); LeftBottom = XMVector3Rotate(LeftBottom, vOrientation); XMVECTOR Corners0 = XMVectorMultiplyAdd(RightTop, vNear, vOrigin); XMVECTOR Corners1 = XMVectorMultiplyAdd(RightBottom, vNear, vOrigin); XMVECTOR Corners2 = XMVectorMultiplyAdd(LeftTop, vNear, vOrigin); XMVECTOR Corners3 = XMVectorMultiplyAdd(LeftBottom, vNear, vOrigin); XMVECTOR Corners4 = XMVectorMultiplyAdd(RightTop, vFar, vOrigin); XMVECTOR Corners5 = XMVectorMultiplyAdd(RightBottom, vFar, vOrigin); XMVECTOR Corners6 = XMVectorMultiplyAdd(LeftTop, vFar, vOrigin); XMVECTOR Corners7 = XMVectorMultiplyAdd(LeftBottom, vFar, vOrigin); XMVECTOR Outside, Inside; DirectX::Internal::FastIntersectFrustumPlane(Corners0, Corners1, Corners2, Corners3, Corners4, Corners5, Corners6, Corners7, Plane, Outside, Inside); // If the frustum is outside any plane it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return FRONT; // If the frustum is inside all planes it is inside. if (XMVector4EqualInt(Inside, XMVectorTrueInt())) return BACK; // The frustum is not inside all planes or outside a plane it intersects. return INTERSECTING; } //----------------------------------------------------------------------------- // Ray vs. frustum test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV BoundingFrustum::Intersects(FXMVECTOR rayOrigin, FXMVECTOR Direction, float& Dist) const noexcept { // If ray starts inside the frustum, return a distance of 0 for the hit if (Contains(rayOrigin) == CONTAINS) { Dist = 0.0f; return true; } // Build the frustum planes. XMVECTOR Planes[6]; Planes[0] = XMVectorSet(0.0f, 0.0f, -1.0f, Near); Planes[1] = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); Planes[2] = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); Planes[3] = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); Planes[4] = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); Planes[5] = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); // Load origin and orientation of the frustum. XMVECTOR frOrigin = XMLoadFloat3(&Origin); XMVECTOR frOrientation = XMLoadFloat4(&Orientation); // This algorithm based on "Fast Ray-Convex Polyhedron Intersectin," in James Arvo, ed., Graphics Gems II pp. 247-250 float tnear = -FLT_MAX; float tfar = FLT_MAX; for (size_t i = 0; i < 6; ++i) { XMVECTOR Plane = DirectX::Internal::XMPlaneTransform(Planes[i], frOrientation, frOrigin); Plane = XMPlaneNormalize(Plane); XMVECTOR AxisDotOrigin = XMPlaneDotCoord(Plane, rayOrigin); XMVECTOR AxisDotDirection = XMVector3Dot(Plane, Direction); if (XMVector3LessOrEqual(XMVectorAbs(AxisDotDirection), g_RayEpsilon)) { // Ray is parallel to plane - check if ray origin is inside plane's if (XMVector3Greater(AxisDotOrigin, g_XMZero)) { // Ray origin is outside half-space. Dist = 0.f; return false; } } else { // Ray not parallel - get distance to plane. float vd = XMVectorGetX(AxisDotDirection); float vn = XMVectorGetX(AxisDotOrigin); float t = -vn / vd; if (vd < 0.0f) { // Front face - T is a near point. if (t > tfar) { Dist = 0.f; return false; } if (t > tnear) { // Hit near face. tnear = t; } } else { // back face - T is far point. if (t < tnear) { Dist = 0.f; return false; } if (t < tfar) { // Hit far face. tfar = t; } } } } // Survived all tests. // Note: if ray originates on polyhedron, may want to change 0.0f to some // epsilon to avoid intersecting the originating face. float distance = (tnear >= 0.0f) ? tnear : tfar; if (distance >= 0.0f) { Dist = distance; return true; } Dist = 0.f; return false; } //----------------------------------------------------------------------------- // Test a frustum vs 6 planes (typically forming another frustum). //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV BoundingFrustum::ContainedBy( FXMVECTOR Plane0, FXMVECTOR Plane1, FXMVECTOR Plane2, GXMVECTOR Plane3, HXMVECTOR Plane4, HXMVECTOR Plane5) const noexcept { // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); assert(DirectX::Internal::XMQuaternionIsUnit(vOrientation)); // Set w of the origin to one so we can dot4 with a plane. vOrigin = XMVectorInsert<0, 0, 0, 0, 1>(vOrigin, XMVectorSplatOne()); // Build the corners of the frustum (in world space). XMVECTOR RightTop = XMVectorSet(RightSlope, TopSlope, 1.0f, 0.0f); XMVECTOR RightBottom = XMVectorSet(RightSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR LeftTop = XMVectorSet(LeftSlope, TopSlope, 1.0f, 0.0f); XMVECTOR LeftBottom = XMVectorSet(LeftSlope, BottomSlope, 1.0f, 0.0f); XMVECTOR vNear = XMVectorReplicatePtr(&Near); XMVECTOR vFar = XMVectorReplicatePtr(&Far); RightTop = XMVector3Rotate(RightTop, vOrientation); RightBottom = XMVector3Rotate(RightBottom, vOrientation); LeftTop = XMVector3Rotate(LeftTop, vOrientation); LeftBottom = XMVector3Rotate(LeftBottom, vOrientation); XMVECTOR Corners0 = XMVectorMultiplyAdd(RightTop, vNear, vOrigin); XMVECTOR Corners1 = XMVectorMultiplyAdd(RightBottom, vNear, vOrigin); XMVECTOR Corners2 = XMVectorMultiplyAdd(LeftTop, vNear, vOrigin); XMVECTOR Corners3 = XMVectorMultiplyAdd(LeftBottom, vNear, vOrigin); XMVECTOR Corners4 = XMVectorMultiplyAdd(RightTop, vFar, vOrigin); XMVECTOR Corners5 = XMVectorMultiplyAdd(RightBottom, vFar, vOrigin); XMVECTOR Corners6 = XMVectorMultiplyAdd(LeftTop, vFar, vOrigin); XMVECTOR Corners7 = XMVectorMultiplyAdd(LeftBottom, vFar, vOrigin); XMVECTOR Outside, Inside; // Test against each plane. DirectX::Internal::FastIntersectFrustumPlane(Corners0, Corners1, Corners2, Corners3, Corners4, Corners5, Corners6, Corners7, Plane0, Outside, Inside); XMVECTOR AnyOutside = Outside; XMVECTOR AllInside = Inside; DirectX::Internal::FastIntersectFrustumPlane(Corners0, Corners1, Corners2, Corners3, Corners4, Corners5, Corners6, Corners7, Plane1, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectFrustumPlane(Corners0, Corners1, Corners2, Corners3, Corners4, Corners5, Corners6, Corners7, Plane2, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectFrustumPlane(Corners0, Corners1, Corners2, Corners3, Corners4, Corners5, Corners6, Corners7, Plane3, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectFrustumPlane(Corners0, Corners1, Corners2, Corners3, Corners4, Corners5, Corners6, Corners7, Plane4, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectFrustumPlane(Corners0, Corners1, Corners2, Corners3, Corners4, Corners5, Corners6, Corners7, Plane5, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); // If the frustum is outside any plane it is outside. if (XMVector4EqualInt(AnyOutside, XMVectorTrueInt())) return DISJOINT; // If the frustum is inside all planes it is inside. if (XMVector4EqualInt(AllInside, XMVectorTrueInt())) return CONTAINS; // The frustum is not inside all planes or outside a plane, it may intersect. return INTERSECTS; } //----------------------------------------------------------------------------- // Build the 6 frustum planes from a frustum. // // The intended use for these routines is for fast culling to a view frustum. // When the volume being tested against a view frustum is small relative to the // view frustum it is usually either inside all six planes of the frustum // (CONTAINS) or outside one of the planes of the frustum (DISJOINT). If neither // of these cases is true then it may or may not be intersecting the frustum // (INTERSECTS) //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void BoundingFrustum::GetPlanes(XMVECTOR* NearPlane, XMVECTOR* FarPlane, XMVECTOR* RightPlane, XMVECTOR* LeftPlane, XMVECTOR* TopPlane, XMVECTOR* BottomPlane) const noexcept { // Load origin and orientation of the frustum. XMVECTOR vOrigin = XMLoadFloat3(&Origin); XMVECTOR vOrientation = XMLoadFloat4(&Orientation); if (NearPlane) { XMVECTOR vNearPlane = XMVectorSet(0.0f, 0.0f, -1.0f, Near); vNearPlane = DirectX::Internal::XMPlaneTransform(vNearPlane, vOrientation, vOrigin); *NearPlane = XMPlaneNormalize(vNearPlane); } if (FarPlane) { XMVECTOR vFarPlane = XMVectorSet(0.0f, 0.0f, 1.0f, -Far); vFarPlane = DirectX::Internal::XMPlaneTransform(vFarPlane, vOrientation, vOrigin); *FarPlane = XMPlaneNormalize(vFarPlane); } if (RightPlane) { XMVECTOR vRightPlane = XMVectorSet(1.0f, 0.0f, -RightSlope, 0.0f); vRightPlane = DirectX::Internal::XMPlaneTransform(vRightPlane, vOrientation, vOrigin); *RightPlane = XMPlaneNormalize(vRightPlane); } if (LeftPlane) { XMVECTOR vLeftPlane = XMVectorSet(-1.0f, 0.0f, LeftSlope, 0.0f); vLeftPlane = DirectX::Internal::XMPlaneTransform(vLeftPlane, vOrientation, vOrigin); *LeftPlane = XMPlaneNormalize(vLeftPlane); } if (TopPlane) { XMVECTOR vTopPlane = XMVectorSet(0.0f, 1.0f, -TopSlope, 0.0f); vTopPlane = DirectX::Internal::XMPlaneTransform(vTopPlane, vOrientation, vOrigin); *TopPlane = XMPlaneNormalize(vTopPlane); } if (BottomPlane) { XMVECTOR vBottomPlane = XMVectorSet(0.0f, -1.0f, BottomSlope, 0.0f); vBottomPlane = DirectX::Internal::XMPlaneTransform(vBottomPlane, vOrientation, vOrigin); *BottomPlane = XMPlaneNormalize(vBottomPlane); } } //----------------------------------------------------------------------------- // Build a frustum from a persepective projection matrix. The matrix may only // contain a projection; any rotation, translation or scale will cause the // constructed frustum to be incorrect. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline void XM_CALLCONV BoundingFrustum::CreateFromMatrix(BoundingFrustum& Out, FXMMATRIX Projection, bool rhcoords) noexcept { // Corners of the projection frustum in homogenous space. static XMVECTORF32 HomogenousPoints[6] = { { { { 1.0f, 0.0f, 1.0f, 1.0f } } }, // right (at far plane) { { { -1.0f, 0.0f, 1.0f, 1.0f } } }, // left { { { 0.0f, 1.0f, 1.0f, 1.0f } } }, // top { { { 0.0f, -1.0f, 1.0f, 1.0f } } }, // bottom { { { 0.0f, 0.0f, 0.0f, 1.0f } } }, // near { { { 0.0f, 0.0f, 1.0f, 1.0f } } } // far }; XMVECTOR Determinant; XMMATRIX matInverse = XMMatrixInverse(&Determinant, Projection); // Compute the frustum corners in world space. XMVECTOR Points[6]; for (size_t i = 0; i < 6; ++i) { // Transform point. Points[i] = XMVector4Transform(HomogenousPoints[i], matInverse); } Out.Origin = XMFLOAT3(0.0f, 0.0f, 0.0f); Out.Orientation = XMFLOAT4(0.0f, 0.0f, 0.0f, 1.0f); // Compute the slopes. Points[0] = XMVectorMultiply(Points[0], XMVectorReciprocal(XMVectorSplatZ(Points[0]))); Points[1] = XMVectorMultiply(Points[1], XMVectorReciprocal(XMVectorSplatZ(Points[1]))); Points[2] = XMVectorMultiply(Points[2], XMVectorReciprocal(XMVectorSplatZ(Points[2]))); Points[3] = XMVectorMultiply(Points[3], XMVectorReciprocal(XMVectorSplatZ(Points[3]))); Out.RightSlope = XMVectorGetX(Points[0]); Out.LeftSlope = XMVectorGetX(Points[1]); Out.TopSlope = XMVectorGetY(Points[2]); Out.BottomSlope = XMVectorGetY(Points[3]); // Compute near and far. Points[4] = XMVectorMultiply(Points[4], XMVectorReciprocal(XMVectorSplatW(Points[4]))); Points[5] = XMVectorMultiply(Points[5], XMVectorReciprocal(XMVectorSplatW(Points[5]))); if (rhcoords) { Out.Near = XMVectorGetZ(Points[5]); Out.Far = XMVectorGetZ(Points[4]); } else { Out.Near = XMVectorGetZ(Points[4]); Out.Far = XMVectorGetZ(Points[5]); } } /**************************************************************************** * * TriangleTests * ****************************************************************************/ namespace TriangleTests { //----------------------------------------------------------------------------- // Compute the intersection of a ray (Origin, Direction) with a triangle // (V0, V1, V2). Return true if there is an intersection and also set *pDist // to the distance along the ray to the intersection. // // The algorithm is based on Moller, Tomas and Trumbore, "Fast, Minimum Storage // Ray-Triangle Intersection", Journal of Graphics Tools, vol. 2, no. 1, // pp 21-28, 1997. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV Intersects( FXMVECTOR Origin, FXMVECTOR Direction, FXMVECTOR V0, GXMVECTOR V1, HXMVECTOR V2, float& Dist) noexcept { assert(DirectX::Internal::XMVector3IsUnit(Direction)); XMVECTOR Zero = XMVectorZero(); XMVECTOR e1 = XMVectorSubtract(V1, V0); XMVECTOR e2 = XMVectorSubtract(V2, V0); // p = Direction ^ e2; XMVECTOR p = XMVector3Cross(Direction, e2); // det = e1 * p; XMVECTOR det = XMVector3Dot(e1, p); XMVECTOR u, v, t; if (XMVector3GreaterOrEqual(det, g_RayEpsilon)) { // Determinate is positive (front side of the triangle). XMVECTOR s = XMVectorSubtract(Origin, V0); // u = s * p; u = XMVector3Dot(s, p); XMVECTOR NoIntersection = XMVectorLess(u, Zero); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(u, det)); // q = s ^ e1; XMVECTOR q = XMVector3Cross(s, e1); // v = Direction * q; v = XMVector3Dot(Direction, q); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(v, Zero)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(XMVectorAdd(u, v), det)); // t = e2 * q; t = XMVector3Dot(e2, q); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(t, Zero)); if (XMVector4EqualInt(NoIntersection, XMVectorTrueInt())) { Dist = 0.f; return false; } } else if (XMVector3LessOrEqual(det, g_RayNegEpsilon)) { // Determinate is negative (back side of the triangle). XMVECTOR s = XMVectorSubtract(Origin, V0); // u = s * p; u = XMVector3Dot(s, p); XMVECTOR NoIntersection = XMVectorGreater(u, Zero); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(u, det)); // q = s ^ e1; XMVECTOR q = XMVector3Cross(s, e1); // v = Direction * q; v = XMVector3Dot(Direction, q); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(v, Zero)); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorLess(XMVectorAdd(u, v), det)); // t = e2 * q; t = XMVector3Dot(e2, q); NoIntersection = XMVectorOrInt(NoIntersection, XMVectorGreater(t, Zero)); if (XMVector4EqualInt(NoIntersection, XMVectorTrueInt())) { Dist = 0.f; return false; } } else { // Parallel ray. Dist = 0.f; return false; } t = XMVectorDivide(t, det); // (u / det) and (v / dev) are the barycentric cooridinates of the intersection. // Store the x-component to *pDist XMStoreFloat(&Dist, t); return true; } //----------------------------------------------------------------------------- // Test if two triangles intersect. // // The final test of algorithm is based on Shen, Heng, and Tang, "A Fast // Triangle-Triangle Overlap Test Using Signed Distances", Journal of Graphics // Tools, vol. 8, no. 1, pp 17-23, 2003 and Guigue and Devillers, "Fast and // Robust Triangle-Triangle Overlap Test Using Orientation Predicates", Journal // of Graphics Tools, vol. 8, no. 1, pp 25-32, 2003. // // The final test could be considered an edge-edge separating plane test with // the 9 possible cases narrowed down to the only two pairs of edges that can // actaully result in a seperation. //----------------------------------------------------------------------------- _Use_decl_annotations_ inline bool XM_CALLCONV Intersects(FXMVECTOR A0, FXMVECTOR A1, FXMVECTOR A2, GXMVECTOR B0, HXMVECTOR B1, HXMVECTOR B2) noexcept { static const XMVECTORU32 SelectY = { { { XM_SELECT_0, XM_SELECT_1, XM_SELECT_0, XM_SELECT_0 } } }; static const XMVECTORU32 SelectZ = { { { XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0 } } }; static const XMVECTORU32 Select0111 = { { { XM_SELECT_0, XM_SELECT_1, XM_SELECT_1, XM_SELECT_1 } } }; static const XMVECTORU32 Select1011 = { { { XM_SELECT_1, XM_SELECT_0, XM_SELECT_1, XM_SELECT_1 } } }; static const XMVECTORU32 Select1101 = { { { XM_SELECT_1, XM_SELECT_1, XM_SELECT_0, XM_SELECT_1 } } }; XMVECTOR Zero = XMVectorZero(); // Compute the normal of triangle A. XMVECTOR N1 = XMVector3Cross(XMVectorSubtract(A1, A0), XMVectorSubtract(A2, A0)); // Assert that the triangle is not degenerate. assert(!XMVector3Equal(N1, Zero)); // Test points of B against the plane of A. XMVECTOR BDist = XMVector3Dot(N1, XMVectorSubtract(B0, A0)); BDist = XMVectorSelect(BDist, XMVector3Dot(N1, XMVectorSubtract(B1, A0)), SelectY); BDist = XMVectorSelect(BDist, XMVector3Dot(N1, XMVectorSubtract(B2, A0)), SelectZ); // Ensure robustness with co-planar triangles by zeroing small distances. uint32_t BDistIsZeroCR; XMVECTOR BDistIsZero = XMVectorGreaterR(&BDistIsZeroCR, g_RayEpsilon, XMVectorAbs(BDist)); BDist = XMVectorSelect(BDist, Zero, BDistIsZero); uint32_t BDistIsLessCR; XMVECTOR BDistIsLess = XMVectorGreaterR(&BDistIsLessCR, Zero, BDist); uint32_t BDistIsGreaterCR; XMVECTOR BDistIsGreater = XMVectorGreaterR(&BDistIsGreaterCR, BDist, Zero); // If all the points are on the same side we don't intersect. if (XMComparisonAllTrue(BDistIsLessCR) || XMComparisonAllTrue(BDistIsGreaterCR)) return false; // Compute the normal of triangle B. XMVECTOR N2 = XMVector3Cross(XMVectorSubtract(B1, B0), XMVectorSubtract(B2, B0)); // Assert that the triangle is not degenerate. assert(!XMVector3Equal(N2, Zero)); // Test points of A against the plane of B. XMVECTOR ADist = XMVector3Dot(N2, XMVectorSubtract(A0, B0)); ADist = XMVectorSelect(ADist, XMVector3Dot(N2, XMVectorSubtract(A1, B0)), SelectY); ADist = XMVectorSelect(ADist, XMVector3Dot(N2, XMVectorSubtract(A2, B0)), SelectZ); // Ensure robustness with co-planar triangles by zeroing small distances. uint32_t ADistIsZeroCR; XMVECTOR ADistIsZero = XMVectorGreaterR(&ADistIsZeroCR, g_RayEpsilon, XMVectorAbs(BDist)); ADist = XMVectorSelect(ADist, Zero, ADistIsZero); uint32_t ADistIsLessCR; XMVECTOR ADistIsLess = XMVectorGreaterR(&ADistIsLessCR, Zero, ADist); uint32_t ADistIsGreaterCR; XMVECTOR ADistIsGreater = XMVectorGreaterR(&ADistIsGreaterCR, ADist, Zero); // If all the points are on the same side we don't intersect. if (XMComparisonAllTrue(ADistIsLessCR) || XMComparisonAllTrue(ADistIsGreaterCR)) return false; // Special case for co-planar triangles. if (XMComparisonAllTrue(ADistIsZeroCR) || XMComparisonAllTrue(BDistIsZeroCR)) { XMVECTOR Axis, Dist, MinDist; // Compute an axis perpindicular to the edge (points out). Axis = XMVector3Cross(N1, XMVectorSubtract(A1, A0)); Dist = XMVector3Dot(Axis, A0); // Test points of B against the axis. MinDist = XMVector3Dot(B0, Axis); MinDist = XMVectorMin(MinDist, XMVector3Dot(B1, Axis)); MinDist = XMVectorMin(MinDist, XMVector3Dot(B2, Axis)); if (XMVector4GreaterOrEqual(MinDist, Dist)) return false; // Edge (A1, A2) Axis = XMVector3Cross(N1, XMVectorSubtract(A2, A1)); Dist = XMVector3Dot(Axis, A1); MinDist = XMVector3Dot(B0, Axis); MinDist = XMVectorMin(MinDist, XMVector3Dot(B1, Axis)); MinDist = XMVectorMin(MinDist, XMVector3Dot(B2, Axis)); if (XMVector4GreaterOrEqual(MinDist, Dist)) return false; // Edge (A2, A0) Axis = XMVector3Cross(N1, XMVectorSubtract(A0, A2)); Dist = XMVector3Dot(Axis, A2); MinDist = XMVector3Dot(B0, Axis); MinDist = XMVectorMin(MinDist, XMVector3Dot(B1, Axis)); MinDist = XMVectorMin(MinDist, XMVector3Dot(B2, Axis)); if (XMVector4GreaterOrEqual(MinDist, Dist)) return false; // Edge (B0, B1) Axis = XMVector3Cross(N2, XMVectorSubtract(B1, B0)); Dist = XMVector3Dot(Axis, B0); MinDist = XMVector3Dot(A0, Axis); MinDist = XMVectorMin(MinDist, XMVector3Dot(A1, Axis)); MinDist = XMVectorMin(MinDist, XMVector3Dot(A2, Axis)); if (XMVector4GreaterOrEqual(MinDist, Dist)) return false; // Edge (B1, B2) Axis = XMVector3Cross(N2, XMVectorSubtract(B2, B1)); Dist = XMVector3Dot(Axis, B1); MinDist = XMVector3Dot(A0, Axis); MinDist = XMVectorMin(MinDist, XMVector3Dot(A1, Axis)); MinDist = XMVectorMin(MinDist, XMVector3Dot(A2, Axis)); if (XMVector4GreaterOrEqual(MinDist, Dist)) return false; // Edge (B2,B0) Axis = XMVector3Cross(N2, XMVectorSubtract(B0, B2)); Dist = XMVector3Dot(Axis, B2); MinDist = XMVector3Dot(A0, Axis); MinDist = XMVectorMin(MinDist, XMVector3Dot(A1, Axis)); MinDist = XMVectorMin(MinDist, XMVector3Dot(A2, Axis)); if (XMVector4GreaterOrEqual(MinDist, Dist)) return false; return true; } // // Find the single vertex of A and B (ie the vertex on the opposite side // of the plane from the other two) and reorder the edges so we can compute // the signed edge/edge distances. // // if ( (V0 >= 0 && V1 < 0 && V2 < 0) || // (V0 > 0 && V1 <= 0 && V2 <= 0) || // (V0 <= 0 && V1 > 0 && V2 > 0) || // (V0 < 0 && V1 >= 0 && V2 >= 0) ) then V0 is singular; // // If our singular vertex is not on the positive side of the plane we reverse // the triangle winding so that the overlap comparisons will compare the // correct edges with the correct signs. // XMVECTOR ADistIsLessEqual = XMVectorOrInt(ADistIsLess, ADistIsZero); XMVECTOR ADistIsGreaterEqual = XMVectorOrInt(ADistIsGreater, ADistIsZero); XMVECTOR AA0, AA1, AA2; bool bPositiveA; if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsGreaterEqual, ADistIsLess, Select0111)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsGreater, ADistIsLessEqual, Select0111))) { // A0 is singular, crossing from positive to negative. AA0 = A0; AA1 = A1; AA2 = A2; bPositiveA = true; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsLessEqual, ADistIsGreater, Select0111)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsLess, ADistIsGreaterEqual, Select0111))) { // A0 is singular, crossing from negative to positive. AA0 = A0; AA1 = A2; AA2 = A1; bPositiveA = false; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsGreaterEqual, ADistIsLess, Select1011)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsGreater, ADistIsLessEqual, Select1011))) { // A1 is singular, crossing from positive to negative. AA0 = A1; AA1 = A2; AA2 = A0; bPositiveA = true; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsLessEqual, ADistIsGreater, Select1011)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsLess, ADistIsGreaterEqual, Select1011))) { // A1 is singular, crossing from negative to positive. AA0 = A1; AA1 = A0; AA2 = A2; bPositiveA = false; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsGreaterEqual, ADistIsLess, Select1101)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsGreater, ADistIsLessEqual, Select1101))) { // A2 is singular, crossing from positive to negative. AA0 = A2; AA1 = A0; AA2 = A1; bPositiveA = true; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsLessEqual, ADistIsGreater, Select1101)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(ADistIsLess, ADistIsGreaterEqual, Select1101))) { // A2 is singular, crossing from negative to positive. AA0 = A2; AA1 = A1; AA2 = A0; bPositiveA = false; } else { assert(false); return false; } XMVECTOR BDistIsLessEqual = XMVectorOrInt(BDistIsLess, BDistIsZero); XMVECTOR BDistIsGreaterEqual = XMVectorOrInt(BDistIsGreater, BDistIsZero); XMVECTOR BB0, BB1, BB2; bool bPositiveB; if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsGreaterEqual, BDistIsLess, Select0111)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsGreater, BDistIsLessEqual, Select0111))) { // B0 is singular, crossing from positive to negative. BB0 = B0; BB1 = B1; BB2 = B2; bPositiveB = true; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsLessEqual, BDistIsGreater, Select0111)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsLess, BDistIsGreaterEqual, Select0111))) { // B0 is singular, crossing from negative to positive. BB0 = B0; BB1 = B2; BB2 = B1; bPositiveB = false; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsGreaterEqual, BDistIsLess, Select1011)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsGreater, BDistIsLessEqual, Select1011))) { // B1 is singular, crossing from positive to negative. BB0 = B1; BB1 = B2; BB2 = B0; bPositiveB = true; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsLessEqual, BDistIsGreater, Select1011)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsLess, BDistIsGreaterEqual, Select1011))) { // B1 is singular, crossing from negative to positive. BB0 = B1; BB1 = B0; BB2 = B2; bPositiveB = false; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsGreaterEqual, BDistIsLess, Select1101)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsGreater, BDistIsLessEqual, Select1101))) { // B2 is singular, crossing from positive to negative. BB0 = B2; BB1 = B0; BB2 = B1; bPositiveB = true; } else if (DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsLessEqual, BDistIsGreater, Select1101)) || DirectX::Internal::XMVector3AllTrue(XMVectorSelect(BDistIsLess, BDistIsGreaterEqual, Select1101))) { // B2 is singular, crossing from negative to positive. BB0 = B2; BB1 = B1; BB2 = B0; bPositiveB = false; } else { assert(false); return false; } XMVECTOR Delta0, Delta1; // Reverse the direction of the test depending on whether the singular vertices are // the same sign or different signs. if (bPositiveA ^ bPositiveB) { Delta0 = XMVectorSubtract(BB0, AA0); Delta1 = XMVectorSubtract(AA0, BB0); } else { Delta0 = XMVectorSubtract(AA0, BB0); Delta1 = XMVectorSubtract(BB0, AA0); } // Check if the triangles overlap on the line of intersection between the // planes of the two triangles by finding the signed line distances. XMVECTOR Dist0 = XMVector3Dot(Delta0, XMVector3Cross(XMVectorSubtract(BB2, BB0), XMVectorSubtract(AA2, AA0))); if (XMVector4Greater(Dist0, Zero)) return false; XMVECTOR Dist1 = XMVector3Dot(Delta1, XMVector3Cross(XMVectorSubtract(BB1, BB0), XMVectorSubtract(AA1, AA0))); if (XMVector4Greater(Dist1, Zero)) return false; return true; } //----------------------------------------------------------------------------- // Ray-triangle test //----------------------------------------------------------------------------- _Use_decl_annotations_ inline PlaneIntersectionType XM_CALLCONV Intersects(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2, GXMVECTOR Plane) noexcept { XMVECTOR One = XMVectorSplatOne(); assert(DirectX::Internal::XMPlaneIsUnit(Plane)); // Set w of the points to one so we can dot4 with a plane. XMVECTOR TV0 = XMVectorInsert<0, 0, 0, 0, 1>(V0, One); XMVECTOR TV1 = XMVectorInsert<0, 0, 0, 0, 1>(V1, One); XMVECTOR TV2 = XMVectorInsert<0, 0, 0, 0, 1>(V2, One); XMVECTOR Outside, Inside; DirectX::Internal::FastIntersectTrianglePlane(TV0, TV1, TV2, Plane, Outside, Inside); // If the triangle is outside any plane it is outside. if (XMVector4EqualInt(Outside, XMVectorTrueInt())) return FRONT; // If the triangle is inside all planes it is inside. if (XMVector4EqualInt(Inside, XMVectorTrueInt())) return BACK; // The triangle is not inside all planes or outside a plane it intersects. return INTERSECTING; } //----------------------------------------------------------------------------- // Test a triangle vs 6 planes (typically forming a frustum). //----------------------------------------------------------------------------- _Use_decl_annotations_ inline ContainmentType XM_CALLCONV ContainedBy( FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR V2, GXMVECTOR Plane0, HXMVECTOR Plane1, HXMVECTOR Plane2, CXMVECTOR Plane3, CXMVECTOR Plane4, CXMVECTOR Plane5) noexcept { XMVECTOR One = XMVectorSplatOne(); // Set w of the points to one so we can dot4 with a plane. XMVECTOR TV0 = XMVectorInsert<0, 0, 0, 0, 1>(V0, One); XMVECTOR TV1 = XMVectorInsert<0, 0, 0, 0, 1>(V1, One); XMVECTOR TV2 = XMVectorInsert<0, 0, 0, 0, 1>(V2, One); XMVECTOR Outside, Inside; // Test against each plane. DirectX::Internal::FastIntersectTrianglePlane(TV0, TV1, TV2, Plane0, Outside, Inside); XMVECTOR AnyOutside = Outside; XMVECTOR AllInside = Inside; DirectX::Internal::FastIntersectTrianglePlane(TV0, TV1, TV2, Plane1, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectTrianglePlane(TV0, TV1, TV2, Plane2, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectTrianglePlane(TV0, TV1, TV2, Plane3, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectTrianglePlane(TV0, TV1, TV2, Plane4, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); DirectX::Internal::FastIntersectTrianglePlane(TV0, TV1, TV2, Plane5, Outside, Inside); AnyOutside = XMVectorOrInt(AnyOutside, Outside); AllInside = XMVectorAndInt(AllInside, Inside); // If the triangle is outside any plane it is outside. if (XMVector4EqualInt(AnyOutside, XMVectorTrueInt())) return DISJOINT; // If the triangle is inside all planes it is inside. if (XMVector4EqualInt(AllInside, XMVectorTrueInt())) return CONTAINS; // The triangle is not inside all planes or outside a plane, it may intersect. return INTERSECTS; } } // namespace TriangleTests