mirror of
https://github.com/ncblakely/GiantsTools
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197 lines
8.0 KiB
C++
197 lines
8.0 KiB
C++
//--------------------------------------------------------------------------------------
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// File: Bezier.h
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//
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// Copyright (c) Microsoft Corporation. All rights reserved.
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// Licensed under the MIT License.
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//
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// http://go.microsoft.com/fwlink/?LinkId=248929
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// http://go.microsoft.com/fwlink/?LinkID=615561
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//--------------------------------------------------------------------------------------
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#pragma once
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#include <array>
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#include <algorithm>
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#include <DirectXMath.h>
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namespace Bezier
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{
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// Performs a cubic bezier interpolation between four control points,
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// returning the value at the specified time (t ranges 0 to 1).
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template<typename T>
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inline T CubicInterpolate(T const& p1, T const& p2, T const& p3, T const& p4, float t) noexcept
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{
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return p1 * (1 - t) * (1 - t) * (1 - t) +
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p2 * 3 * t * (1 - t) * (1 - t) +
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p3 * 3 * t * t * (1 - t) +
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p4 * t * t * t;
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}
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template<>
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inline DirectX::XMVECTOR CubicInterpolate(DirectX::XMVECTOR const& p1, DirectX::XMVECTOR const& p2, DirectX::XMVECTOR const& p3, DirectX::XMVECTOR const& p4, float t) noexcept
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{
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using namespace DirectX;
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XMVECTOR T0 = XMVectorReplicate((1 - t) * (1 - t) * (1 - t));
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XMVECTOR T1 = XMVectorReplicate(3 * t * (1 - t) * (1 - t));
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XMVECTOR T2 = XMVectorReplicate(3 * t * t * (1 - t));
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XMVECTOR T3 = XMVectorReplicate(t * t * t);
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XMVECTOR Result = XMVectorMultiply(p1, T0);
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Result = XMVectorMultiplyAdd(p2, T1, Result);
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Result = XMVectorMultiplyAdd(p3, T2, Result);
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Result = XMVectorMultiplyAdd(p4, T3, Result);
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return Result;
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}
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// Computes the tangent of a cubic bezier curve at the specified time.
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template<typename T>
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inline T CubicTangent(T const& p1, T const& p2, T const& p3, T const& p4, float t) noexcept
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{
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using DirectX::operator*;
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using DirectX::operator+;
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return p1 * (-1 + 2 * t - t * t) +
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p2 * (1 - 4 * t + 3 * t * t) +
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p3 * (2 * t - 3 * t * t) +
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p4 * (t * t);
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}
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template<>
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inline DirectX::XMVECTOR CubicTangent(DirectX::XMVECTOR const& p1, DirectX::XMVECTOR const& p2, DirectX::XMVECTOR const& p3, DirectX::XMVECTOR const& p4, float t) noexcept
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{
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using namespace DirectX;
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XMVECTOR T0 = XMVectorReplicate(-1 + 2 * t - t * t);
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XMVECTOR T1 = XMVectorReplicate(1 - 4 * t + 3 * t * t);
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XMVECTOR T2 = XMVectorReplicate(2 * t - 3 * t * t);
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XMVECTOR T3 = XMVectorReplicate(t * t);
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XMVECTOR Result = XMVectorMultiply(p1, T0);
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Result = XMVectorMultiplyAdd(p2, T1, Result);
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Result = XMVectorMultiplyAdd(p3, T2, Result);
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Result = XMVectorMultiplyAdd(p4, T3, Result);
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return Result;
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}
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// Creates vertices for a patch that is tessellated at the specified level.
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// Calls the specified outputVertex function for each generated vertex,
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// passing the position, normal, and texture coordinate as parameters.
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template<typename TOutputFunc>
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void CreatePatchVertices(_In_reads_(16) DirectX::XMVECTOR patch[16], size_t tessellation, bool isMirrored, TOutputFunc outputVertex)
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{
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using namespace DirectX;
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for (size_t i = 0; i <= tessellation; i++)
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{
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float u = float(i) / float(tessellation);
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for (size_t j = 0; j <= tessellation; j++)
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{
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float v = float(j) / float(tessellation);
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// Perform four horizontal bezier interpolations
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// between the control points of this patch.
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XMVECTOR p1 = CubicInterpolate(patch[0], patch[1], patch[2], patch[3], u);
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XMVECTOR p2 = CubicInterpolate(patch[4], patch[5], patch[6], patch[7], u);
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XMVECTOR p3 = CubicInterpolate(patch[8], patch[9], patch[10], patch[11], u);
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XMVECTOR p4 = CubicInterpolate(patch[12], patch[13], patch[14], patch[15], u);
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// Perform a vertical interpolation between the results of the
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// previous horizontal interpolations, to compute the position.
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XMVECTOR position = CubicInterpolate(p1, p2, p3, p4, v);
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// Perform another four bezier interpolations between the control
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// points, but this time vertically rather than horizontally.
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XMVECTOR q1 = CubicInterpolate(patch[0], patch[4], patch[8], patch[12], v);
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XMVECTOR q2 = CubicInterpolate(patch[1], patch[5], patch[9], patch[13], v);
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XMVECTOR q3 = CubicInterpolate(patch[2], patch[6], patch[10], patch[14], v);
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XMVECTOR q4 = CubicInterpolate(patch[3], patch[7], patch[11], patch[15], v);
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// Compute vertical and horizontal tangent vectors.
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XMVECTOR tangent1 = CubicTangent(p1, p2, p3, p4, v);
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XMVECTOR tangent2 = CubicTangent(q1, q2, q3, q4, u);
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// Cross the two tangent vectors to compute the normal.
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XMVECTOR normal = XMVector3Cross(tangent1, tangent2);
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if (!XMVector3NearEqual(normal, XMVectorZero(), g_XMEpsilon))
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{
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normal = XMVector3Normalize(normal);
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// If this patch is mirrored, we must invert the normal.
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if (isMirrored)
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{
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normal = XMVectorNegate(normal);
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}
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}
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else
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{
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// In a tidy and well constructed bezier patch, the preceding
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// normal computation will always work. But the classic teapot
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// model is not tidy or well constructed! At the top and bottom
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// of the teapot, it contains degenerate geometry where a patch
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// has several control points in the same place, which causes
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// the tangent computation to fail and produce a zero normal.
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// We 'fix' these cases by just hard-coding a normal that points
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// either straight up or straight down, depending on whether we
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// are on the top or bottom of the teapot. This is not a robust
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// solution for all possible degenerate bezier patches, but hey,
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// it's good enough to make the teapot work correctly!
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normal = XMVectorSelect(g_XMIdentityR1, g_XMNegIdentityR1, XMVectorLess(position, XMVectorZero()));
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}
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// Compute the texture coordinate.
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float mirroredU = isMirrored ? 1 - u : u;
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XMVECTOR textureCoordinate = XMVectorSet(mirroredU, v, 0, 0);
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// Output this vertex.
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outputVertex(position, normal, textureCoordinate);
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}
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}
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}
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// Creates indices for a patch that is tessellated at the specified level.
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// Calls the specified outputIndex function for each generated index value.
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template<typename TOutputFunc>
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void CreatePatchIndices(size_t tessellation, bool isMirrored, TOutputFunc outputIndex)
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{
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size_t stride = tessellation + 1;
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for (size_t i = 0; i < tessellation; i++)
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{
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for (size_t j = 0; j < tessellation; j++)
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{
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// Make a list of six index values (two triangles).
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std::array<size_t, 6> indices =
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{
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i * stride + j,
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(i + 1) * stride + j,
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(i + 1) * stride + j + 1,
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i * stride + j,
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(i + 1) * stride + j + 1,
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i * stride + j + 1,
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};
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// If this patch is mirrored, reverse indices to fix the winding order.
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if (isMirrored)
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{
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std::reverse(indices.begin(), indices.end());
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}
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// Output these index values.
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std::for_each(indices.begin(), indices.end(), outputIndex);
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}
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}
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}
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}
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