170 lines
7.0 KiB
C
170 lines
7.0 KiB
C
|
//--------------------------------------------------------------------------------------
|
||
|
|
// File: Bezier.h
|
||
|
|
//
|
||
|
|
// THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF
|
||
|
|
// ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO
|
||
|
|
// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
|
||
|
|
// PARTICULAR PURPOSE.
|
||
|
|
//
|
||
|
|
// Copyright (c) Microsoft Corporation. All rights reserved.
|
||
|
|
//
|
||
|
|
// http://go.microsoft.com/fwlink/?LinkId=248929
|
||
|
|
//--------------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
#pragma once
|
||
|
|
|
||
|
|
#include <array>
|
||
|
|
#include <algorithm>
|
||
|
|
#include <DirectXMath.h>
|
||
|
|
|
||
|
|
|
||
|
|
namespace Bezier
|
||
|
|
{
|
||
|
|
// Performs a cubic bezier interpolation between four control points,
|
||
|
|
// returning the value at the specified time (t ranges 0 to 1).
|
||
|
|
// This template implementation can be used to interpolate XMVECTOR,
|
||
|
|
// float, or any other types that define suitable * and + operators.
|
||
|
|
template<typename T>
|
||
|
|
T CubicInterpolate(T const& p1, T const& p2, T const& p3, T const& p4, float t)
|
||
|
|
{
|
||
|
|
using DirectX::operator*;
|
||
|
|
using DirectX::operator+;
|
||
|
|
|
||
|
|
return p1 * (1 - t) * (1 - t) * (1 - t) +
|
||
|
|
p2 * 3 * t * (1 - t) * (1 - t) +
|
||
|
|
p3 * 3 * t * t * (1 - t) +
|
||
|
|
p4 * t * t * t;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Computes the tangent of a cubic bezier curve at the specified time.
|
||
|
|
// Template supports XMVECTOR, float, or any other types with * and + operators.
|
||
|
|
template<typename T>
|
||
|
|
T CubicTangent(T const& p1, T const& p2, T const& p3, T const& p4, float t)
|
||
|
|
{
|
||
|
|
using DirectX::operator*;
|
||
|
|
using DirectX::operator+;
|
||
|
|
|
||
|
|
return p1 * (-1 + 2 * t - t * t) +
|
||
|
|
p2 * (1 - 4 * t + 3 * t * t) +
|
||
|
|
p3 * (2 * t - 3 * t * t) +
|
||
|
|
p4 * (t * t);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Creates vertices for a patch that is tessellated at the specified level.
|
||
|
|
// Calls the specified outputVertex function for each generated vertex,
|
||
|
|
// passing the position, normal, and texture coordinate as parameters.
|
||
|
|
template<typename TOutputFunc>
|
||
|
|
void CreatePatchVertices(_In_reads_(16) DirectX::XMVECTOR patch[16], size_t tessellation, bool isMirrored, TOutputFunc outputVertex)
|
||
|
|
{
|
||
|
|
using namespace DirectX;
|
||
|
|
|
||
|
|
for (size_t i = 0; i <= tessellation; i++)
|
||
|
|
{
|
||
|
|
float u = (float)i / tessellation;
|
||
|
|
|
||
|
|
for (size_t j = 0; j <= tessellation; j++)
|
||
|
|
{
|
||
|
|
float v = (float)j / tessellation;
|
||
|
|
|
||
|
|
// Perform four horizontal bezier interpolations
|
||
|
|
// between the control points of this patch.
|
||
|
|
XMVECTOR p1 = CubicInterpolate(patch[0], patch[1], patch[2], patch[3], u);
|
||
|
|
XMVECTOR p2 = CubicInterpolate(patch[4], patch[5], patch[6], patch[7], u);
|
||
|
|
XMVECTOR p3 = CubicInterpolate(patch[8], patch[9], patch[10], patch[11], u);
|
||
|
|
XMVECTOR p4 = CubicInterpolate(patch[12], patch[13], patch[14], patch[15], u);
|
||
|
|
|
||
|
|
// Perform a vertical interpolation between the results of the
|
||
|
|
// previous horizontal interpolations, to compute the position.
|
||
|
|
XMVECTOR position = CubicInterpolate(p1, p2, p3, p4, v);
|
||
|
|
|
||
|
|
// Perform another four bezier interpolations between the control
|
||
|
|
// points, but this time vertically rather than horizontally.
|
||
|
|
XMVECTOR q1 = CubicInterpolate(patch[0], patch[4], patch[8], patch[12], v);
|
||
|
|
XMVECTOR q2 = CubicInterpolate(patch[1], patch[5], patch[9], patch[13], v);
|
||
|
|
XMVECTOR q3 = CubicInterpolate(patch[2], patch[6], patch[10], patch[14], v);
|
||
|
|
XMVECTOR q4 = CubicInterpolate(patch[3], patch[7], patch[11], patch[15], v);
|
||
|
|
|
||
|
|
// Compute vertical and horizontal tangent vectors.
|
||
|
|
XMVECTOR tangent1 = CubicTangent(p1, p2, p3, p4, v);
|
||
|
|
XMVECTOR tangent2 = CubicTangent(q1, q2, q3, q4, u);
|
||
|
|
|
||
|
|
// Cross the two tangent vectors to compute the normal.
|
||
|
|
XMVECTOR normal = XMVector3Cross(tangent1, tangent2);
|
||
|
|
|
||
|
|
if (!XMVector3NearEqual(normal, XMVectorZero(), g_XMEpsilon))
|
||
|
|
{
|
||
|
|
normal = XMVector3Normalize(normal);
|
||
|
|
|
||
|
|
// If this patch is mirrored, we must invert the normal.
|
||
|
|
if (isMirrored)
|
||
|
|
{
|
||
|
|
normal = -normal;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// In a tidy and well constructed bezier patch, the preceding
|
||
|
|
// normal computation will always work. But the classic teapot
|
||
|
|
// model is not tidy or well constructed! At the top and bottom
|
||
|
|
// of the teapot, it contains degenerate geometry where a patch
|
||
|
|
// has several control points in the same place, which causes
|
||
|
|
// the tangent computation to fail and produce a zero normal.
|
||
|
|
// We 'fix' these cases by just hard-coding a normal that points
|
||
|
|
// either straight up or straight down, depending on whether we
|
||
|
|
// are on the top or bottom of the teapot. This is not a robust
|
||
|
|
// solution for all possible degenerate bezier patches, but hey,
|
||
|
|
// it's good enough to make the teapot work correctly!
|
||
|
|
|
||
|
|
normal = XMVectorSelect(g_XMIdentityR1, g_XMNegIdentityR1, XMVectorLess(position, XMVectorZero()));
|
||
|
|
}
|
||
|
|
|
||
|
|
// Compute the texture coordinate.
|
||
|
|
float mirroredU = isMirrored ? 1 - u : u;
|
||
|
|
|
||
|
|
XMVECTOR textureCoordinate = XMVectorSet(mirroredU, v, 0, 0);
|
||
|
|
|
||
|
|
// Output this vertex.
|
||
|
|
outputVertex(position, normal, textureCoordinate);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// Creates indices for a patch that is tessellated at the specified level.
|
||
|
|
// Calls the specified outputIndex function for each generated index value.
|
||
|
|
template<typename TOutputFunc>
|
||
|
|
void CreatePatchIndices(size_t tessellation, bool isMirrored, TOutputFunc outputIndex)
|
||
|
|
{
|
||
|
|
size_t stride = tessellation + 1;
|
||
|
|
|
||
|
|
for (size_t i = 0; i < tessellation; i++)
|
||
|
|
{
|
||
|
|
for (size_t j = 0; j < tessellation; j++)
|
||
|
|
{
|
||
|
|
// Make a list of six index values (two triangles).
|
||
|
|
std::array<size_t, 6> indices =
|
||
|
|
{
|
||
|
|
i * stride + j,
|
||
|
|
(i + 1) * stride + j,
|
||
|
|
(i + 1) * stride + j + 1,
|
||
|
|
|
||
|
|
i * stride + j,
|
||
|
|
(i + 1) * stride + j + 1,
|
||
|
|
i * stride + j + 1,
|
||
|
|
};
|
||
|
|
|
||
|
|
// If this patch is mirrored, reverse indices to fix the winding order.
|
||
|
|
if (isMirrored)
|
||
|
|
{
|
||
|
|
std::reverse(indices.begin(), indices.end());
|
||
|
|
}
|
||
|
|
|
||
|
|
// Output these index values.
|
||
|
|
std::for_each(indices.begin(), indices.end(), outputIndex);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|