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/******************************************************************************
* The MIT License (MIT)
*
* Copyright (c) 2015-2018 Baldur Karlsson
* Copyright (c) 2014 Crytek
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
******************************************************************************/
#include "matrix.h"
#include <float.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include "quat.h"
#include "vec.h"
// colour ramp from http://www.ncl.ucar.edu/Document/Graphics/ColorTables/GMT_wysiwyg.shtml
const Vec4f overdrawRamp[128] = {
Vec4f(0.000000f, 0.000000f, 0.000000f, 0.0f), Vec4f(0.250980f, 0.000000f, 0.250980f, 1.0f),
Vec4f(0.250980f, 0.000000f, 0.752941f, 1.0f), Vec4f(0.000000f, 0.250980f, 1.000000f, 1.0f),
Vec4f(0.000000f, 0.501961f, 1.000000f, 1.0f), Vec4f(0.000000f, 0.627451f, 1.000000f, 1.0f),
Vec4f(0.250980f, 0.752941f, 1.000000f, 1.0f), Vec4f(0.250980f, 0.878431f, 1.000000f, 1.0f),
Vec4f(0.250980f, 1.000000f, 1.000000f, 1.0f), Vec4f(0.250980f, 1.000000f, 0.752941f, 1.0f),
Vec4f(0.250980f, 1.000000f, 0.250980f, 1.0f), Vec4f(0.501961f, 1.000000f, 0.250980f, 1.0f),
Vec4f(0.752941f, 1.000000f, 0.250980f, 1.0f), Vec4f(1.000000f, 1.000000f, 0.250980f, 1.0f),
Vec4f(1.000000f, 0.878431f, 0.250980f, 1.0f), Vec4f(1.000000f, 0.627451f, 0.250980f, 1.0f),
Vec4f(1.000000f, 0.376471f, 0.250980f, 1.0f), Vec4f(1.000000f, 0.125490f, 0.250980f, 1.0f),
Vec4f(1.000000f, 0.376471f, 0.752941f, 1.0f), Vec4f(1.000000f, 0.627451f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.878431f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.878600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.878700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.878800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.878900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.879000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.879100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.879200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.879300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.879400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.879500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.879600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.879700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.879800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.879900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.880000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.880100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.880200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.880300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.880400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.880500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.880600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.880700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.880800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.880900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.881000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.881100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.881200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.881300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.881400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.881500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.881600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.881700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.881800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.881900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.882000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.882100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.882200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.882300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.882400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.882500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.882600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.882700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.882800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.882900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.883000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.883100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.883200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.883300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.883400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.883500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.883600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.883700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.883800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.883900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.884000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.884100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.884200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.884300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.884400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.884500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.884600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.884700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.884800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.884900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.885000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.885100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.885200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.885300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.885400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.885500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.885600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.885700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.885800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.885900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.886000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.886100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.886200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.886300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.886400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.886500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.886600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.886700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.886800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.886900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.887000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.887100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.887200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.887300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.887400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.887500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.887600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.887700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.887800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.887900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.888000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.888100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.888200f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.888300f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.888400f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.888500f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.888600f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.888700f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.888800f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.888900f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.889000f, 1.000000f, 1.0f),
Vec4f(1.000000f, 0.889100f, 1.000000f, 1.0f), Vec4f(1.000000f, 0.889200f, 1.000000f, 1.0f),
};
static inline size_t matIdx(const size_t x, const size_t y)
{
return x + y * 4;
}
Matrix4f Matrix4f::Mul(const Matrix4f &o) const
{
Matrix4f m;
for(size_t x = 0; x < 4; x++)
{
for(size_t y = 0; y < 4; y++)
{
m[matIdx(x, y)] =
(*this)[matIdx(x, 0)] * o[matIdx(0, y)] + (*this)[matIdx(x, 1)] * o[matIdx(1, y)] +
(*this)[matIdx(x, 2)] * o[matIdx(2, y)] + (*this)[matIdx(x, 3)] * o[matIdx(3, y)];
}
}
return m;
}
Matrix4f Matrix4f::Transpose() const
{
Matrix4f m;
for(size_t x = 0; x < 4; x++)
for(size_t y = 0; y < 4; y++)
m[matIdx(x, y)] = (*this)[matIdx(y, x)];
return m;
}
Matrix4f Matrix4f::Inverse() const
{
float a0 = (*this)[0] * (*this)[5] - (*this)[1] * (*this)[4];
float a1 = (*this)[0] * (*this)[6] - (*this)[2] * (*this)[4];
float a2 = (*this)[0] * (*this)[7] - (*this)[3] * (*this)[4];
float a3 = (*this)[1] * (*this)[6] - (*this)[2] * (*this)[5];
float a4 = (*this)[1] * (*this)[7] - (*this)[3] * (*this)[5];
float a5 = (*this)[2] * (*this)[7] - (*this)[3] * (*this)[6];
float b0 = (*this)[8] * (*this)[13] - (*this)[9] * (*this)[12];
float b1 = (*this)[8] * (*this)[14] - (*this)[10] * (*this)[12];
float b2 = (*this)[8] * (*this)[15] - (*this)[11] * (*this)[12];
float b3 = (*this)[9] * (*this)[14] - (*this)[10] * (*this)[13];
float b4 = (*this)[9] * (*this)[15] - (*this)[11] * (*this)[13];
float b5 = (*this)[10] * (*this)[15] - (*this)[11] * (*this)[14];
float det = a0 * b5 - a1 * b4 + a2 * b3 + a3 * b2 - a4 * b1 + a5 * b0;
if(fabsf(det) > FLT_EPSILON)
{
Matrix4f inverse;
inverse[0] = +(*this)[5] * b5 - (*this)[6] * b4 + (*this)[7] * b3;
inverse[4] = -(*this)[4] * b5 + (*this)[6] * b2 - (*this)[7] * b1;
inverse[8] = +(*this)[4] * b4 - (*this)[5] * b2 + (*this)[7] * b0;
inverse[12] = -(*this)[4] * b3 + (*this)[5] * b1 - (*this)[6] * b0;
inverse[1] = -(*this)[1] * b5 + (*this)[2] * b4 - (*this)[3] * b3;
inverse[5] = +(*this)[0] * b5 - (*this)[2] * b2 + (*this)[3] * b1;
inverse[9] = -(*this)[0] * b4 + (*this)[1] * b2 - (*this)[3] * b0;
inverse[13] = +(*this)[0] * b3 - (*this)[1] * b1 + (*this)[2] * b0;
inverse[2] = +(*this)[13] * a5 - (*this)[14] * a4 + (*this)[15] * a3;
inverse[6] = -(*this)[12] * a5 + (*this)[14] * a2 - (*this)[15] * a1;
inverse[10] = +(*this)[12] * a4 - (*this)[13] * a2 + (*this)[15] * a0;
inverse[14] = -(*this)[12] * a3 + (*this)[13] * a1 - (*this)[14] * a0;
inverse[3] = -(*this)[9] * a5 + (*this)[10] * a4 - (*this)[11] * a3;
inverse[7] = +(*this)[8] * a5 - (*this)[10] * a2 + (*this)[11] * a1;
inverse[11] = -(*this)[8] * a4 + (*this)[9] * a2 - (*this)[11] * a0;
inverse[15] = +(*this)[8] * a3 - (*this)[9] * a1 + (*this)[10] * a0;
float invDet = 1.0f / det;
inverse[0] *= invDet;
inverse[1] *= invDet;
inverse[2] *= invDet;
inverse[3] *= invDet;
inverse[4] *= invDet;
inverse[5] *= invDet;
inverse[6] *= invDet;
inverse[7] *= invDet;
inverse[8] *= invDet;
inverse[9] *= invDet;
inverse[10] *= invDet;
inverse[11] *= invDet;
inverse[12] *= invDet;
inverse[13] *= invDet;
inverse[14] *= invDet;
inverse[15] *= invDet;
return inverse;
}
// no inverse
return Matrix4f::Identity();
}
Vec3f Matrix4f::Transform(const Vec3f &v, const float w) const
{
Vec3f vout = Vec3f((*this)[matIdx(0, 0)] * v.x + (*this)[matIdx(0, 1)] * v.y +
(*this)[matIdx(0, 2)] * v.z + (*this)[matIdx(0, 3)] * w,
(*this)[matIdx(1, 0)] * v.x + (*this)[matIdx(1, 1)] * v.y +
(*this)[matIdx(1, 2)] * v.z + (*this)[matIdx(1, 3)] * w,
(*this)[matIdx(2, 0)] * v.x + (*this)[matIdx(2, 1)] * v.y +
(*this)[matIdx(2, 2)] * v.z + (*this)[matIdx(2, 3)] * w);
float wout = (*this)[matIdx(3, 0)] * v.x + (*this)[matIdx(3, 1)] * v.y +
(*this)[matIdx(3, 2)] * v.z + (*this)[matIdx(3, 3)] * w;
return vout * (1.0f / wout);
}
const Vec3f Matrix4f::GetPosition() const
{
return Vec3f(f[12], f[13], f[14]);
}
const Vec3f Matrix4f::GetForward() const
{
return Vec3f(f[8], f[9], f[10]);
}
const Vec3f Matrix4f::GetRight() const
{
return Vec3f(f[0], f[1], f[2]);
}
const Vec3f Matrix4f::GetUp() const
{
return Vec3f(f[4], f[5], f[6]);
}
Matrix4f Matrix4f::Translation(const Vec3f &t)
{
Matrix4f trans = Matrix4f::Identity();
trans[12] = t.x;
trans[13] = t.y;
trans[14] = t.z;
return trans;
}
Matrix4f Matrix4f::RotationX(const float r)
{
float m[16] = {
1.0f, 0.0f, 0.0f, 0.0f, 0.0f, cosf(r), -sinf(r), 0.0f,
0.0f, sinf(r), cosf(r), 0.0f, 0.0f, 0.0f, 0.0f, 1.0f,
};
return Matrix4f(m);
}
Matrix4f Matrix4f::RotationY(const float r)
{
float m[16] = {
cosf(r), 0.0f, sinf(r), 0.0f, 0.0f, 1.0f, 0.0f, 0.0f,
-sinf(r), 0.0f, cosf(r), 0.0f, 0.0f, 0.0f, 0.0f, 1.0f,
};
return Matrix4f(m);
}
Matrix4f Matrix4f::RotationZ(const float r)
{
float m[16] = {
cosf(r), -sinf(r), 0.0f, 0.0f, sinf(r), cosf(r), 0.0f, 0.0f,
0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f,
};
return Matrix4f(m);
}
Matrix4f Matrix4f::RotationZYX(const Vec3f &rot)
{
Quatf Qx = Quatf::AxisAngle(Vec3f(1.0f, 0.0f, 0.0f), rot.x);
Quatf Qy = Quatf::AxisAngle(Vec3f(0.0f, 1.0f, 0.0f), rot.y);
Quatf Qz = Quatf::AxisAngle(Vec3f(0.0f, 0.0f, 1.0f), rot.z);
Quatf R = Qx * Qy * Qz;
return R.GetMatrix();
}
Matrix4f Matrix4f::RotationXYZ(const Vec3f &rot)
{
Quatf Qx = Quatf::AxisAngle(Vec3f(1.0f, 0.0f, 0.0f), rot.x);
Quatf Qy = Quatf::AxisAngle(Vec3f(0.0f, 1.0f, 0.0f), rot.y);
Quatf Qz = Quatf::AxisAngle(Vec3f(0.0f, 0.0f, 1.0f), rot.z);
Quatf R = Qz * Qy * Qx;
return R.GetMatrix();
}
Matrix4f Matrix4f::Orthographic(const float Near, const float Far)
{
float L = -10.0f;
float R = 10.0f;
float T = 10.0f;
float B = -10.0f;
float N = -fabsf(Far - Near) * 0.5f;
float F = fabsf(Far - Near) * 0.5f;
if(Far < Near)
{
float tmp = F;
F = N;
N = tmp;
}
float ortho[16] = {
2.0f / (R - L), 0.0f, 0.0f, (L + R) / (L - R),
0.0f, 2.0f / (T - B), 0.0f, (T + B) / (B - T),
0.0f, 0.0f, 1.0f / (F - N), (F + N) / (N - F),
0.0f, 0.0f, 0.0f, 1.0f,
};
return Matrix4f(ortho);
}
Matrix4f Matrix4f::Perspective(const float degfov, const float N, const float F, const float A)
{
const float radfov = degfov * (3.1415926535f / 180.0f);
float S = 1 / tanf(radfov * 0.5f);
float persp[16] = {
S / A, 0.0f, 0.0f, 0.0f, 0.0f,
S, 0.0f, 0.0f, 0.0f, 0.0f,
F / (F - N), 1.0f, 0.0f, 0.0f, -(F * N) / (F - N),
0.0f,
};
return Matrix4f(persp);
}
Matrix4f Matrix4f::ReversePerspective(const float degfov, const float N, const float A)
{
const float radfov = degfov * (3.1415926535f / 180.0f);
float S = 1 / tanf(radfov * 0.5f);
float persp[16] = {
S / A, 0.0f, 0.0f, 0.0f, 0.0f, S, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, N, 0.0f,
};
return Matrix4f(persp);
}
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