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raze/source/common/utility/matrix.cpp

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/* --------------------------------------------------
Lighthouse3D
VSMatrix - Very Simple Matrix Library
http://www.lighthouse3d.com/very-simple-libs
This is a simplified version of VSMatrix that has been adjusted for GZDoom's needs.
----------------------------------------------------*/
#include <algorithm>
#include <math.h>
#include "matrix.h"
#ifdef _MSC_VER
#pragma warning(disable : 4244) // truncate from double to float
#endif
static inline FLOATTYPE
DegToRad(FLOATTYPE degrees)
{
return (FLOATTYPE)(degrees * (pi::pif() / 180.0f));
};
// sets the square matrix mat to the identity matrix,
// size refers to the number of rows (or columns)
void
VSMatrix::setIdentityMatrix( FLOATTYPE *mat, int size) {
// fill matrix with 0s
for (int i = 0; i < size * size; ++i)
mat[i] = 0.0f;
// fill diagonal with 1s
for (int i = 0; i < size; ++i)
mat[i + i * size] = 1.0f;
}
// gl LoadIdentity implementation
void
VSMatrix::loadIdentity()
{
// fill matrix with 0s
for (int i = 0; i < 16; ++i)
mMatrix[i] = 0.0f;
// fill diagonal with 1s
for (int i = 0; i < 4; ++i)
mMatrix[i + i * 4] = 1.0f;
}
// gl MultMatrix implementation
void
VSMatrix::multMatrix(const FLOATTYPE *aMatrix)
{
FLOATTYPE res[16];
for (int i = 0; i < 4; ++i)
{
for (int j = 0; j < 4; ++j)
{
res[j*4 + i] = 0.0f;
for (int k = 0; k < 4; ++k)
{
res[j*4 + i] += mMatrix[k*4 + i] * aMatrix[j*4 + k];
}
}
}
memcpy(mMatrix, res, 16 * sizeof(FLOATTYPE));
}
#ifdef USE_DOUBLE
// gl MultMatrix implementation
void
VSMatrix::multMatrix(const float *aMatrix)
{
FLOATTYPE res[16];
for (int i = 0; i < 4; ++i)
{
for (int j = 0; j < 4; ++j)
{
res[j * 4 + i] = 0.0f;
for (int k = 0; k < 4; ++k)
{
res[j*4 + i] += mMatrix[k*4 + i] * aMatrix[j*4 + k];
}
}
}
memcpy(mMatrix, res, 16 * sizeof(FLOATTYPE));
}
#endif
// gl LoadMatrix implementation
void
VSMatrix::loadMatrix(const FLOATTYPE *aMatrix)
{
memcpy(mMatrix, aMatrix, 16 * sizeof(FLOATTYPE));
}
#ifdef USE_DOUBLE
// gl LoadMatrix implementation
void
VSMatrix::loadMatrix(const float *aMatrix)
{
for (int i = 0; i < 16; ++i)
{
mMatrix[i] = aMatrix[i];
}
}
#endif
// gl Translate implementation
void
VSMatrix::translate(FLOATTYPE x, FLOATTYPE y, FLOATTYPE z)
{
mMatrix[12] = mMatrix[0] * x + mMatrix[4] * y + mMatrix[8] * z + mMatrix[12];
mMatrix[13] = mMatrix[1] * x + mMatrix[5] * y + mMatrix[9] * z + mMatrix[13];
mMatrix[14] = mMatrix[2] * x + mMatrix[6] * y + mMatrix[10] * z + mMatrix[14];
}
// gl Scale implementation
void
VSMatrix::scale(FLOATTYPE x, FLOATTYPE y, FLOATTYPE z)
{
mMatrix[0] *= x; mMatrix[1] *= x; mMatrix[2] *= x; mMatrix[3] *= x;
mMatrix[4] *= y; mMatrix[5] *= y; mMatrix[6] *= y; mMatrix[7] *= y;
mMatrix[8] *= z; mMatrix[9] *= z; mMatrix[10] *= z; mMatrix[11] *= z;
}
// gl Rotate implementation
void
VSMatrix::rotate(FLOATTYPE angle, FLOATTYPE x, FLOATTYPE y, FLOATTYPE z)
{
FLOATTYPE mat[16];
FLOATTYPE v[3];
v[0] = x;
v[1] = y;
v[2] = z;
FLOATTYPE radAngle = DegToRad(angle);
FLOATTYPE co = cos(radAngle);
FLOATTYPE si = sin(radAngle);
normalize(v);
FLOATTYPE x2 = v[0]*v[0];
FLOATTYPE y2 = v[1]*v[1];
FLOATTYPE z2 = v[2]*v[2];
// mat[0] = x2 + (y2 + z2) * co;
mat[0] = co + x2 * (1 - co);// + (y2 + z2) * co;
mat[4] = v[0] * v[1] * (1 - co) - v[2] * si;
mat[8] = v[0] * v[2] * (1 - co) + v[1] * si;
mat[12]= 0.0f;
mat[1] = v[0] * v[1] * (1 - co) + v[2] * si;
// mat[5] = y2 + (x2 + z2) * co;
mat[5] = co + y2 * (1 - co);
mat[9] = v[1] * v[2] * (1 - co) - v[0] * si;
mat[13]= 0.0f;
mat[2] = v[0] * v[2] * (1 - co) - v[1] * si;
mat[6] = v[1] * v[2] * (1 - co) + v[0] * si;
// mat[10]= z2 + (x2 + y2) * co;
mat[10]= co + z2 * (1 - co);
mat[14]= 0.0f;
mat[3] = 0.0f;
mat[7] = 0.0f;
mat[11]= 0.0f;
mat[15]= 1.0f;
multMatrix(mat);
}
// gluLookAt implementation
void
VSMatrix::lookAt(FLOATTYPE xPos, FLOATTYPE yPos, FLOATTYPE zPos,
FLOATTYPE xLook, FLOATTYPE yLook, FLOATTYPE zLook,
FLOATTYPE xUp, FLOATTYPE yUp, FLOATTYPE zUp)
{
FLOATTYPE dir[3], right[3], up[3];
up[0] = xUp; up[1] = yUp; up[2] = zUp;
dir[0] = (xLook - xPos);
dir[1] = (yLook - yPos);
dir[2] = (zLook - zPos);
normalize(dir);
crossProduct(dir,up,right);
normalize(right);
crossProduct(right,dir,up);
normalize(up);
FLOATTYPE m1[16],m2[16];
m1[0] = right[0];
m1[4] = right[1];
m1[8] = right[2];
m1[12] = 0.0f;
m1[1] = up[0];
m1[5] = up[1];
m1[9] = up[2];
m1[13] = 0.0f;
m1[2] = -dir[0];
m1[6] = -dir[1];
m1[10] = -dir[2];
m1[14] = 0.0f;
m1[3] = 0.0f;
m1[7] = 0.0f;
m1[11] = 0.0f;
m1[15] = 1.0f;
setIdentityMatrix(m2,4);
m2[12] = -xPos;
m2[13] = -yPos;
m2[14] = -zPos;
multMatrix(m1);
multMatrix(m2);
}
// gluPerspective implementation
void
VSMatrix::perspective(FLOATTYPE fov, FLOATTYPE ratio, FLOATTYPE nearp, FLOATTYPE farp)
{
FLOATTYPE f = 1.0f / tan (fov * (pi::pif() / 360.0f));
loadIdentity();
mMatrix[0] = f / ratio;
mMatrix[1 * 4 + 1] = f;
mMatrix[2 * 4 + 2] = (farp + nearp) / (nearp - farp);
mMatrix[3 * 4 + 2] = (2.0f * farp * nearp) / (nearp - farp);
mMatrix[2 * 4 + 3] = -1.0f;
mMatrix[3 * 4 + 3] = 0.0f;
}
// gl Ortho implementation
void
VSMatrix::ortho(FLOATTYPE left, FLOATTYPE right,
FLOATTYPE bottom, FLOATTYPE top,
FLOATTYPE nearp, FLOATTYPE farp)
{
loadIdentity();
mMatrix[0 * 4 + 0] = 2 / (right - left);
mMatrix[1 * 4 + 1] = 2 / (top - bottom);
mMatrix[2 * 4 + 2] = -2 / (farp - nearp);
mMatrix[3 * 4 + 0] = -(right + left) / (right - left);
mMatrix[3 * 4 + 1] = -(top + bottom) / (top - bottom);
mMatrix[3 * 4 + 2] = -(farp + nearp) / (farp - nearp);
}
// gl Frustum implementation
void
VSMatrix::frustum(FLOATTYPE left, FLOATTYPE right,
FLOATTYPE bottom, FLOATTYPE top,
FLOATTYPE nearp, FLOATTYPE farp)
{
FLOATTYPE m[16];
setIdentityMatrix(m,4);
m[0 * 4 + 0] = 2 * nearp / (right-left);
m[1 * 4 + 1] = 2 * nearp / (top - bottom);
m[2 * 4 + 0] = (right + left) / (right - left);
m[2 * 4 + 1] = (top + bottom) / (top - bottom);
m[2 * 4 + 2] = - (farp + nearp) / (farp - nearp);
m[2 * 4 + 3] = -1.0f;
m[3 * 4 + 2] = - 2 * farp * nearp / (farp-nearp);
m[3 * 4 + 3] = 0.0f;
multMatrix(m);
}
/*
// returns a pointer to the requested matrix
FLOATTYPE *
VSMatrix::get(MatrixTypes aType)
{
return mMatrix[aType];
}
*/
/* -----------------------------------------------------
SEND MATRICES TO OPENGL
------------------------------------------------------*/
// -----------------------------------------------------
// AUX functions
// -----------------------------------------------------
// Compute res = M * point
void
VSMatrix::multMatrixPoint(const FLOATTYPE *point, FLOATTYPE *res)
{
for (int i = 0; i < 4; ++i)
{
res[i] = 0.0f;
for (int j = 0; j < 4; j++) {
res[i] += point[j] * mMatrix[j*4 + i];
}
}
}
// res = a cross b;
void
VSMatrix::crossProduct(const FLOATTYPE *a, const FLOATTYPE *b, FLOATTYPE *res) {
res[0] = a[1] * b[2] - b[1] * a[2];
res[1] = a[2] * b[0] - b[2] * a[0];
res[2] = a[0] * b[1] - b[0] * a[1];
}
// returns a . b
FLOATTYPE
VSMatrix::dotProduct(const FLOATTYPE *a, const FLOATTYPE *b) {
FLOATTYPE res = a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
return res;
}
// Normalize a vec3
void
VSMatrix::normalize(FLOATTYPE *a) {
FLOATTYPE mag = sqrt(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
a[0] /= mag;
a[1] /= mag;
a[2] /= mag;
}
// res = b - a
void
VSMatrix::subtract(const FLOATTYPE *a, const FLOATTYPE *b, FLOATTYPE *res) {
res[0] = b[0] - a[0];
res[1] = b[1] - a[1];
res[2] = b[2] - a[2];
}
// res = a + b
void
VSMatrix::add(const FLOATTYPE *a, const FLOATTYPE *b, FLOATTYPE *res) {
res[0] = b[0] + a[0];
res[1] = b[1] + a[1];
res[2] = b[2] + a[2];
}
// returns |a|
FLOATTYPE
VSMatrix::length(const FLOATTYPE *a) {
return(sqrt(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]));
}
static inline int
M3(int i, int j)
{
return (i*3+j);
};
// computes the derived normal matrix for the view matrix
void
VSMatrix::computeNormalMatrix(const FLOATTYPE *aMatrix)
{
double mMat3x3[9];
mMat3x3[0] = aMatrix[0];
mMat3x3[1] = aMatrix[1];
mMat3x3[2] = aMatrix[2];
mMat3x3[3] = aMatrix[4];
mMat3x3[4] = aMatrix[5];
mMat3x3[5] = aMatrix[6];
mMat3x3[6] = aMatrix[8];
mMat3x3[7] = aMatrix[9];
mMat3x3[8] = aMatrix[10];
double det, invDet;
det = mMat3x3[0] * (mMat3x3[4] * mMat3x3[8] - mMat3x3[5] * mMat3x3[7]) +
mMat3x3[1] * (mMat3x3[5] * mMat3x3[6] - mMat3x3[8] * mMat3x3[3]) +
mMat3x3[2] * (mMat3x3[3] * mMat3x3[7] - mMat3x3[4] * mMat3x3[6]);
invDet = 1.0/det;
mMatrix[0] = (mMat3x3[4] * mMat3x3[8] - mMat3x3[5] * mMat3x3[7]) * invDet;
mMatrix[1] = (mMat3x3[5] * mMat3x3[6] - mMat3x3[8] * mMat3x3[3]) * invDet;
mMatrix[2] = (mMat3x3[3] * mMat3x3[7] - mMat3x3[4] * mMat3x3[6]) * invDet;
mMatrix[3] = 0.0f;
mMatrix[4] = (mMat3x3[2] * mMat3x3[7] - mMat3x3[1] * mMat3x3[8]) * invDet;
mMatrix[5] = (mMat3x3[0] * mMat3x3[8] - mMat3x3[2] * mMat3x3[6]) * invDet;
mMatrix[6] = (mMat3x3[1] * mMat3x3[6] - mMat3x3[7] * mMat3x3[0]) * invDet;
mMatrix[7] = 0.0f;
mMatrix[8] = (mMat3x3[1] * mMat3x3[5] - mMat3x3[4] * mMat3x3[2]) * invDet;
mMatrix[9] = (mMat3x3[2] * mMat3x3[3] - mMat3x3[0] * mMat3x3[5]) * invDet;
mMatrix[10] =(mMat3x3[0] * mMat3x3[4] - mMat3x3[3] * mMat3x3[1]) * invDet;
mMatrix[11] = 0.0;
mMatrix[12] = 0.0;
mMatrix[13] = 0.0;
mMatrix[14] = 0.0;
mMatrix[15] = 1.0;
}
// aux function resMat = resMat * aMatrix
void
VSMatrix::multMatrix(FLOATTYPE *resMat, const FLOATTYPE *aMatrix)
{
FLOATTYPE res[16];
for (int i = 0; i < 4; ++i)
{
for (int j = 0; j < 4; ++j)
{
res[j*4 + i] = 0.0f;
for (int k = 0; k < 4; ++k)
{
res[j*4 + i] += resMat[k*4 + i] * aMatrix[j*4 + k];
}
}
}
memcpy(resMat, res, 16 * sizeof(FLOATTYPE));
}
static double mat3Determinant(const FLOATTYPE *mMat3x3)
{
return mMat3x3[0] * (mMat3x3[4] * mMat3x3[8] - mMat3x3[5] * mMat3x3[7]) +
mMat3x3[1] * (mMat3x3[5] * mMat3x3[6] - mMat3x3[8] * mMat3x3[3]) +
mMat3x3[2] * (mMat3x3[3] * mMat3x3[7] - mMat3x3[4] * mMat3x3[6]);
}
static double mat4Determinant(const FLOATTYPE *matrix)
{
FLOATTYPE mMat3x3_a[9] =
{
matrix[1 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[1 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2],
matrix[1 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_b[9] =
{
matrix[1 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[1 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2],
matrix[1 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_c[9] =
{
matrix[1 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[1 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[1 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_d[9] =
{
matrix[1 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[1 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[1 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2]
};
FLOATTYPE a, b, c, d;
FLOATTYPE value;
a = mat3Determinant(mMat3x3_a);
b = mat3Determinant(mMat3x3_b);
c = mat3Determinant(mMat3x3_c);
d = mat3Determinant(mMat3x3_d);
value = matrix[0 * 4 + 0] * a;
value -= matrix[0 * 4 + 1] * b;
value += matrix[0 * 4 + 2] * c;
value -= matrix[0 * 4 + 3] * d;
return value;
}
static void mat4Adjoint(const FLOATTYPE *matrix, FLOATTYPE *result)
{
FLOATTYPE mMat3x3_a[9] =
{
matrix[1 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[1 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2],
matrix[1 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_b[9] =
{
matrix[1 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[1 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2],
matrix[1 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_c[9] =
{
matrix[1 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[1 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[1 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_d[9] =
{
matrix[1 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[1 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[1 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2]
};
FLOATTYPE mMat3x3_e[9] =
{
matrix[0 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[0 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2],
matrix[0 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_f[9] =
{
matrix[0 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[0 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2],
matrix[0 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_g[9] =
{
matrix[0 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[0 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[0 * 4 + 3], matrix[2 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_h[9] =
{
matrix[0 * 4 + 0], matrix[2 * 4 + 0], matrix[3 * 4 + 0],
matrix[0 * 4 + 1], matrix[2 * 4 + 1], matrix[3 * 4 + 1],
matrix[0 * 4 + 2], matrix[2 * 4 + 2], matrix[3 * 4 + 2]
};
FLOATTYPE mMat3x3_i[9] =
{
matrix[0 * 4 + 1], matrix[1 * 4 + 1], matrix[3 * 4 + 1],
matrix[0 * 4 + 2], matrix[1 * 4 + 2], matrix[3 * 4 + 2],
matrix[0 * 4 + 3], matrix[1 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_j[9] =
{
matrix[0 * 4 + 0], matrix[1 * 4 + 0], matrix[3 * 4 + 0],
matrix[0 * 4 + 2], matrix[1 * 4 + 2], matrix[3 * 4 + 2],
matrix[0 * 4 + 3], matrix[1 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_k[9] =
{
matrix[0 * 4 + 0], matrix[1 * 4 + 0], matrix[3 * 4 + 0],
matrix[0 * 4 + 1], matrix[1 * 4 + 1], matrix[3 * 4 + 1],
matrix[0 * 4 + 3], matrix[1 * 4 + 3], matrix[3 * 4 + 3]
};
FLOATTYPE mMat3x3_l[9] =
{
matrix[0 * 4 + 0], matrix[1 * 4 + 0], matrix[3 * 4 + 0],
matrix[0 * 4 + 1], matrix[1 * 4 + 1], matrix[3 * 4 + 1],
matrix[0 * 4 + 2], matrix[1 * 4 + 2], matrix[3 * 4 + 2]
};
FLOATTYPE mMat3x3_m[9] =
{
matrix[0 * 4 + 1], matrix[1 * 4 + 1], matrix[2 * 4 + 1],
matrix[0 * 4 + 2], matrix[1 * 4 + 2], matrix[2 * 4 + 2],
matrix[0 * 4 + 3], matrix[1 * 4 + 3], matrix[2 * 4 + 3]
};
FLOATTYPE mMat3x3_n[9] =
{
matrix[0 * 4 + 0], matrix[1 * 4 + 0], matrix[2 * 4 + 0],
matrix[0 * 4 + 2], matrix[1 * 4 + 2], matrix[2 * 4 + 2],
matrix[0 * 4 + 3], matrix[1 * 4 + 3], matrix[2 * 4 + 3]
};
FLOATTYPE mMat3x3_o[9] =
{
matrix[0 * 4 + 0], matrix[1 * 4 + 0], matrix[2 * 4 + 0],
matrix[0 * 4 + 1], matrix[1 * 4 + 1], matrix[2 * 4 + 1],
matrix[0 * 4 + 3], matrix[1 * 4 + 3], matrix[2 * 4 + 3]
};
FLOATTYPE mMat3x3_p[9] =
{
matrix[0 * 4 + 0], matrix[1 * 4 + 0], matrix[2 * 4 + 0],
matrix[0 * 4 + 1], matrix[1 * 4 + 1], matrix[2 * 4 + 1],
matrix[0 * 4 + 2], matrix[1 * 4 + 2], matrix[2 * 4 + 2]
};
result[0 * 4 + 0] = mat3Determinant(mMat3x3_a);
result[1 * 4 + 0] = -mat3Determinant(mMat3x3_b);
result[2 * 4 + 0] = mat3Determinant(mMat3x3_c);
result[3 * 4 + 0] = -mat3Determinant(mMat3x3_d);
result[0 * 4 + 1] = -mat3Determinant(mMat3x3_e);
result[1 * 4 + 1] = mat3Determinant(mMat3x3_f);
result[2 * 4 + 1] = -mat3Determinant(mMat3x3_g);
result[3 * 4 + 1] = mat3Determinant(mMat3x3_h);
result[0 * 4 + 2] = mat3Determinant(mMat3x3_i);
result[1 * 4 + 2] = -mat3Determinant(mMat3x3_j);
result[2 * 4 + 2] = mat3Determinant(mMat3x3_k);
result[3 * 4 + 2] = -mat3Determinant(mMat3x3_l);
result[0 * 4 + 3] = -mat3Determinant(mMat3x3_m);
result[1 * 4 + 3] = mat3Determinant(mMat3x3_n);
result[2 * 4 + 3] = -mat3Determinant(mMat3x3_o);
result[3 * 4 + 3] = mat3Determinant(mMat3x3_p);
}
bool VSMatrix::inverseMatrix(VSMatrix &result)
{
// Calculate mat4 determinant
FLOATTYPE det = mat4Determinant(mMatrix);
// Inverse unknown when determinant is close to zero
if (fabs(det) < 1e-15)
{
for (int i = 0; i < 16; i++)
result.mMatrix[i] = FLOATTYPE(0.0);
return false;
}
else
{
mat4Adjoint(mMatrix, result.mMatrix);
FLOATTYPE invDet = FLOATTYPE(1.0) / det;
for (int i = 0; i < 16; i++)
{
result.mMatrix[i] = result.mMatrix[i] * invDet;
}
}
return true;
}
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