GluProject and gluUnProject code
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GLU - the OpenGL Utility library is an additional library that contains a handful of functions for additional tasks.
It is traditional and can be found in a lot of tutorials and examples.
Here, we will only list the source code for glhProjectf and glhUnProjectf. Edit: the glhProjectf (works only from perspective projection. With the orthogonal projection it gives different results than standard gluProject.
int glhProjectf(float objx, float objy, float objz, float *modelview, float *projection, int *viewport, float *windowCoordinate)
{
// Transformation vectors
float fTempo[8];
// Modelview transform
fTempo[0]=modelview[0]*objx+modelview[4]*objy+modelview[8]*objz+modelview[12]; // w is always 1
fTempo[1]=modelview[1]*objx+modelview[5]*objy+modelview[9]*objz+modelview[13];
fTempo[2]=modelview[2]*objx+modelview[6]*objy+modelview[10]*objz+modelview[14];
fTempo[3]=modelview[3]*objx+modelview[7]*objy+modelview[11]*objz+modelview[15];
// Projection transform, the final row of projection matrix is always [0 0 -1 0]
// so we optimize for that.
fTempo[4]=projection[0]*fTempo[0]+projection[4]*fTempo[1]+projection[8]*fTempo[2]+projection[12]*fTempo[3];
fTempo[5]=projection[1]*fTempo[0]+projection[5]*fTempo[1]+projection[9]*fTempo[2]+projection[13]*fTempo[3];
fTempo[6]=projection[2]*fTempo[0]+projection[6]*fTempo[1]+projection[10]*fTempo[2]+projection[14]*fTempo[3];
fTempo[7]=-fTempo[2];
// The result normalizes between -1 and 1
if(fTempo[7]==0.0) // The w value
return 0;
fTempo[7]=1.0/fTempo[7];
// Perspective division
fTempo[4]*=fTempo[7];
fTempo[5]*=fTempo[7];
fTempo[6]*=fTempo[7];
// Window coordinates
// Map x, y to range 0-1
windowCoordinate[0]=(fTempo[4]*0.5+0.5)*viewport[2]+viewport[0];
windowCoordinate[1]=(fTempo[5]*0.5+0.5)*viewport[3]+viewport[1];
// This is only correct when glDepthRange(0.0, 1.0)
windowCoordinate[2]=(1.0+fTempo[6])*0.5; // Between 0 and 1
return 1;
}
int glhUnProjectf(float winx, float winy, float winz, float *modelview, float *projection, int *viewport, float *objectCoordinate)
{
// Transformation matrices
float m[16], A[16];
float in[4], out[4];
// Calculation for inverting a matrix, compute projection x modelview
// and store in A[16]
MultiplyMatrices4by4OpenGL_FLOAT(A, projection, modelview);
// Now compute the inverse of matrix A
if(glhInvertMatrixf2(A, m)==0)
return 0;
// Transformation of normalized coordinates between -1 and 1
in[0]=(winx-(float)viewport[0])/(float)viewport[2]*2.0-1.0;
in[1]=(winy-(float)viewport[1])/(float)viewport[3]*2.0-1.0;
in[2]=2.0*winz-1.0;
in[3]=1.0;
// Objects coordinates
MultiplyMatrixByVector4by4OpenGL_FLOAT(out, m, in);
if(out[3]==0.0)
return 0;
out[3]=1.0/out[3];
objectCoordinate[0]=out[0]*out[3];
objectCoordinate[1]=out[1]*out[3];
objectCoordinate[2]=out[2]*out[3];
return 1;
}
void MultiplyMatrices4by4OpenGL_FLOAT(float *result, float *matrix1, float *matrix2)
{
result[0]=matrix1[0]*matrix2[0]+
matrix1[4]*matrix2[1]+
matrix1[8]*matrix2[2]+
matrix1[12]*matrix2[3];
result[4]=matrix1[0]*matrix2[4]+
matrix1[4]*matrix2[5]+
matrix1[8]*matrix2[6]+
matrix1[12]*matrix2[7];
result[8]=matrix1[0]*matrix2[8]+
matrix1[4]*matrix2[9]+
matrix1[8]*matrix2[10]+
matrix1[12]*matrix2[11];
result[12]=matrix1[0]*matrix2[12]+
matrix1[4]*matrix2[13]+
matrix1[8]*matrix2[14]+
matrix1[12]*matrix2[15];
result[1]=matrix1[1]*matrix2[0]+
matrix1[5]*matrix2[1]+
matrix1[9]*matrix2[2]+
matrix1[13]*matrix2[3];
result[5]=matrix1[1]*matrix2[4]+
matrix1[5]*matrix2[5]+
matrix1[9]*matrix2[6]+
matrix1[13]*matrix2[7];
result[9]=matrix1[1]*matrix2[8]+
matrix1[5]*matrix2[9]+
matrix1[9]*matrix2[10]+
matrix1[13]*matrix2[11];
result[13]=matrix1[1]*matrix2[12]+
matrix1[5]*matrix2[13]+
matrix1[9]*matrix2[14]+
matrix1[13]*matrix2[15];
result[2]=matrix1[2]*matrix2[0]+
matrix1[6]*matrix2[1]+
matrix1[10]*matrix2[2]+
matrix1[14]*matrix2[3];
result[6]=matrix1[2]*matrix2[4]+
matrix1[6]*matrix2[5]+
matrix1[10]*matrix2[6]+
matrix1[14]*matrix2[7];
result[10]=matrix1[2]*matrix2[8]+
matrix1[6]*matrix2[9]+
matrix1[10]*matrix2[10]+
matrix1[14]*matrix2[11];
result[14]=matrix1[2]*matrix2[12]+
matrix1[6]*matrix2[13]+
matrix1[10]*matrix2[14]+
matrix1[14]*matrix2[15];
result[3]=matrix1[3]*matrix2[0]+
matrix1[7]*matrix2[1]+
matrix1[11]*matrix2[2]+
matrix1[15]*matrix2[3];
result[7]=matrix1[3]*matrix2[4]+
matrix1[7]*matrix2[5]+
matrix1[11]*matrix2[6]+
matrix1[15]*matrix2[7];
result[11]=matrix1[3]*matrix2[8]+
matrix1[7]*matrix2[9]+
matrix1[11]*matrix2[10]+
matrix1[15]*matrix2[11];
result[15]=matrix1[3]*matrix2[12]+
matrix1[7]*matrix2[13]+
matrix1[11]*matrix2[14]+
matrix1[15]*matrix2[15];
}
void MultiplyMatrixByVector4by4OpenGL_FLOAT(float *resultvector, const float *matrix, const float *pvector)
{
resultvector[0]=matrix[0]*pvector[0]+matrix[4]*pvector[1]+matrix[8]*pvector[2]+matrix[12]*pvector[3];
resultvector[1]=matrix[1]*pvector[0]+matrix[5]*pvector[1]+matrix[9]*pvector[2]+matrix[13]*pvector[3];
resultvector[2]=matrix[2]*pvector[0]+matrix[6]*pvector[1]+matrix[10]*pvector[2]+matrix[14]*pvector[3];
resultvector[3]=matrix[3]*pvector[0]+matrix[7]*pvector[1]+matrix[11]*pvector[2]+matrix[15]*pvector[3];
}
define SWAP_ROWS_DOUBLE(a, b) { double *_tmp = a; (a)=(b); (b)=_tmp; }
define SWAP_ROWS_FLOAT(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
define MAT(m,r,c) (m)[(c)*4+(r)]
// This code comes directly from GLU except that it is for float
int glhInvertMatrixf2(float *m, float *out)
{
float wtmp[4][8];
float m0, m1, m2, m3, s;
float *r0, *r1, *r2, *r3;
r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
/* choose pivot - or die */
if (fabsf(r3[0]) > fabsf(r2[0]))
SWAP_ROWS_FLOAT(r3, r2);
if (fabsf(r2[0]) > fabsf(r1[0]))
SWAP_ROWS_FLOAT(r2, r1);
if (fabsf(r1[0]) > fabsf(r0[0]))
SWAP_ROWS_FLOAT(r1, r0);
if (0.0 == r0[0])
return 0;
/* eliminate first variable */
m1 = r1[0] / r0[0];
m2 = r2[0] / r0[0];
m3 = r3[0] / r0[0];
s = r0[1];
r1[1] -= m1 * s;
r2[1] -= m2 * s;
r3[1] -= m3 * s;
s = r0[2];
r1[2] -= m1 * s;
r2[2] -= m2 * s;
r3[2] -= m3 * s;
s = r0[3];
r1[3] -= m1 * s;
r2[3] -= m2 * s;
r3[3] -= m3 * s;
s = r0[4];
if (s != 0.0) {
r1[4] -= m1 * s;
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r0[5];
if (s != 0.0) {
r1[5] -= m1 * s;
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r0[6];
if (s != 0.0) {
r1[6] -= m1 * s;
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r0[7];
if (s != 0.0) {
r1[7] -= m1 * s;
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (fabsf(r3[1]) > fabsf(r2[1]))
SWAP_ROWS_FLOAT(r3, r2);
if (fabsf(r2[1]) > fabsf(r1[1]))
SWAP_ROWS_FLOAT(r2, r1);
if (0.0 == r1[1])
return 0;
/* eliminate second variable */
m2 = r2[1] / r1[1];
m3 = r3[1] / r1[1];
r2[2] -= m2 * r1[2];
r3[2] -= m3 * r1[2];
r2[3] -= m2 * r1[3];
r3[3] -= m3 * r1[3];
s = r1[4];
if (0.0 != s) {
r2[4] -= m2 * s;
r3[4] -= m3 * s;
}
s = r1[5];
if (0.0 != s) {
r2[5] -= m2 * s;
r3[5] -= m3 * s;
}
s = r1[6];
if (0.0 != s) {
r2[6] -= m2 * s;
r3[6] -= m3 * s;
}
s = r1[7];
if (0.0 != s) {
r2[7] -= m2 * s;
r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (fabsf(r3[2]) > fabsf(r2[2]))
SWAP_ROWS_FLOAT(r3, r2);
if (0.0 == r2[2])
return 0;
/* eliminate third variable */
m3 = r3[2] / r2[2];
r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];
/* last check */
if (0.0 == r3[3])
return 0;
s = 1.0 / r3[3]; /* now back substitute row 3 */
r3[4] *= s;
r3[5] *= s;
r3[6] *= s;
r3[7] *= s;
m2 = r2[3]; /* now back substitute row 2 */
s = 1.0 / r2[2];
r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
m1 = r1[3];
r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
m0 = r0[3];
r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
m1 = r1[2]; /* now back substitute row 1 */
s = 1.0 / r1[1];
r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
m0 = r0[2];
r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
m0 = r0[1]; /* now back substitute row 0 */
s = 1.0 / r0[0];
r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
MAT(out, 0, 0) = r0[4];
MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
MAT(out, 3, 3) = r3[7];
return 1;
}