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;
  }