GluProject and gluUnProject code代码

参考 http://www.opengl.org/wiki/GluProject_and_gluUnProject_code

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.

最关键的搞清楚opengl的矩阵存储方式

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;  }

//还有一种常用的是这样的 其实没有区别
/*Transform a point(column vector) by a 4x4 matrix. Then, out = m * inInput: m ----- the 4x4 matrix, in ---- the 4x1 vectorOutput: out ---- the resulting 4x1 vector观察transform_point函数中矩阵元素和列向量的相乘过程可知，这个矩阵是被转置后再和列向量相乘的。这就是为什么说OpenGL的矩阵相乘是遵循列主元的，而我们使用gluProject函数的时候输入的矩阵参数却是按照行主元的方式。*/static void transform_point(GLdouble out[4], const GLdouble m[16], const GLdouble in[4]){#define M(row,col) m[col*4+row]out[0] = M(0, 0) * in[0] + M(0, 1) * in[1] + M(0, 2) * in[2] + M(0, 3) * in[3];out[1] = M(1, 0) * in[0] + M(1, 1) * in[1] + M(1, 2) * in[2] + M(1, 3) * in[3];out[2] = M(2, 0) * in[0] + M(2, 1) * in[1] + M(2, 2) * in[2] + M(2, 3) * in[3];out[3] = M(3, 0) * in[0] + M(3, 1) * in[1] + M(3, 2) * in[2] + M(3, 3) * in[3];#undef M}// gluProject source code (说明见OpenGL API文档)GLint gluProject(GLdouble objx, GLdouble objy, GLdouble objz,const GLdouble  modelMatrix[16], const GLdouble projMatrix[16],const GLint viewport[4], GLdouble *winx, GLdouble *winy, GLdouble *winz){// matrice transformationGLdouble in[4], out[4];//initialize matrice and column vector as a transformerin[0] = objx;in[1] = objy;in[2] = objz;in[3] = 1.0;transform_point(out, modelMatrix, in);  //乘以模型视图矩阵transform_point(in, projMatrix, out);   //乘以投影矩阵//齐次向量的第四项不能为0if(in[3] == 0.0)return GL_FALSE;//向量齐次化标准化in[0] /= in[3];in[1] /= in[3];in[2] /= in[3];//视口向量的作用*winx = viewport[0] + (1 + in[0]) * viewport[2] / 2;*winy = viewport[1] + (1 + in[1]) * viewport[3] / 2;*winz = (1 + in[2]) / 2;return GL_TRUE;}