// create a shadow matrix that will project the desired shadow
void buildShadowMatrix(GLfloat shadowMat[16], GLfloat plane[4], GLfloat lightpos[4]) 
{
 GLfloat dot; // dot product of light position and ground plane normal
 dot = plane[0]*lightpos[0] + plane[1]*lightpos[1] +
  plane[2]*lightpos[2] + plane[3]*lightpos[3];

 shadowMat[0] = dot – lightpos[0] * plane[0];
 shadowMat[1] = – lightpos[0] * plane[1];
 shadowMat[2] = – lightpos[0] * plane[2];
 shadowMat[3] = – lightpos[0] * plane[3];

 shadowMat[4] = – lightpos[1] * plane[0];
 shadowMat[5] = dot – lightpos[1] * plane[1];
 shadowMat[6] = – lightpos[1] * plane[2];
 shadowMat[7] = – lightpos[1] * plane[3];

 shadowMat[8] = – lightpos[2] * plane[0];
 shadowMat[9] = – lightpos[2] * plane[1];
 shadowMat[10] = dot – lightpos[2] * plane[2];
 shadowMat[11] = – lightpos[2] * plane[3];

 shadowMat[12] = – lightpos[3] * plane[0];
 shadowMat[13] = – lightpos[3] * plane[1];
 shadowMat[14] = – lightpos[3] * plane[2];
 shadowMat[15] = dot – lightpos[3] * plane[3];
}

// create a reflection matrix that will project the desired shadow
void buildReflectionMatrix(GLfloat reflectionMat[16], GLfloat plane[4]) 
{
 reflectionMat[0] =  1 – 2 * plane[0] * plane[0];
 reflectionMat[1] =    – 2 * plane[0] * plane[1];
 reflectionMat[2] =    – 2 * plane[0] * plane[2];
 reflectionMat[3] =    – 2 * plane[0] * plane[3];

 reflectionMat[4] =    – 2 * plane[1] * plane[0];
 reflectionMat[5] =  1 – 2 * plane[1] * plane[1];
 reflectionMat[6] =    – 2 * plane[1] * plane[2];
 reflectionMat[7] =    – 2 * plane[1] * plane[3];

 reflectionMat[8] =    – 2 * plane[2] * plane[0];
 reflectionMat[9] =    – 2 * plane[2] * plane[1];
 reflectionMat[10] = 1 – 2 * plane[2] * plane[2];
 reflectionMat[11] =   – 2 * plane[2] * plane[3];

 reflectionMat[12] = 0.0;
 reflectionMat[13] = 0.0;
 reflectionMat[14] = 0.0;
 reflectionMat[15] = 1.0;
}