/* Matrix arithmetic functions.
   Tested with Borland C++ 2.0 in the small model */

/* Matrix multiplies Xform by SourceVec, and stores the result in
   DestVec. Multiplies a 4x4 matrix times a 4x1 matrix; the result
   is a 4x1 matrix, as follows:
   --     --     -- --     -- --
   |       |     | 4 |     | 4 |
   |  4x4  |  X  | x |  =  | x |
   |       |     | 1 |     | 1 |
   --     --     -- --     -- -- */
void XformVec(double Xform[4][4], double * SourceVec,
   double * DestVec)
{
   int i,j;

   for (i=0; i<4; i++) {
      DestVec[i] = 0;
      for (j=0; j<4; j++)
         DestVec[i] += Xform[i][j] * SourceVec[j];
   }
}

/* Matrix multiplies SourceXform1 by SourceXform2 and stores the
   result in DestXform. Multiplies a 4x4 matrix times a 4x4 matrix;
   the result is a 4x4 matrix, as follows:
   --     --     --     --     --     --
   |       |     |       |     |       |
   |  4x4  |  X  |  4x4  |  =  |  4x4  |
   |       |     |       |     |       |
   --     --     --     --     --     -- */
void ConcatXforms(double SourceXform1[4][4], double SourceXform2[4][4],
   double DestXform[4][4])
{
   int i,j,k;

   for (i=0; i<4; i++) {
      for (j=0; j<4; j++) {
         DestXform[i][j] = 0;
         for (k=0; k<4; k++)
            DestXform[i][j] += SourceXform1[i][k] * SourceXform2[k][j];
      }
   }
}