/********************************************************/
/*						       	*/
/*						       	*/
/*  This method transforms a Tuple based on a		*/
/*	tranformation matrix			*/
/********************************************************/

Tuple Tuple::matrixMultiply(float m[])
{
	// m is a 4x4 matrix stored in column-major order
	// in a length 16 array
	// 
	// to compute the multiplication we should convert
	// this into a 4-tuple with a 1 in the new dimension
	// perform the multiplication, then strip off the
	// last dimension
	//
	// the following achieves the same effect
	// without the conversion
	Tuple tmp(0,0,0);
	for (int j=0; j<3; j++) { // for each row of the matrix 
		for (int k=0; k<3; k++) {  // for each column
			tmp[j] += m[j+4*k]*data[k];  // the matrix is column-major
		}
		tmp[j]+=m[j+12];
	}

	return tmp;

}