From pdxgate!ogicse!uwm.edu!spool.mu.edu!agate!doc.ic.ac.uk!cc.ic.ac.uk!!tparso Sun Feb  7 15:27:34 PST 1993

In article <1993Feb1.125118.1427@uoft02.utoledo.edu> prungta@.cse.utoledo.edu writes:
>Keywords: 
>
>Dear freinds,
>  this seems to be a simple problem, but I am having a hard time solving
>it. I have to map points inside a four sided polygon to a square. the
>quadilateral can be of any shape. If anyone has any ideas let me know.
>
>bye
>
>Pankaj Rungta
>email:parungta@jupiter.cse.edu
>.
>
Try this, mate...

/************************************************************************/
void BillinearMapping(
  PosVector *mncoords, 
  PosVector *xycoords, 
  PosVector *corners)
{
  /* Purpose: Transform a point in m,n-space, (contained in the PosVector
   * that 'coords' points to), lying within a square of side 2 centred on 
   * the origin, into a point in x,y-space lying within the quadrilateral 
   * defined by the four corner points contained within the array that 
   * 'corners' points to. The final position is placed back into the 
   * PosVector that 'coords' points to.                                 */

  /* Definitions: Local Variables...                                    */
  double a0, a1, a2, a3;
  double w0, w1, w2, w3;

  /* Calculate coefficients of the final expression...                  */
  a0 = (1+mncoords->x);
  a1 = (1-mncoords->x);
  a2 = (1+mncoords->y); 
  a3 = (1-mncoords->y); 

  w0 = a1*a3; 
  w1 = a0*a3; 
  w2 = a1*a2; 
  w3 = a0*a2;

  /* The final expression...                                            */
  xycoords->x = 0.25 *
	 (w0*corners[0].x + 
 	  w1*corners[1].x + 
	  w2*corners[2].x + 
	  w3*corners[3].x);
  xycoords->y = 0.25 *
	 (w0*corners[0].y + 
	  w1*corners[1].y + 
	  w2*corners[2].y + 
	  w3*corners[3].y);
}

/****************************************************************************/

Ohh, and you'll need this too...

typedef struct {
  double x,y;
} PosVector;

Hope that helps!


                             Tim Parsons
 .               +           _________________________________________________
       .                .    Department of Aeronautics
 .               .    .      Imperial College of Science,Technology & Medicine
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