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/*
 *   NAME
 *     linear_comb
 *
 *   PURPOSE
 *     Form a linear combination of two vectors
 *
 *   NOTES
 *     
 *
 *   HISTORY
 *      wiener - May 8, 1995: Created.
 */

#include <euclid/copyright.h>
#include <euclid/geometry.h>

/*
 * Assume that u, v are vectors defining a coordinate system and that w
 * is a vector having coordinates with respect to u and v.  Specifically,
 *
 * u = (u.x, u.y) with respect to some standard basis
 * v = (v.x, v.y) with respect to some standard basis
 * w = (w.x, w.y) with respect to u, v
 *
 * Express w with regard to the standard basis.  I.e., find z = w.x (u) +
 * w.y (v).  Note that this is simply matrix multiplication:
 *
 * Matrix  Vector
 *
 * z   = (u v)   w
 *
 * z   = u   * w.x + v   * w.y
 *
 * z.x = u.x * w.x + v.x * w.y
 * z.y = u.y * w.x + v.y * w.y 
 */
void EG_linear_comb(Point_d *u, Point_d *v, Point_d *w, Point_d *z)
{
  z->x = u->x * w->x + v->x * w->y;
  z->y = u->y * w->x + v->y * w->y;
}