projectionFactor method

double projectionFactor(Coordinate p)

Computes the Projection Factor for the projection of the point p onto this LineSegment. The Projection Factor is the constant r by which the vector for this segment must be multiplied to equal the vector for the projection of p on the line defined by this segment.

The projection factor will lie in the range (-inf, +inf), or be NaN if the line segment has zero length..

@param p the point to compute the factor for @return the projection factor for the point

Implementation

double projectionFactor(Coordinate p) {
  if (p.equals(p0)) return 0.0;
  if (p.equals(p1)) return 1.0;
  // Otherwise, use comp.graphics.algorithms Frequently Asked Questions method
  /*     	      AC dot AB
                 r = ---------
                       ||AB||^2
              r has the following meaning:
              r=0 P = A
              r=1 P = B
              r<0 P is on the backward extension of AB
              r>1 P is on the forward extension of AB
              0<r<1 P is interior to AB
      */
  double dx = p1.x - p0.x;
  double dy = p1.y - p0.y;
  double len = dx * dx + dy * dy;

  // handle zero-length segments
  if (len <= 0.0) return double.nan;

  double r = ((p.x - p0.x) * dx + (p.y - p0.y) * dy) / len;
  return r;
}