// Returns the point on the given line nearest to this, ie the point such
// that the vector point->this is perpendicular to the line.
// The line is defined as a line_point and a dir_vector for its direction.
FCOORD FCOORD::nearest_pt_on_line(const FCOORD& line_point,
const FCOORD& dir_vector) const {
FCOORD point_vector(*this - line_point);
// The dot product (%) is |dir_vector||point_vector|cos theta, so dividing by
// the square of the length of dir_vector gives us the fraction of dir_vector
// to add to line1 to get the appropriate point, so
// result = line1 + lambda dir_vector.
double lambda = point_vector % dir_vector / dir_vector.sqlength();
return line_point + (dir_vector * lambda);
}
