bool_point_pair intersection_points (const Point& p0, const Point& p1)  const function 
bool_point_pair intersection_points (const Path& p)  const function 
These functions find the intersections of the
Polygon and a line.
In the first version, the Point arguments are the end points of
the line. The argument to the second version must be a linear
Path .
A line and a regular polygon or rectangle^{1}
can intersect at two points at most.
Let When the Point A(1, 1, 1); Reg_Polygon r(origin, 5, 3); Transform t; t.rotate(15, 12, 11); t.shift(A); Point P(2, 0, 1); Point Q(2, 0, 1); P *= Q *= r *= t; bool_point_pair bpp = r.intersection_points(P, Q); bpp.first.pt.dotlabel("$f$", "rt"); bpp.second.pt.dotlabel("$s$");
In [next figure] , the lines BC and PQ are not coplanar with the Point B(r.get_point(3).mediate(r.get_point(4))); Point C(B); B.shift(0, 2, .5); C.shift(0, 2, .5); Point P(1, 2, 1); Point Q(0, 2, 1); B *= C *= P *= Q *= r *= t; bool_point_pair bpp = r.intersection_points(B, C); bpp.first.pt.dotlabel("$i_0$", "rt"); bpp = r.intersection_points(P, Q); bpp.first.pt.dotlabel("$i_1$", "rt");
In [next figure] , the intersection point of r with the line PQ does not lie on the line segment PQ. bpp = r.intersection_points(P, Q); bpp.first.pt.dotlabel("$i$", "rt"); cout << "bpp.first.b == " << bpp.first.b << endl << flush;  bpp.first.b == 0

vector<Point> intersection_points (const Polygon& r)  const function 
Finds the intersection points of two Polygons .
Let v be the vector<Point> returned by
intersection_points() . If the Polygons are coplanar,
v
will contain the intersection points of the edges of the
Polygons , as in [next figure]
.
Rectangle r(origin, 4, 4); Reg_Polygon rp(origin, 5, 5, 0, 36); rp.shift(0, 0, .25); vector <Point> v = r.intersection_points(rp);
If the Point A(1, 1, 1); Rectangle r(A, 4, 4); Reg_Polygon p(A, 5, 5); p.rotate(90, 30); p.shift(2, 0, 3); vector <Point> v = r.intersection_points(p);
In [next figure]
, the Point A(1, 1, 1); Rectangle r(A, 4, 4); Reg_Polygon p(A, 5, 5); p.rotate(90, 30); p.shift(4, 3, 3); vector <Point> v = r.intersection_points(p); int i = 0; for (vector<Point>::iterator iter = v.begin(); iter != v.end(); ++iter) iter>dotlabel(i++, "bot");
