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Intersections

bool_point intersection_point (const Point& p0, const Point& p1) const function
bool_point intersection_point (const Path& p) const function
These functions find the intersection point of the Plane and a line. In the first version, the line is defined by the two Point arguments. In the second version, the Path p must be linear, i.e., p.is_linear() must be true.

Both versions of intersection_point() return a bool_point bp, where bp.pt is the intersection point, or INVALID_POINT, if there is none. If an intersection point is found, bp.b will be true, otherwise false. Returning a bool_point makes it possible to test for success without comparing the Point returned against INVALID_POINT. 

          Point center(2, 2, 3.5);
          Reg_Polygon h(center, 6, 4, 80, 30, 10);
          Plane q = h.get_plane();
          Point P0 = center.mediate(h.get_point(2));
          P0.shift(5 * (N - center));
          Point P1(P0);
          P1.rotate(h.get_point(1), h.get_point(4));
          P1 = 3 * (P1 - P0);
          P1.shift(P0);
          P1.shift(3, -.5, -2);
          bool_point bp = q.intersection_point(P0, P1);
          Point i_P = bp.pt;
          Point P4 = h.get_point(3).mediate(h.get_point(0), .75);
          P4.shift(N - center);
          Point P5(P4);
          P5.rotate(h.get_point(3), h.get_point(0));
          P4.shift(-1, 2);
          Path theta(P4, P5);
          bp = q.intersection_point(theta);
          Point i_theta = bp.pt;
          draw_axes();


[Figure 107. Not displayed.]

Fig. 107.

Line intersection_line (const Plane& p) const function
Returns a Line l. representing the line of intersection of two Planes. See Line Reference.

In [next figure] , intersection_line() is used to find the line of intersection of the Planes derived from the Rectangles r_0 and r_1 using get_plane() (see Paths Reference; Querying). Please note that there is no guarantee that l.position will be in a convenient place for your drawing. A bit of fiddling was needed to find the Points P_2 and P_3. I plan to add functions for finding the intersection lines of plane figures, but haven't done so yet. 

          Rectangle r0(origin, 5, 5, 10, 15, 6);
          Rectangle r1(origin, 5, 5, 90, 50, 10);
          r1 *= r0.rotate(30, 30, 30);
          r1 *= r0.shift(1, -1, 3);
          Plane q0 = r0.get_plane();
          Plane q1 = r1.get_plane();
          Line l = q0.intersection_line(q1);
          l.show("l:");
          -| l:
             position: (0, 11.2193, 20.0759)
             direction: (0.0466595, -0.570146, -0.796753)
          Point P0(l.direction);
          P0.shift(l.position);
          P0.show("P0:");
          -| P0: (0.0466595, 10.6491, 19.2791)
          Point P1(-l.direction);
          P1.shift(l.position);
          Point P2(P0 - P1);
          P2 *= 12.5;
          P2.shift(P0);
          cout << P2.is_on_plane(q0);
          -| 1
          cout << P2.is_on_plane(q1);
          -| 1
          Point P3(P0 - P1);
          P3 *= 7;
          P3.shift(P0);
          cout << P3.is_on_plane(q0);
          -| 1
          cout << P3.is_on_plane(q1);
          -| 1


[Figure 108. Not displayed.]

Fig. 108.