Shearing

Shearing is more complicated than shifting or scaling. The function shear() takes six real arguments. If p is a Point, then p.shear(a, b, c, d, e, f) sets x_p to x_p + ay_p + bz_p, y_p to y_p + cx_p + dz_p, and z_p to z_p + ex_p + fy_p. In this way, each coordinate of a Point is modified based on the values of the other two coordinates, whereby the influence of the other coordinates on the new value is weighted according to the arguments.

     Point p(1, 1, 1);
     p.shear(1);
     p.show("p:");
     -| p: (2, 1, 1)
     p.set(1, 1, 1);
     p.shear(1, 1);
     p.show("p:");
     -| p: (3, 1, 1)
     p.set(1, 1, 1);
     p.shear(1, 1, 2, 2, 3, 3);
     p.show("p:");
     -| p: (3, 5, 7)
     

[next figure] demonstrates the effect of shearing the points of a rectangle in the x-y plane.

     Point P0;
     Point P1(3);
     Point P2(3, 3);
     Point P3(0, 3);
     Rectangle r(p0, p1, p2, p3);
     r.draw();
     Rectangle q(r);
     q.shear(1.5);
     q.draw(black, "evenly");
     

Fig. 1.