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Alignment with an Axis

Transform align_with_axis (Point p0, Point p1, [char axis = 'z']) Function
Returns the Transform that would align the line through p0 and p1 with the major axis denoted by the axis argument. The default is the z-axis. This function is used in the functions that find intersections. 
          Point P0(1, 1, 1);
          Point P1(2, 3, 4);
          P0.draw(P1);
          P0.dotlabel("$P_0$");
          P1.dotlabel("$P_1$");
          Transform t;
          t.align_with_axis(P0, P1, 'z');
          P0 *= P1 *= t;
          t.show("t:");
          -| t:
               0.949  -0.169   0.267       0
                   0   0.845   0.535       0
              -0.316  -0.507   0.802       0
              -0.632  -0.169    -1.6       1
          P0.show("P0:");
          -| P0: (0, 0, 0)
          P1.show("P1:");
          -| P1: (0, 0, 3.74)

The following example shows how align_with_axis() can be used for putting plane figures into a major plane. 

          default_focus.set(2, 3, -10, 2, 3, 10, 10);
          Circle c(origin, 3, 75, 25, 6);
          c.shift(2, 3);
          c.draw();
          Point n = c.get_normal();
          n.shift(c.get_center());
          Transform t;
          t.align_with_axis(c.get_center(), n, 'y');
          t.show("t:");
          -| t:
            0.686   0.379  -0.621       0
            0.543     0.3   0.784       0
            0.483  -0.875       0       0
               -3   -1.66   -1.11       1
          n *= c *= t;
          c.draw();
          c.show("c:");
          -| c:
          fill_draw_value == 0
          (1.31, 0, -0.728) .. (1.49, 0, -0.171) ..
          (1.44, 0, 0.413) .. (1.17, 0, 0.933) ..
          (0.728, 0, 1.31) .. (0.171, 0, 1.49) ..
          (-0.413, 0, 1.44) .. (-0.933, 0, 1.17) ..
          (-1.31, 0, 0.728) .. (-1.49, 0, 0.171) ..
          (-1.44, 0, -0.413) .. (-1.17, 0, -0.933) ..
          (-0.728, 0, -1.31) .. (-0.171, 0, -1.49) ..
          (0.413, 0, -1.44) .. (0.933, 0, -1.17) .. cycle;
          n.show("n:");
          -| n: (0, 1, 0)


[Figure 75. Not displayed.]

Fig. 75.