Transform which, if applied to the
Path, would align it with the major axis indicated by the
axis argument.
The first and second versions can only be called
for Paths where line_switch is true. The first
version is const, so the Path remains unchanged. The second
version should only be called with assign = true, so that the
Transform is applied to the Path, actually aligning it with
the axis indicated. If the second version is called with
assign = false, a warning message is issued to the standard error
output (stderr), since one might as well use the first version in
this case, but it won't do any harm. The third version creates a
Transform t locally that would align the line from p0 to
p1 with the axis indicated, and applies t to the Path.
Point A(2, 3, 2);
Point B(-1, 1, 3);
Path p(A, B);
Transform t = p.align_with_axis(true, 'z');
t.show("t:");
-| t:
-0.316 0.507 -0.802 0
0 -0.845 -0.535 0
-0.949 -0.169 0.267 0
2.53 1.86 2.67 1
p *= t;
p.show("p:");
-| p:
(2.53, 1.86, 2.67) -- (-1.02, 1.23, 3.67);
Point C(1);
C *= t.inverse();
Path q;
q += "..";
q += C;
for (int i = 0; i < 15; ++i)
{
C.rotate(A, B, 360.0/16);
q += C;
}
q.set_cycle(true);
q.show("q:");
-| q:
(1.68, 3, 1.05) .. (1.9, 2.68, 1.06) ..
(2.13, 2.4, 1.21) .. (2.35, 2.22, 1.48) ..
(2.51, 2.15, 1.83) .. (2.59, 2.22, 2.21) ..
(2.58, 2.4, 2.55) .. (2.49, 2.68, 2.81) ..
(2.32, 3, 2.95) .. (2.1, 3.32, 2.94) ..
(1.87, 3.6, 2.79) .. (1.65, 3.78, 2.52) ..
(1.49, 3.85, 2.17) .. (1.41, 3.78, 1.79) ..
(1.42, 3.6, 1.45) .. (1.51, 3.32, 1.19) .. cycle;
q.align_with_axis(A, B, 'z');
q.show("q:");
-| q:
(1, 0, 0) .. (0.924, 0.383, 0) ..
(0.707, 0.707, 0) .. (0.383, 0.924, 0) ..
(0, 1, 0) .. (-0.383, 0.924, 0) ..
(-0.707, 0.707, 0) .. (-0.924, 0.383, 0) ..
(-1, 0, 0) .. (-0.924, -0.383, 0) ..
(-0.707, -0.707, 0) .. (-0.383, -0.924, 0) ..
(0, -1, 0) .. (0.383, -0.924, 0) ..
(0.707, -0.707, 0) .. (0.924, -0.383, 0) .. cycle;
![[Figure 119. Not displayed.]](./graphics/png/3DLDF119.png)
Fig. 119.