Practical Algorithms for 3D Computer Graphics, 2nd Edition

10.7. Orienting surface normals 405

Curve

(a)

(b)

E

Bevel

Overlap

Figure 10.33: Resolving th e problem that can occur if th e curvatu r e is too great to

accommodate the required bevel depth. In (a) the edges in the bevel overlap. By

preventing the creation of a vertex and edge ass ociated with edge E in the original

curve, the overlap is avoided (b).

curve C. This will be true for cases where α < 180

◦

. If 180

◦

< α < 270

◦

the edge in th e bevel will be longer than the one it is parallel to in the

curve C.

Figure 10.32 illustrates the result of applying this p r ocedur e to th e curve

fragments of figure 10.31.

There is one irritating complication when beveling ...