Page 208 - Geometric Modeling and Algebraic Geometry

11 Subdivision Methods for the Topology of 2d and 3d Implicit Curves 211

(a) ridge curve (b) self-intersection curve

Fig. 11.1. Topological descriptions of high complexity curves

g(x)= x + y + z − 2
2
2
2
time: 20 msec
3) f(x)=2x + y + z − 4
2
2
2
g(x)= x +2xy + y − 2yz − 2z +2zx
2
2
2
time: 30 msec
4) f(x)= x + y +2x y +2x +2y − x − y − z
4
2 2
2
2
4
g(x)= x +2x y + y +3x y − y + z 2
4
2
3
4
2 2
time: 130 msec
(a) Example 1 (b) Example 2 (c) Example 3 (d) Example 4
Fig. 11.2. Topological descriptions of the intersection curve for 4 pairs of low-order algebraic
surfaces.