Self-intersection elimination in metamorphosis of two-dimensional curves

摘要

We consider two methods of self-intersec- tion elimination in the metamorphosis of free-form planar curves. Both algorithms exploit a matching algorithm and construct the best correspondence of the relative pa- rameterizations of the initial and final curves. The first algorithm investigates building and employing a homotopy H:[0,1]×R~3→#~3, where K(t,r)for t = And t = 1 are two given planar curves C)1(r) And C_2(r). The first t parameter defines The time of fixing the intermediate meta- Morphosis curve. The locus of H(t,r)coin- Cides with the ruled surface between C_1(r) And C_2(r), but each isoparametric curve of H(t,r)is self-intersection free.