Self-intersection elimination in metamorphosis of two-dimensional curves

We consider two methods of self-intersection elimination in the metamorphos is of free-form planar curves. Both algorithms exploit a matching algorithm and construct the best correspondence of the relative parameterizations of the initial and final curves. The first algorithm investigates building an d employing a homotopy H:[0, 1]xIR(3)-->IR3, where H(t, r) for t=0 and t=1 are two given planar curves C-1(r) and C-2(r). The first t parameter define s the time of fixing the intermediate metamorphosis curve. The locus of H(t , r) coincides with the ruled surface between C-1(r) and C-2(r), but each i soparametric curve of H(r, r) is self-intersection free. The second algorit hm suits morphing operations of planar curves. First, it constructs the bes t correspondence of the relative parameterizations of the initial and final curves. Then it eliminates the remaining self-intersections and flips back the domains that self-intersect.