Self-intersection elimination in metamorphosis of two-dimensional curves

H :[0, 1]× ³→ ³, 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 defines 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 isoparametric curve of H(t, r) is self-intersection free. The second algorithm suits morphing operations of planar curves. First, it constructs the best 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.