Advanced metamorphosis based on bounded space-time blending

We further develop a new approach to shape metamorphosis using bounded blending operations in space-time. The key steps of the metamorphosis algorithm are: dimension increase by converting two input kD shapes into half-cylinders in (k+1)D space-time, applying bounded blending union with added material to the half-cylinders, and making cross-sections for getting intermediate shapes under the transformation. This approach is extended here in two directions. First, the problem of "jump" in animation or the rapid transition between shapes in the given interval is solved using "smoothed" versions of half-cylinders which undergo bounded blending. Second, the approach is extended to 3D initial and final shapes with the bounded blending union operation applied to the corresponding "smoothed" 4D space-time half-cylinders.