Space–time blending
Galina Pasko, Alexander Pasko, Tosiyasu L. Kunii · Computer Animation and Virtual Worlds · 2004
Abstract Shape transformation between objects of different topology and positions in space is an open modelling problem. We propose a new approach to solving this problem for two given 2D or 3D shapes. The key steps of the proposed algorithm are: increase dimension by converting two input kD shapes into half‐cylinders in (k+1)D space–time, applying bounded blending with added material to the half‐cylinders, and making cross‐sections for getting intermediate shapes under the transformation. The additional dimension is considered as a time coordinate for making animation. We use the bounded blending set operations in space–time defined using R‐functions and displacement functions with the localized area of influence applied to the functionally defined half‐cylinders. The proposed approach is general enough to handle input shapes with arbitrary topology defined as polygonal objects with holes and disjoint components, set‐theoretic objects, or analytically defined implicit surfaces. The obtained unusual amoeba‐like behaviour of the shape combines metamorphosis with the non‐linear motion. Copyright © 2004 John Wiley & Sons, Ltd.