Space-time blending with improved user control in real-time

Most of the existing methods of metamorphosis are based on the interpolation schemes, space-time blending is a geometric operation of bounded blending performed in the higher-dimensional space. It provides transformations between shapes of different topology without necessarily establishing their alignment or correspondence. The original formulation of space-time blending had several problems: fast uncontrolled transition between shapes within the given time interval, generation of disconnected components, and lack of intuitive user control over the transformation process. We improve the original technique to provide the user with a set of more intuitive controls. The problem of the fast transition between the shapes is solved by the introduction of additional controllable affine transformations applied to initial objects in space-time. The approach is further extended with the introduction of an additional non-linear deformation operation. The proposed techniques have been implemented and tested within an industrial computer animation system. We have also implemented our method on the GPU, so that it can be employed in real-time applications.