This paper presents a deformable fast computation elastic model for real-time processing applications. 'Gradational element resolution model' is introduced with fewer elements for fast computation, in which small elements are laid around the object surface and large elements are laid in the center of the object. Elastic element layout is changed dynamically according to the deformation of cutting or tearing objects. The element reconstruction procedure is applied little by little for each step of the recursive motion generation process to avoid an increase in motion computation time.

This letter presents the connectivity number of 1-voxels in a 3-D digitized binary picture, and gives the necessary and sufficient condition that a 1-voxel in a 3-D picture is deletable. A shrinking algorithm for a 3-D object is suggested by using these results.

This letter presents definitions of connectivity among volume cells of a three-dimensional (3-D) digitized binary picture, and an explicit formula to calculate the Euler number of a 3-D object in a given 3-D picture.