We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For d > 1, the volume of the fragments is characterized by a single scale 1/t, while other geometric properties such as the length are characterized by an infin...

Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. Especially, curvature estimation of a mesh is an active research area [GI04, CSM03, CP03] with many applications. The most important curvature measures on a surface are the mean curvature H, the Gaussian curvature K, and the curv...

This work presents an approach to plan motion strategies for robotics tasks constrained by uncertainty in position, orientation and control. Our approach operates in a (x, y, θ) configuration space and it combines two local functions: a contact-based attraction function and an exploration function. Compliant motions are used to reduce the position/orientation uncertainty. An explicit geometric ...

This paper describes a simple model-based approach to boundary detection for blob shaped objects. A geometric model is used to focus attention on relevant portions of the image during boundary generation. The boundary generated is that which is a globally optimal match to the shape and edge description parameters of the model. The method is illustrated using images of stained transverse section...

Mathematical models to solve optimization connection problems in nonsimply connected regions under typical technological restrictions on geometric and topological parameters of routes, first all, curvature the number bends, have been investigated developed. The are linked with extant prospective topogeodesic territory polygonal images. solution involves search for optimum trajectories routes ne...