In algebraic approaches to geometric computing, the general procedure is as follows [11]: first, the geometric configuration, including both the hypotheses and the conclusion, is translated into an algebraic formulation in a prerequisite algebraic language; second, algebraic computations are carried out to the conclusion by utilizing the computational rules of the algebra and the given hypothes...

Braids are intimately related to configuration spaces of points. These configuration spaces give a useful model of autonomous agents (or robots) in an environment. Problems of relevance to autonomous engineering systems (e.g., motion planning, coordination, cooperation, assembly) are directly related to topological and geometric properties of configuration spaces, including their braid groups. ...

Line-to-Point Registration with Applications in Geometric Reconstruction of Coronary Stents By Claire Y. Lin Registration is a process of geometrically transforming one object to correspond to the other. It can utilized to align images, surfaces, or point clouds. The Iterative Closest Point algorithm is widely used in registration to achieve reconstruction of geometric shapes, but has drawbacks...

We use a Riemannian (or pseudo-Riemannian) geometric framework to formulate the theory of the classical r-matrix for integrable systems. In this picture the r-matrix is related to a fourth rank tensor, named the r-tensor, on the configuration space. The r-matrix itself carries one connection type index and three tensorial indices. Being defined on the configuration space it has no momentum depe...

This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each rigid body is viewed as evolving on a configuration manifold that is a Lie group. Discrete-time dynamics of each rigid body are developed that evolve on the ...