Few existing Computer Aided Design (CAD) systems provide assistance to designers in developing geometric concepts at the early design stages. Instead they require a high level of precision and detail suited to detail design. To support the early geometric design, a CAD system should provide utilities for the rapid capture and iterative development of vague geometric models. This paper presents ...

Geometric mechanics involves the application of geometric and symmetry techniques to the study of Lagrangian or Hamiltonian mechanics. The goal of computational geometric mechanics is to construct computational algorithms which preserve the geometric properties of mechanical systems [1]. My research is focused on developing computational geometric methods for numerical integration, optimal cont...

An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by symbolically reasoning about geometry. This approach, called degrees of freedom analysis, employs a set of specialized routines called plan fragments that specify h...

This paper presents a coordinate-invariant differential geometric analysis of kinematic singularities for closed kinematic chains containing both active and passive joints. Using the geometric framework developed in Park and Kim (1996) for closed chain manipulability analysis, we classify closed chain singularities into three basic types: (i) those corresponding to singular points of the joint ...

A computer simulation of stereotactic breast biopsy was developed that paralleled the geometric configuration of a currently available breast biopsy system. This model was developed to define and improve the targeting of breast lesions with stereotactic biopsy techniques. Lesions must be clearly identified and accurately targeted on both views for successful localization. Nonvisualization of a ...

This paper treats the geometric formulation of optimal control problems for rigid bodies and it presents computational procedures based on this geometric formulation that can be used for numerical solution of 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 develop...

Modeling the 3D geometric configuration of yarn is the base of building the 3D fabric structure. The surfaces of the yarns are modeled by many facets. To improve the efficiency of modeling, 3D yarn is usually designed by Bezier curve, spline curve or B-spline curve on the principle of Computer Graphics. The paper reviews different 3D modeling methods for single yarn from the view of cross-secti...

In this paper we formulate a geometric theory of thermal stresses. Given a temperature distribution, we associate a Riemannian material manifold to the body, with a metric that explicitly depends on the temperature distribution. A change in temperature corresponds to a change in the material metric. In this sense, a temperature change is a concrete example of the so-called referential evolution...

In the paper we show that all combinatorial triangle-free configurations for v ≤ 18 are geometrically realizable. We also show that there is a unique smallest astral (183) triangle-free configuration and its Levi graph is the generalized Petersen graph G(18, 5). In addition, we present geometric realizations of the unique flag transitive triangle-free configuration (203) and the unique point tr...

We leverage a mix of classical concepts such as stratifications of semialgebraic sets, and recent theoretical results concerning configuration spaces with a convex parametrization. These lead to a key observation that most regions of assembly and packing configuration spaces indeed have a convex parametrization. In this they differ starkly by from configuration spaces used for folding, or struc...