Article history: Received 14 November 2009 Received in revised form 29 April 2010 Accepted 6 May 2010

Given a simple generalized polygonA of line segments and arcs that is free to move and rotate and an oriented monotone chainB composed of smooth parametric curved edges, the positions and orientations forA to gouge-freely contactB (i.e., the contact configurations) is a C0 continuous surface in a three dimensional space R3. Past results either limitB to be polygonal or depend on the very compli...

Several key techniques in 3D geological modeling including planar mesh generation, spatial interpolation, and surface intersection are summarized in this paper. Note that these techniques are generic and widely used in various applications but play a key role in 3D geological modeling. There are two essential procedures in 3D geological modeling: the first is the simulation of geological interf...

The 9-intersection is an extension of the 9-intersection, which distinguishes the topological relations between various spatial objects by the pattern of a nested matrix. This paper develops a small set of constraints on this matrix, which is applicable to arbitrary pairs of spatial objects in various spaces. Based on this set of universal constraints, the sets of matrix patterns, each represen...

Intersection traffic delay research has traditionally placed greater emphasis on the study of through and left-turning vehicles than right-turning ones, which often renders existing methods or models inapplicable to intersections with heavy pedestrian and non-motorized traffic. In the meantime, there is also a need for understanding the relations between different types of delay and how they ea...

We present efficient and accurate algorithms for interference detection among objects undergoing polynomial deformation. The scope of our algorithms include physically-based models undergoing dynamic simulation subject to non-penetration constraints, variational models, deformable models used in soft object animation, geometric models including polygonal meshes, parametric surfaces such as Bézi...

We do a qualitative study on the mixed initial-boundary value problem in the elastodynamic theory of microstretch bodies. After we transform this problem in a temporally evolutionary equation on a Hilbert space, we will use some results from the theory of semigroups of linear operators in order to prove the continuous dependence of the solutions upon initial data and supply terms.

Integral geometry, as it is understood here, deals with measures on sets of geometric objects, and in particular with the determination of the total measure of various such sets having geometric significance. For example, given two convex bodies in Euclidean space, what is the total invariant measure of the set of all rigid motions which bring the first set into a position where it has nonempty...

In this paper we present a new method for Boolean operations (intersection, union and difference) of triangulated solids, and its applications in three-dimensional (3D) computerized geological modelling (3DGM). This method is adapted to arbitrary (convex or concave), close geological solids. Three major steps are included in this method: (1) Calculate intersection points between triangles. Our ...