Investigations on reproducing kernel particle method enriched by partition of unity and visibility criterion

This work introduces a numerical integration technique based on partition of unity (PU) to reproducing kernel particle method (RKPM) and presents an implementation of the visibility criterion for meshfree methods. According to the theory of PU and the inherent features of Gaussian quadrature, the convergence property of the PU integration is studied in the paper. Moreover, the practical approaches to implement the PU integration are presented in different strategies. And a method to carry out visibility criterion is presented to handle the problems with a complex domain. Furthermore, numerical examples have been performed on the h-version and p-like version convergence studies of the PU integration and the validity of visibility criterion. The results demonstrate that PU integration is a feasible and effective numerical integration technique, and RKPM enriched by PU integration and visibility criterion is of more efficiency, versatility and high performance.The project is supported by National Natural Science Foundation of China under grant number 10202018.     

Online algorithms for searching and exploration in the plane

In this paper, we survey online algorithms in computational geometry that have been designed for mobile robots for searching a target and for exploring a region in the plane.     

Carving: a novel method of visibility preprocess- ing for un-restricted three-dimensional environments

carving , for visibility preprocessing of unrestricted (nonaxial) models. It is different from visibility preprocessing applied directly to nonaxial data. As a sculptor carves a statue, carving splits the nonaxial portion of a model, and results in a model with only axial polygons and a set of cuttings. The visibility information of the carved axial model can then be computed with the cuttings as detail objects.     

Visibility-based conformal cooling channel generation for rapid tooling

In plastic injection moulding process, cooling channel design is an essential factor that affects the quality of the moulded parts and the productivity of the process. Non-uniform cooling or long cooling cycle time would result if a poorly designed cooling channel is adopted. Due to limitations of traditional machining processes, the cooling channel is usually formed from straight-line drilled holes and only simple shapes are allowed, regardless of the shape complexity of the part being moulded. With the advent of rapid tooling technology, cooling channels in complex shapes can now be possible. However, there are not many design methodologies for supporting this type of cooling channel. In this paper, a methodology called visibility-based cooling channel generation is proposed for automatic preliminary cooling channel design for rapid tooling. The cooling process between a mould surface and a cooling channel is considered analogous to whether they can be visible from each other. Without loss of generality, the mould surface is approximated by a polyhedral terrain and is normally offset. A number of point light sources together that can illuminate the whole polyhedral terrain are assigned to suitable terrain offset vertices. A cooling channel is then generated by connecting all the assigned light sources. When comparing the conventional verification and redesign methods by melt flow analysis, computer-aided design and, a better design of cooling channel for its mould surface results in a short time independent of the experience of mould engineer.     

平面内一组线段的可见性

给定平面内一组互不相交的线段,本文讨论其相对于某点的可见性,给出了时间复杂性为O(mlogm)的算法,并证明了这一算法在时间上是最优的.     

Characterizing and recognizing the visibility graph of a funnel-shaped polygon

A funnel, which is notable for its fundamental role in visibility algorithms, is defined as a polygon that has exactly three convex vertices, two of which are connected by a boundary edge. In this paper we investigate the visibility graph of a funnel which we call an F-graph.We first present two characterizations of an F-graph, one of whose sufficiency proof itself is a linear time Real RAM algorithm for drawing a funnel on the plane that corresponds to an F-graph. We next give a linear-time algorithm for recognizing an F-graph. When the algorithm recognizes an F-graph, it also reports one of the Hamiltonian cycles defining the boundary of its corresponding funnel. This recognition algorithm takes linear time even on a RAM.We finally show that an F-graph is weakly triangulated and therefore perfect, which agrees with the fact that perfect graphs are related to geometric structures.This work was supported in part by the Korea Science and Engineering Foundation under Grant 91-01-01.     

Visibility and Dead-Zones in Digital Terrain Maps

The problem of detecting the visible and hidden areas of a topographic surface from a given viewpoint is well known, and has applications in GIS and other fields. The computational geometry literature is rich with solutions based on a polygonal representation of the surface. This work confronts the problem by working directly on the Digital Elevation Map which represents the terrain surface. We present an algorithm that processes discrete lines of sight from the viewpoint to the surface perimeter, and tests the unit-sized terrain elements along the discrete cross-sections defined by these lines. The algorithm is very efficient, performing O(n) testing operations, consisting of a few additions and no more than one multiplication each, where n is the number of the terrain elements in the map.