Work

Determining an optimal penetration among weighted regions in two and three dimensions

Year: 1999

Type: conference-paper

Abstract: We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a line segment) among weighted regions in 2-D and 3-D spaces.This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering.Our algorithms are based on a combination of geometric techniques and optimization methods.Our geometric analysis shows that the optimal penetration problem in d-D (d = 2,3) can be reduced to solving O(n2td-l)) instances of certain special types of nonlinear optimization problems, where n is the total number of vertices of the regions.We also give implementation results of our 2-D algorithms. IntroductionIn this paper, we study the following geometric optimization problem (called optimal penetration problem): Given a subdivision R with a total of n vertices in 2-D or 3-D space, divided in m regions R..i, i = 1,2,. . ., m, find a ray L such that L

Source: Annual Symposium on Computational Geometry (SoCG)

DOI: 10.1145/304893.304986

Authors: Danny Z. Chen, Ovidiu Daescu, Xiaobo (Sharon) Hu, Xiaodong Wu, Jinhui Xu

Institution: University of Notre Dame

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, University of Notre Dame, School of Medicine, University of Maryland

Awards: CAREER: Performance Analysis and Tradeoff for System-Level Design Exploration of Real-Time Embedded Systems, CAREER: Theoretical and Practical Solutions for Geometric Path Planning and Related Problems