Properties of a Level Set Algorithm for the Visibility Problems

Authors:
Chiu-Yen Kao;Richard Tsai
Affiliations:
Department of Mathematics, The Ohio State University, Columbus, USA 43210;Department of Mathematics, University of Texas at Austin, Austin, USA 78712
Venue:
Journal of Scientific Computing
Year:
2008

Citing 11
Cited 1

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
Intersecting line segments, ray shooting, and other applications of geometric partitioning techniques

No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit

Nonlinear Analysis: Theory, Methods & Applications
Ray Shooting Amidst Convex Polyhedra and PolyhedralTerrains in Three Dimensions

SIAM Journal on Computing
Ray shooting amidst convex polygons in 2D

Journal of Algorithms
Ray Shooting Amidst Spheres in Three Dimensions and Related Problems

SIAM Journal on Computing
Temporally coherent conservative visibility

Selected papers from the 12th annual symposium on Computational Geometry
Conservative volumetric visibility with occluder fusion

Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Visibility and its dynamics in a PDE based implicit framework

Journal of Computational Physics
Fast Sweeping Methods for Static Hamilton--Jacobi Equations

SIAM Journal on Numerical Analysis
Computational Study of Fast Methods for the Eikonal Equation

SIAM Journal on Scientific Computing

Information-Seeking Control Under Visibility-Based Uncertainty

Journal of Mathematical Imaging and Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study an implicit visibility formulation and show that the corresponding closed form formula satisfies a dynamic programming principle, and is the viscosity solution of a Hamilton-Jacobi type equation involving jump discontinuities in the Hamiltonian. We derive the corresponding discretization in multi-dimensions and prove convergence of the corresponding numerical approximations. Finally, we introduce a generalization of the original Hamilton-Jacobi equation and the corresponding discretization that can be solved efficiently using either the fast sweeping or the fast marching methods. Thus, the visibility of an observer in non-constant media can be computed. We also introduce a specialization of the algorithms for environments in which occluders are described by the graph of a function.