Monte Carlo approximation of form factors with error bounded a priori
type: Item
instance of: scholarly article
title: Monte Carlo approximation of form factors with error bounded a priori
zbMATH Open document ID: 0872.65002
DOI: 10.1007/PL00009297
published in: Discrete \& Computational Geometry
publication date: 1997-05-19T00:00:00Z
review text: A form factor is the fraction of energy leaving a surface element which directly reaches another surface element. In this paper, an integral geometric interpretation to form factors is given using the style and notation of \textit{L. A. Santaló} [Integral geometry and geometric probability (1976; Zbl 0342.53049)]. With this interpretation, the author develops a new and asymptotically efficient Monte Carlo method for the simultaneous approximation of all form factors in an occluded polyhedral environment. This algorithm is, for typical scences, one order of magnitude faster than methods based on the hemisphere paradigm or on Monte Carlo ray-shooting, and the error is bounded without recourse to special hypothesis.
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 52C99
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 1011312
zbMATH Keywords: error bounds
zbMATH Keywords: form factor
zbMATH Keywords: surface element
zbMATH Keywords: integral geometric interpretation
zbMATH Keywords: Monte Carlo method
zbMATH Keywords: algorithm
author: Marco Pellegrini
reviewed by: Y.-J. Xiao
describes a project that uses: ARVO
MaRDI profile type: Publication
cites work: Ray Shooting and Parametric Search
cites work: Q5514935
cites work: Algorithms for Reporting and Counting Geometric Intersections
cites work: Q4060253
cites work: Q5538132
cites work: Radiosity in Flatland
cites work: Q4844982
cites work: Random generation of combinatorial structures from a uniform distribution
cites work: A Monte-Carlo Algorithm for Estimating the Permanent
cites work: Ray shooting on triangles in 3-space
cites work: Q4875183
cites work: Q3992847
cites work: Dynamic planar point location with optimal query time
cites work: Q4110292
cites work: Q3481743
full work available at URL: pl00009297
OpenAlex ID: W2036397899
description: scientific article; zbMATH DE number 1011312