On the tangent model for the density of lines and a Monte Carlo method for computing hypersurface area

El Khaldi Khaldoun () and Saleeby Elias G. ()
Additional contact information
El Khaldi Khaldoun: Department of Computer Science, Notre Dame University-Louaize, Zouk Mosbeh, Lebanon
Saleeby Elias G.: Department of Mathematics and Natural Science, American University of Iraq,Sulaimani, Iraq

Monte Carlo Methods and Applications, 2017, vol. 23, issue 1, 13-20

Abstract: Methods to estimate surface areas of geometric objects in 3D are well known. A number of these methods are of Monte Carlo type, and some are based on the Cauchy–Crofton formula from integral geometry. Employing this formula requires the generation of sets of random lines that are uniformly distributed in 3D. One model to generate sets of random lines that are uniformly distributed in 3D is called the tangent model (see [4]). In this paper, we present an extension of this model to higher dimensions, and we examine its performance by estimating hypersurface areas of n-ellipsoids. Then we apply this method to estimate surface areas of hypersurfaces defined by Fermat-type varieties of even degree.

Keywords: Tangent model; Cauchy–Crofton formula; hypersurface area; Monte Carlo method (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1515/mcma-2017-0100 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:23:y:2017:i:1:p:13-20:n:2

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/mcma-2017-0100

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().