Truncation error for simplex propagation

1004 Downloads (Pure)

Abstract

Cube propagation has been suggested as an alternative to Jacobian integration for estimating the volume change under a deformation in three dimensions [Pai et al., 2013]. Cube propagation estimates the change in volume by approximating a three dimensional volume as a mesh of tetrahedra, which covers the interior of the volume and approximates the boundary as piece-wise triangular surface patches, and then estimate the change in volume under deformation of the volume as the sum of the change of volumes of the tetrahedra. This is an instance of the more general simplex counting, and in this technical report we derive the truncation error for simplex counting in 2 and 3 dimensions. In the appendix, we give a short review of numerical quadrature in 1 and 3 dimensions.
Original languageEnglish
PublisherDatalogisk Institut
Number of pages8
Publication statusPublished - 2013
SeriesKoebenhavns Universitet. Datalogisk Institut. Rapport
Number01/2013
ISSN0107-8283

Fingerprint

Dive into the research topics of 'Truncation error for simplex propagation'. Together they form a unique fingerprint.

Cite this