Interpolation and Intersection Algorithms and GPU

Date issued

2012

Journal Title

Journal ISSN

Volume Title

Publisher

IARIA

Abstract

Interpolation and intersection methods are closely related and used in computer graphics, visualization, computer vision etc. The Euclidean representation is used nearly exclusively not only in computational methods, but also in education despite it might lead to instability in computation in many cases. The projective geometry, resp. projective extension of the Euclidean space, offers many positive features from the computational and educational points of view with higher robustness and stability of computation. This paper presents simple examples of projective representation advantages, especially from the educational point of view. In particular, how interpolation and intersection can be applied to fundamental algorithms, which are becoming more robust, stable and faster due to compact formulation. Another advantage of the proposed approach is a simple implementation on vector-vector architectures, e.g. GPU, as it is based on matrixvector operations.

Description

Subject(s)

interpolační algoritmy, algoritmy průsečíků, princip duality, barycentrické souřadnice, lineární systém rovnic

Citation

ICONS 2012, Saint Gilles, Reunion Island, p. 193-198.