Projective Geometry, Duality and Plucker Coordinates for Geometric Computations with Determinants on GPUs

TL;DR

This paper explores the use of projective geometry, duality, and Plucker coordinates to improve geometric computations on GPUs, focusing on stability and efficiency for large data processing.

Contribution

It introduces a novel approach linking projective geometry and Plucker coordinates for more stable and efficient GPU-based geometric algorithms.

Findings

Relations between projective representation, duality, and Plucker coordinates are demonstrated.

The approach enhances computational stability on GPU architectures.

Geometric algorithms benefit from the proposed methods in large data scenarios.

Abstract

Many algorithms used are based on geometrical computation. There are several criteria in selecting appropriate algorithm from already known. Recently, the fastest algorithms have been preferred. Nowadays, algorithms with a high stability are preferred. Also technology and computer architecture, like GPU etc., plays a significant role for large data processing. However, some algorithms are ill-conditioned due to numerical representation used; result of the floating point representation. In this paper, relations between projective representation, duality and Plucker coordinates will be explored with demonstration on simple geometric examples. The presented approach is convenient especially for application on GPUs or vector-vector computational architectures