Ortogonal Approach for Haptic Rendering Algorithm based in Conformal Geometric Algebra

Authors

Gabriel Sep?lveda-Cervantes, Instituto Polit´ecnico Nacional, CIDETEC, D.F, M´exicoFollow
Edgar A. Portilla-Flores, Instituto Polit´ecnico Nacional, CIDETEC, D.F, M´exicoFollow

Author Country (or Countries)

M´exico

Abstract

This work presents a novel method for haptic rendering contact force and surface properties for virtual objects using the Conformal Geometric Algebra orthogonal decomposition approach. The mathematical representation of geometric primitives along with collision algorithms based on its mathematical properties is presented. The orthogonal decomposition of contact and interaction forces is achieved using the same framework and dynamic properties in both subspaces are rendered simultaneously. Comparing with vector calculus, the Conformal Geometric Algebra (CGA) approach provides an easier and more intuitive way to deal with haptic rendering problems due to its inner properties and a simpler representation of geometric objects and linear transformation. The results of the evaluation of the method using a 3 DOF haptic device are presented.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090116

Recommended Citation

Sep?lveda-Cervantes, Gabriel and A. Portilla-Flores, Edgar (2023) "Ortogonal Approach for Haptic Rendering Algorithm based in Conformal Geometric Algebra," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 23.
DOI: http://dx.doi.org/10.12785/amis/090116
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/23