Applications of Clifford Algebras in Computer Graphics

• Grant number: 16/21370-9
• Support Opportunities: Scholarships abroad - Research
• Effective date (Start): August 01, 2017
• Effective date (End): July 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computational Mathematics
• Valor Concedido/Desembolsado (R$): 137,855.47 / 137,855.47
• Principal Investigator: Jayme Vaz Junior
• Grantee: Jayme Vaz Junior
• Host Investigator: Stephen Alan Mann
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Research place: University of Waterloo, Canada

Abstract

We plan to investigate some applications of Clifford algebras in computer graphics through the analysis of three problems, namely: (i) the development of algebraic models for the description of geometric objects and their transformations, (ii) the formulation of discrete versions of the Clifford calculus, for applications in the discretization of continuum problems, (iii) the study of the use of the concept of spinors in the formulation of conformal immersions for the parametrization of surfaces.

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

VAZ, JR., JAYME; MANN, STEPHEN. Paravectors and the Geometry of 3D Euclidean Space. Advances in Applied Clifford Algebras, v. 28, n. 5, NOV 2018. (16/21370-9)

VAZ, JR., JAYME. On Paravectors and Their Associated Algebras. Advances in Applied Clifford Algebras, v. 29, n. 2, APR 2019. (16/21370-9)

VAZ, JR., JAYME; MANN, STEPHEN. DKP algebra, DKP equation, and differential forms. Journal of Mathematical Physics, v. 59, n. 8, AUG 2018. (16/21370-9)

VAZ, JR., JAYME; MANN, STEPHEN. On the Clifford Algebraic Description of Transformations in a 3D Euclidean Space. Advances in Applied Clifford Algebras, v. 30, n. 4, AUG 2 2020. (16/21370-9)