Modeling and visualization of 3D polygonal mesh surfaces using geometric algebra

• Published in: Computers & graphics Vol. 28; no. 4; pp. 519 - 526
• Main Authors: Zaharia, M.D., Dorst, L.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2004
• Subjects: Boundary representations; Conformal model; Geometric algebra; Geometric transformations; Graphics data structures and data types; Polygonal mesh; Surface representations; Visualization; Visualization; Graphics data structures and data types; Surface representations; Conformal model; Geometric algebra; Polygonal mesh; Geometric transformations; Boundary representations
• ISSN: 0097-8493; 1873-7684
• DOI: 10.1016/j.cag.2004.04.007

The language of geometric algebra can be used in the development of computer graphics applications. This paper proposes a method to describe a 3D polygonal mesh model using a representation technique based on geometric algebra and the conformal model of the 3D Euclidean space. It describes also the stages necessary to develop an application that uses this formalism. The current application was used to validate the implementation of the main abstract operations characteristic to a geometric algebra computational environment (programming module GAP). The data structures that characterize this geometric algebra based modeling approach as well as the implementation of geometric algebra based methods for model visualization/transformation are developed in detail. The paper emphasizes the elegance and generality of the geometric algebra approach referring also to the necessary computational resources.