2002/03/22 by Chris Doran, A. Lasenby, Anthony Lasenby +4
Computer Science · Mathematics · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #I.3.5 #I.3.6 #Mathematics and Applications #Metric Geometry (math.MG) #cs.CG #cs.GR #math.MG
paper · pdf · doi:10.48550/arxiv.cs/0203026
Proceedings, "Uncertainty in Geometric Computations", Sheffield 2001
arxiv created 2002/03/22 · openalex publication_date 2002/03/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to programming complicated geometrical operations. But there is a fundamental weakness in this approach - the Euclidean distance between points is not handled in a straightforward manner. Here we discuss a solution to this problem, based on conformal geometry. The language of geometric algebra is best suited to exploiting this geometry, as it handles the interior and exterior products in a single, unified framework. A number of applications are discussed, including a compact formula for reflecting a line off a general spherical surface.