Applications of Conformal Geometric Algebra in Computer Vision and Graphics

Abstract

AbstractThis paper introduces the mathematical framework of conformal geometric algebra (CGA) as a language for computer graphics and computer vision. Specifically it discusses a new method for pose and position interpolation based on CGA which firstly allows for existing interpolation methods to be cleanly extended to pose and position interpolation, but also allows for this to be extended to higher-dimension spaces and all conformal transforms (including dilations). In addition, we discuss a method of dealing with conics in CGA and the intersection and reflections of rays with such conic surfaces. Possible applications for these algorithms are also discussed.KeywordsComputer GraphicGeometric AlgebraDisplacement RotorParabolic MirrorQuadratic InterpolationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.