Ray-Tracing Objects and Novel Surface Representations in CGA

  • Sushant Achawal
  • Joan Lasenby
  • Hugo HadfieldEmail author
  • Anthony Lasenby
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11542)


Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds great promise in the field of computer graphics [1, 2, 3]. In this paper we implement a simple ray tracer in CGA with a Blinn-Phong lighting model and use it to examine ray intersections with surfaces generated from interpolating between objects [7]. An analytical method for finding the normal line to these interpolated surfaces is described. The expression is closely related to the concept of surface principal curvature from differential geometry and provides a novel way of describing the curvature of evolving surfaces.


Conformal Geometric Algebra Ray-tracing Direct object interpolation Surface curvature 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of EngineeringCambridge UniversityCambridgeUK
  2. 2.Department of PhysicsCambridge UniversityCambridgeUK

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