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2019 | OriginalPaper | Chapter

Ray-Tracing Objects and Novel Surface Representations in CGA

Authors : Sushant Achawal, Joan Lasenby, Hugo Hadfield, Anthony Lasenby

Published in: Advances in Computer Graphics

Publisher: Springer International Publishing

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Abstract

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 [1‐3]. 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.

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previous chapter GAC Application to Corner Detection Based on Eccentricity
Literature
1.
2.
Lasenby, A., Lasenby, J., Wareham, R.: A Covariant Approach to Geometry Using Geometric Algebra., Cambridge University Engineering Department (2004)
3.
Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry, 1st edn. Elsevier; Morgan Kaufmann, Amsterdam (2007)
4.
Breuils, S., Nozick, V., Fuchs, L.: Garamon: geometric algebra library generator. In: AACA: Topical Collection AGACSE 2018, IMECC UNICAM, Campinas, Brazil (2018)
5.
Hildenbrand, D.: Geometric computing in computer graphics using conformal geometric algebra. Comput. Graph. 29(5), 802–810 (2005)CrossRef
6.
Wareham, R.J., Lasenby, J.: Generating fractals using geometric algebra. Adv. Appl. Clifford Algebras 21(3), 647–659 (2011)MathSciNetCrossRef
7.
Hadfield, H., Lasenby, J.: Direct linear interpolation of conformal geometric objects. In: AACA: Topical Collection AGACSE 2018, IMECC UNICAM, Campinas, Brazil (2018)
8.
9.
Blinn, J.: Models of light reflection for computer synthesized pictures. ACM SIGGRAPH Comput. Graph. 11(2), 192–198 (1977)CrossRef
10.
Doran, C., Lasenby, A.: Geometric Algebra for Physicists, 1st edn. Cambridge University Press, Cambridge (2003)CrossRef
Metadata
Title
Ray-Tracing Objects and Novel Surface Representations in CGA
Authors
Sushant Achawal
Joan Lasenby
Hugo Hadfield
Anthony Lasenby
Copyright Year
2019
Book
Advances in Computer Graphics

Print ISBN: 978-3-030-22513-1

Electronic ISBN: 978-3-030-22514-8

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-22514-8_58

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