An introduction to ray tracing
An introduction to ray tracing
Oriented projective geometry
Illicit expressions in vector algebra
ACM Transactions on Graphics (TOG)
On the algebraic and geometric foundations of computer graphics
ACM Transactions on Graphics (TOG)
Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2)
IEEE Computer Graphics and Applications
Geometric Algebra: A computational framework for geometrical applications Part 1
IEEE Computer Graphics and Applications
Lines in Space: Part 3--The Two Matrices
IEEE Computer Graphics and Applications
Computer Graphics in its Fifth Decade: Ferment at the Foundations
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Gaigen 2:: a geometric algebra implementation generator
Proceedings of the 5th international conference on Generative programming and component engineering
Skinning with dual quaternions
Proceedings of the 2007 symposium on Interactive 3D graphics and games
Geometric skinning with approximate dual quaternion blending
ACM Transactions on Graphics (TOG)
An embedded, FPGA-based computer graphics coprocessor with native geometric algebra support
Integration, the VLSI Journal
Tutorial: Geometric computing in computer graphics using conformal geometric algebra
Computers and Graphics
Proceedings of the 20th ACM SIGPLAN workshop on Partial evaluation and program manipulation
Geometric algebra rotors for skinned character animation blending
SIGGRAPH Asia 2013 Technical Briefs
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Computations of 3D Euclidean geometry can be performed using various computational models of different effectiveness. In this article, the authors compare five alternatives: 3D linear algebra, 3D geometric algebra, a mix of 4D homogeneous coordinates and Plücker coordinates, a 4D homogeneous model using geometric algebra, and the 5D conformal model using geometric algebra. Higher dimensional models and models using geometric algebra can express geometric primitives, computations, and constructions more elegantly, but this elegance might come at a performance penalty. The authors explore these issues using the implementation of a simple ray tracer as a practical goal and guide and show how to implement the most important geometric computations of the ray-tracing algorithm using each of the five models as well as benchmark each implementation.