Graphics gems
Using quaternions for coding 3D transformations
Graphics gems
Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2)
IEEE Computer Graphics and Applications
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IEEE Computer Graphics and Applications
Deriving Linear Transformations in 3D Using Quaternion Algebra
IEEE Computer Graphics and Applications
Using Geometric Algebra for 3D Linear Transformations
Computing in Science and Engineering
Computational Aesthetics'05 Proceedings of the First Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging
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Elementary problems in 3D geometry can often be reduced to solving two simple simultaneous vector equations-one involving only the dot product and the other only the cross product-in one vector unknown. This article presents a general technique for solving such equations and then applies this method to derive explicit formulas for many of the linear transformations used in the standard 3D graphics pipeline.