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Deriving Linear Transformations in 3D Using Quaternion Algebra
March/April 2005 (vol. 25 no. 2)
pp. 93-95
Hua Zhang, Southwest Jiaotong University
Changqian Zhu, Southwest Jiaotong University
The recent method of deriving linear transformation in 3D physical space described by R. Goldman (see IEEE CG&A, vol. 23, no. 3, 2003, pp. 66-71) provided a unified framework, and works well with quaternion techniques in many transformations, but the other two kinds of the transformations, which are the parallel projection onto a plane and parallel projection onto a line, still work in the vector method. In this article, we propose a novel method to make the deriving linear transformation in the two parallel projections work well with quaternion techniques, therefore all the transformations described in Goldman's article could be derived with quaternion techniques.

1. R. Goldman, "Deriving Linear Transformations in Three Dimensions," IEEE Computer Graphics and Applications, vol. 23, no. 3, 2003, pp. 66-71.
2. M.R. Spiegel, Vector Analysis and an Introduction to Tensor Analysis, McGraw-Hill, 1974.
3. D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus, D. Reidel, 1984, pp. 1-41.
4. L. Dorst and S. Mann, "Geometric Algebra: A Computational Framework for Geometric Applications, Part 1," IEEE Computer Graphics and Applications, vol. 22, no. 3, 2002, pp. 24-31.
5. S. Mann and L. Dorst, "Geometric Algebra: A Computational Framework for Geometric Applications, Part 2," IEEE Computer Graphics and Applications, vol. 22, no. 4, 2002, pp. 58-67.

Index Terms:
quaternion and linear transformation
Citation:
Hua Zhang, Changqian Zhu, "Deriving Linear Transformations in 3D Using Quaternion Algebra," IEEE Computer Graphics and Applications, vol. 25, no. 2, pp. 93-95, March-April 2005, doi:10.1109/MCG.2005.38
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