Issue No. 03 - May/June (2006 vol. 8)

ISSN: 1521-9615

pp: 68-75

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MCSE.2006.54

Hua Zhang , Southwest Jiaotong University

Changqian Zhu , Southwest Jiaotong University

Qiang Peng , Southwest Jiaotong University

Jim X. Chen , George Mason University

ABSTRACT

Different methods exist for deriving a 3D linear transformation, including vector algebra, geometric algebra, and matrix algebra. In this installment of Visualization Corner, we introduce Ron Goldman's unified derivation method in vector algebra combined with our developments in geometric algebra. Our work includes using a unified method to derive various geometrical transformations, which are different from the current ray-tracing and transformation methods implemented in graphics algorithms and hardware. We hope that these derivations extend the geometric algebra research and applications to the computer graphics field.

INDEX TERMS

geometric algebra, computer graphics, linear transforms

CITATION

C. Zhu, Q. Peng, J. X. Chen and H. Zhang, "Using Geometric Algebra for 3D Linear Transformations," in

*Computing in Science & Engineering*, vol. 8, no. , pp. 68-75, 2006.

doi:10.1109/MCSE.2006.54

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