Issue No.03 - May/June (2006 vol.8)
Changqian Zhu , Southwest Jiaotong University
Qiang Peng , Southwest Jiaotong University
Hua Zhang , Southwest Jiaotong University
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MCSE.2006.54
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.
geometric algebra, computer graphics, linear transforms
Changqian Zhu, Qiang Peng, Hua Zhang, "Using Geometric Algebra for 3D Linear Transformations", Computing in Science & Engineering, vol.8, no. 3, pp. 68-75, May/June 2006, doi:10.1109/MCSE.2006.54