Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2)
IEEE Computer Graphics and Applications
Deriving Linear Transformations in Three Dimensions
IEEE Computer Graphics and Applications
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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.