A Unified Framework of Elementary Geometric Transformation Representation
This provides a foundational mathematical framework for computer graphics and geometry, though it appears incremental as an extension of existing projective concepts.
The paper tackles the problem of representing diverse geometric transformations in a unified, coordinate-independent manner by proposing stereohomology as an extension of projective homology, resulting in a framework where transformations like reflection and translation are represented as Householder-Chen elementary matrices.
As an extension of projective homology, stereohomology is proposed via an extension of Desargues theorem and the extended Desargues configuration. Geometric transformations such as reflection, translation, central symmetry, central projection, parallel projection, shearing, central dilation, scaling, and so on are all included in stereohomology and represented as Householder-Chen elementary matrices. Hence all these geometric transformations are called elementary. This makes it possible to represent these elementary geometric transformations in homogeneous square matrices independent of a particular choice of coordinate system.