Foundations of Conic Conformal Geometric Algebra and Compact Versors for Rotation, Translation and Scaling

被引：0
作者：
Eckhard Hitzer
Stephen J. Sangwine
机构：
[1] International Christian University,School of Computer Science and Electronic Engineering
[2] University of Essex,undefined
来源：
Advances in Applied Clifford Algebras | 2019年 / 29卷
关键词：
Clifford algebra; Conformal geometric algebra; Conics; Versors; Primary 15A66; Secondary 11E88; 15A15; 15A09;
D O I：
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摘要：
This paper explains in algebraic detail how two-dimensional conics can be defined by the outer products of conformal geometric algebra (CGA) points in higher dimensions. These multivector expressions code all types of conics in arbitrary scale, location and orientation. Conformal geometric algebra of two-dimensional Euclidean geometry is fully embedded as an algebraic subset. With small model preserving modifications, it is possible to consistently define in conic CGA versors for rotation, translation and scaling, similar to Hrdina et al. (Appl Clifford Algebras 28(66), 1–21, https://doi.org/10.1007/s00006-018-0879-2, 2018), but simpler, especially for translations.
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