Cubic Curves and Cubic Surfaces from Contact Points in Conformal Geometric Algebra

  • Eckhard HitzerEmail author
  • Dietmar Hildenbrand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11542)


This work explains how to extend standard conformal geometric algebra of the Euclidean plane in a novel way to describe cubic curves in the Euclidean plane from nine contact points or from the ten coefficients of their implicit equations. As algebraic framework serves the Clifford algebra Cl(9, 7) over the real sixteen dimensional vector space \(\mathbb {R}^{9,7}\). These cubic curves can be intersected using the outer product based meet operation of geometric algebra. An analogous approach is explained for the description and operation with cubic surfaces in three Euclidean dimensions, using as framework Cl(19, 16).


Clifford algebra Conformal geometric algebra Cubic curves Cubic surfaces Intersections 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.International Christian UniversityMitaka-shiJapan
  2. 2.Technical University of DarmstadtDarmstadtGermany

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