Hitzer & Hildenbrand: Cubic Curves and Cubic Surfaces from Contact Points in Conformal Geometric Algebra


E. Hitzer and D. Hildenbrand, Cubic Curves and Cubic Surfaces from Contact Points in Conformal Geometric Algebra, accepted for M. Gavrilova et al (eds.), Proceedings of Workshop ENGAGE 2019 at CGI 2019 with Springer LNCS, April 2019, 1 table. Preprint (PDF): http://vixra.org/pdf/1905.0026v3.pdf

Abstract: 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 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).

Keywords: Clifford algebra, conformal geometric algebra, cubic curves, cubic surfaces, intersections

Source: http://vixra.org/abs/1905.0026, accessed: 03 May 2019.

Advertisements

Leave a comment

Filed under publications

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s