Generation of real algebraic loci via complex detours
Abstract
We discuss the locus generation algorithm used by the dynamic geometry software Cinderella, and how it uses complex detours to resolve singularities. We show that the algorithm is independent of the orientation of its complex detours. We conjecture that the algorithm terminates if it takes small enough complex detours and small enough steps on every complex detour. Moreover, we introduce a variant of the algorithm that possibly generates entire real connected components of real algebraic loci. Several examples illustrate its use for organic generation of real algebraic loci. Another example shows how we can apply the algorithm to simulate mechanical linkages. Apparently, the use of complex detours produces physically reasonable motion of such linkages.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.05464
 Bibcode:
 2015arXiv151005464K
 Keywords:

 Mathematics  Algebraic Geometry;
 Computer Science  Computational Geometry;
 Mathematics  Complex Variables
 EPrint:
 minor revisions