Abstract
In geometric constraint solving, it is usual to consider Cayley-Menger determinants in particular in robotics and molecular chemistry, but also in CAD. The idea is to regard distances as coordinates and to build systems where the unknowns are distances between points. In some cases, this allows to drastically reduce the size of the system to solve. On the negative part, it is difficult to know in advance if the yielded systems will be small and then to build these systems. In this paper, we describe two algorithms which allow to generate such systems with a minimum number of equations according to a chosen reference with 3 or 4 fixed points. We can then compute the smaller systems by enumeration of references. We also discuss what are the criteria so that such system can be efficiently solved by homotopy.
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Mathis, P., Schreck, P. (2013). Equation Systems with Free-Coordinates Determinants. In: Ida, T., Fleuriot, J. (eds) Automated Deduction in Geometry. ADG 2012. Lecture Notes in Computer Science(), vol 7993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40672-0_5
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DOI: https://doi.org/10.1007/978-3-642-40672-0_5
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