Abstract
The representation of polynomials in the Bernstein basis has advantages over the usual monomial basis since it allows a simple geometric interpretation of the coefficients. It is shown how this so-called Bézier representation can be used for the calculation of the solution manifold of algebraic systems. In this contribution, the manifold is represented by a hierarchy of cuts describing its complete topology. The location of the cuts is calculated by iterated subdivision excluding non-relevant partition elements by using the convex hull property of the Bézier representation.
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© 1991 Springer-Verlag Berlin Heidelberg
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Müller, H., Otte, M. (1991). Solving algebraic systems in Bernstein-Bézier representation. In: Bieri, H., Noltemeier, H. (eds) Computational Geometry-Methods, Algorithms and Applications. CG 1991. Lecture Notes in Computer Science, vol 553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54891-2_12
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DOI: https://doi.org/10.1007/3-540-54891-2_12
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Online ISBN: 978-3-540-46459-4
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