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Interpolation of syzygies for implicit matrix representations

Abstract : We examine matrix representations of curves and surfaces based on syzygies and constructed by interpolation through points. They are implicit representations of objects given as point clouds. The corresponding theory, including moving lines, curves and surfaces, has been developed for parametric models. Our contribution is to show how to compute the required syzygies by interpolation, when the geometric object is given by a point cloud whose sampling satisfies mild assumptions. We focus on planar and space curves, where the theory of syzygies allows us to design an exact algorithm yielding the optimal implicit expression. The method extends readily to surfaces without base points defined over triangular patches. Our Maple implementation has served to produce the examples in this paper and is available upon demand by the authors.
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Contributor : Christos Konaxis Connect in order to contact the contributor
Submitted on : Tuesday, December 27, 2016 - 7:09:34 PM
Last modification on : Wednesday, November 3, 2021 - 4:18:48 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 5:22:56 AM


  • HAL Id : hal-01421866, version 1



Ioannis Emiris, Konstantinos Gavriil, Christos Konaxis. Interpolation of syzygies for implicit matrix representations. 2016. ⟨hal-01421866⟩



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