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Cauchy problems for discrete affine minimal surfaces

Marcos Craizer, Thomas Lewiner, Ralph Teixeira (2012)

Archivum Mathematicum

In this paper we discuss planar quadrilateral (PQ) nets as discrete models for convex affine surfaces. As a main result, we prove a necessary and sufficient condition for a PQ net to admit a Lelieuvre co-normal vector field. Particular attention is given to the class of surfaces with discrete harmonic co-normals, which we call discrete affine minimal surfaces, and the subclass of surfaces with co-planar discrete harmonic co-normals, which we call discrete improper affine spheres. Within this classes,...

Close-to-optimal algorithm for rectangular decomposition of 3D shapes

Cyril Höschl IV, Jan Flusser (2019)

Kybernetika

In this paper, we propose a novel algorithm for a decomposition of 3D binary shapes to rectangular blocks. The aim is to minimize the number of blocks. Theoretically optimal brute-force algorithm is known to be NP-hard and practically infeasible. We introduce its sub-optimal polynomial heuristic approximation, which transforms the decomposition problem onto a graph-theoretical problem. We compare its performance with the state of the art Octree and Delta methods. We show by extensive experiments...

Courbure discrète ponctuelle

Vincent Borrelli (2006/2007)

Séminaire de théorie spectrale et géométrie

Soient S une surface de l’espace euclidien 𝔼 3 et M un ensemble de triangles euclidiens formant une approximation linéaire par morceaux de S autour d’un point P S , la courbure discrète ponctuelle K d ( P ) au sommet P de M est, par définition, le quotient du défaut angulaire par la somme des aires des triangles ayant P comme sommet. Un problème naturel est d’estimer la différence entre cette courbure discrète K d ( S ) et la courbure lisse K ( P ) de S en P . Nous présentons dans cet article des résultats obtenus dans [4], [5],...

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