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Anisotropic mesh quality measures and adaptation for polygonal meshes [PDF]
Journal of Computational Physics, 2020 Anisotropic mesh quality measures and anisotropic mesh adaptation are studied for polygonal meshes. Three sets of alignment and equidistribution measures are developed, one based on least squares fitting, one based on generalized barycentric mapping, and the other based on singular value decomposition of edge matrices.
Weizhang Huang, Yanqiu Wang
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Discrete Laplacians on general polygonal meshes [PDF]
ACM Transactions on Graphics, 2011 While the theory and applications of discrete Laplacians on triangulated surfaces are well developed, far less is known about the general polygonal case. We present here a principled approach for constructing geometric discrete Laplacians on surfaces with arbitrary polygonal faces ...
Marc Alexa, Max Wardetzky
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The Diamond Laplace for Polygonal and Polyhedral Meshes
Computer Graphics Forum, 2021 AbstractWe introduce a construction for discrete gradient operators that can be directly applied to arbitrary polygonal surface as well as polyhedral volume meshes. The main idea is to associate the gradient of functions defined at vertices of the mesh with diamonds: the region spanned by a dual edge together with its corresponding primal element — an ...
A. Bunge, M. Botsch, M. Alexa
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Progressive compression of manifold polygon meshes [PDF]
Computers & Graphics, 2012 This paper presents a new algorithm for the progressive compression of manifold polygon meshes. The input surface is decimated by several traversals that generate successive levels of detail through a specific patch decimation operator which combines vertex removal and local remeshing.
Maglo, Adrien +3 more
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Polylidar - Polygons From Triangular Meshes [PDF]
IEEE Robotics and Automation Letters, 2020 This paper presents Polylidar, an efficient algorithm to extract non-convex polygons from 2D point sets, including interior holes. Plane segmented point clouds can be input into Polylidar to extract their polygonal counterpart, thereby reducing map size and improving visualization.
Jeremy Castagno, Ella Atkins
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A steganalytic algorithm for 3D polygonal meshes [PDF]
2014 IEEE International Conference on Image Processing (ICIP), 2014 We propose a steganalytic algorithm for watermarks embedded by Cho et al.'s mean-based algorithm [1]. The main observation is that while in a clean model the means of Cho et al.'s normalized histogram bins are expected to follow a Gaussian distribution, in a marked model their distribution will be bimodal. The proposed algorithm estimates the number of
Yang, Ying +3 more
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Data hiding on 3D polygonal meshes [PDF]
Proceedings of the 2004 workshop on Multimedia and security, 2004 This paper presents a high-capacity method to embed information into the geometry of a 3D polygonal mesh. The method extends a previously reported work, to which several improvements have been brought. By construction, the new embedding algorithm is robust against rotation, scaling and translation attacks.
Maret, Y., Ebrahimi, T.
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Discrete differential operators on polygonal meshes [PDF]
ACM Transactions on Graphics, 2020 Geometry processing of surface meshes relies heavily on the discretization of differential operators such as gradient, Laplacian, and covariant derivative. While a variety of discrete operators over triangulated meshes have been developed and used for decades, a similar construction over polygonal meshes remains far less explored despite the prevalence
de Goes, Fernando +2 more
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Colour interpolants for polygonal gradient meshes [PDF]
Computer Aided Geometric Design, 2019 The gradient mesh is a powerful vector graphics primitive capable of representing detailed and scalable images. Borrowing techniques from 3D graphics such as subdivision surfaces and generalised barycentric coordinates, it has been recently extended from its original form supporting only rectangular arrays to (gradient) meshes of arbitrary manifold ...
Gerben J. Hettinga +2 more
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Approximating uniform triangular meshes in polygons
Theoretical Computer Science, 2000 AbstractWe consider the problem of triangulating a convex polygon using n Steiner points under the following optimality criteria: (1) minimizing the overall edge length ratio; (2) minimizing the maximum edge length; and (3) minimizing the maximum triangle perimeter. We establish a relation of these problems to a certain extreme packing problem.
Aurenhammer, F +4 more
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