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Similarity search is a core component in various applications such as image matching, product recommendation and low-shot classification. However, single machine solutions are usually insufficient due to the large cardinality of modern…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-06-26 Shiyuan Deng , Xiao Yan , Kelvin K. W. Ng , Chenyu Jiang , James Cheng

Polyhedral compilers can perform complex loop optimizations that improve parallelism and cache behaviour of loops in the input program. These transformations result in significant performance gains on modern processors which have large…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-03-29 Aravind Acharya , Uday Bondhugula , Albert Cohen

This paper presents a new algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes. Drawing inspiration from the principle of minimal surfaces that minimize squared…

Graphics · Computer Science 2024-09-10 Kaixin Yu , Yifu Wang , Peng Song , Xiangqiao Meng , Ying He , Jianjun Chen

The honeycomb problem on the sphere asks for the perimeter-minimizing partition of the sphere into N equal areas. This article solves the problem when N=12. The unique minimizer is a tiling of 12 regular pentagons in the dodecahedral…

Metric Geometry · Mathematics 2007-05-23 Thomas C. Hales

We provide a number of new construction techniques for cubical complexes and cubical polytopes, and thus for cubifications (hexahedral mesh generation). As an application we obtain an instance of a cubical 4-polytope that has a…

Combinatorics · Mathematics 2007-05-23 Alexander Schwartz , Guenter M. Ziegler

Experimental mechanisms that yield the growth of homochiral copolymers over their heterochiral counterparts have been advocated by Lahav and co-workers. These chiral amplification mechanisms proceed through racemic {\beta}-sheet-controlled…

Quantitative Methods · Quantitative Biology 2012-12-19 Celia Blanco , David Hochberg

This article answers an important theoretical question: How many different subdivisions of the hexahedron into tetrahedra are there? It is well known that the cube has five subdivisions into 6 tetrahedra and one subdivision into 5…

Computational Geometry · Computer Science 2018-12-14 Jeanne Pellerin , Kilian Verhetsel , Jean-Francois Remacle

Checking mesh validity is a mandatory step before doing any finite element analysis. If checking the validity of tetrahedra is trivial, checking the validity of hexahedral elements is far from being obvious. In this paper, a method that…

Computational Geometry · Computer Science 2017-08-08 Amaury Johnen , Jean-Christophe Weill , Jean-François Remacle

Constructing an adaptive hexahedral tessellation to fit an input triangle boundary is a key challenge in grid-based methods. The conventional method first removes outside elements (RO) and then projects the axis-aligned boundary onto the…

Computational Geometry · Computer Science 2026-01-07 Hua Tong , Yongjie Jessica Zhang

The problem of image registration is finding a transformation that aligns two images, such that the corresponding points are in the same location. This paper introduces a simple, end-to-end trainable algorithm that is implementable in a few…

Computer Vision and Pattern Recognition · Computer Science 2025-10-07 Stefan Dirnstorfer

This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…

Computational Geometry · Computer Science 2017-05-30 Vitoriano Ruas

In this paper we provide a general method to construct four-parameter families of complex Hadamard matrices of order six. Our approach is to write a 6-dimensional matrix as composed of four blocks, each one in the form of a circulant…

Mathematical Physics · Physics 2012-07-29 Petre Dita

We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap…

Numerical Analysis · Mathematics 2023-03-28 Tobias Jonsson , Mats G. Larson , Karl Larsson

We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with…

Graphics · Computer Science 2024-08-01 Ryan Capouellez , Denis Zorin

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…

Numerical Analysis · Mathematics 2022-05-11 Pablo Antolin , Xiaodong Wei , Annalisa Buffa

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to…

Graphics · Computer Science 2022-02-04 Yixin Hu , Teseo Schneider , Bolun Wang , Denis Zorin , Daniele Panozzo

The new concept of a system of hex equations is introduced as an overdetermined system of six five-point face-centered quad equations defined on six vertices of a hexagon. For a consistent system of hex equations, two variables on…

Mathematical Physics · Physics 2022-05-06 Andrew P. Kels

The results of experimental tests of a novel method for moving large (pyramid construction size) stone blocks by rolling them are presented. The method is implemented by tying 12 identical rods of appropriately chosen radius to the faces of…

Popular Physics · Physics 2015-02-26 Joseph West , Greg Gallagher , Kevin Waters , Stephen Ward , Tia Ward

It is known that the chain complex of a simplex on $q$ vertices can be used to construct a free resolution of any ideal generated by $q$ monomials, and as a direct result, the Betti numbers always have binomial upper bounds, given by the…

Commutative Algebra · Mathematics 2025-05-14 Louis Bu , Sara Faridi , Iresha Madduwe Hewalage , Thiago Holleben , Hasan Mahmood , Dharm Veer , Kyle Wang , Scott Wesley

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…

Graphics · Computer Science 2016-11-08 Kaimo Hu , Dong-Ming Yan , David Bommes , Pierre Alliez , Bedrich Benes