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Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space

Naama Mayer, Efi Fogel, Dan Halperin
2010 Proceedings of the 14th ACM Symposium on Solid and Physical Modeling - SPM '10  
Abstract We present a novel algorithm for maintaining exact Minkowski sums of pairs of polytopes in R 3 , while one of the polytopes rotates.  ...  It efficiently handles the algebra of exact rotations about an arbitrary axis in R 3 , and it well balances between preprocessing time and space on the one hand, and query time on the other.  ...  The first approach decomposes the input polyhedra into convex pieces, computes the Minkowski sums between each pair of convex pieces, and obtains the union of their sums.  ... 
doi:10.1145/1839778.1839780 dblp:conf/sma/MayerFH10 fatcat:lozk3gn3ovfebpy3sbpzbpfpyq

Efficient Path Planning in Narrow Passages for Robots with Ellipsoidal Components [article]

Sipu Ruan, Karen L. Poblete, Hongtao Wu, Qianli Ma, Gregory S. Chirikjian
2022 arXiv   pre-print
Path planning has long been one of the major research areas in robotics, with PRM and RRT being two of the most effective classes of planners.  ...  robots and those with higher dimensional configuration spaces.  ...  III, computing an exact boundary of Minkowski sum between two general non-convex polytopes in R 3 can be as high as O(N 3 1 N 3 2 ), where N 1 and N 2 are the complexities (i.e., the number of facets)  ... 
arXiv:2104.04658v2 fatcat:jialxdjvfrdophrh6hcadumtaq

Minkowski Sum Construction and other Applications of Arrangements of Geodesic Arcs on the Sphere [article]

Efi Fogel
2009 arXiv   pre-print
We present two exact implementations of efficient output-sensitive algorithms that compute Minkowski sums of two convex polyhedra in 3D. We do not assume general position.  ...  These software components together with exact rational-arithmetic enable a robust, efficient, and elegant implementation of the Minkowski-sum constructions and the related applications.  ...  This sentense is far short of describing the magnitude of positive influence Danny had on this research and this researcher.  ... 
arXiv:0906.3240v1 fatcat:ajfjh2xxnjcqjb5yapo23nllb4

Mesh arrangements for solid geometry

Qingnan Zhou, Eitan Grinspun, Denis Zorin, Alec Jacobson
2016 ACM Transactions on Graphics  
We demonstrate the superior effectiveness and robustness of our method on a dataset of 10,000 "real-world" meshes from a popular online repository.  ...  Existing methods for 3D triangle meshes fall short in one way or another. Some methods are fast but fail to produce closed, self-intersection free output.  ...  A ∪ B A ∩ B A \ B B \ A ×1400 Minkowski sums Traditional binary boolean tests A traditional test for a boolean algorithm is to select two meshes, randomly rotate them, then conduct a binary operation  ... 
doi:10.1145/2897824.2925901 fatcat:vnvviey2gbdc3gnnjtkuzletf4

Collision detection and proximity queries

Sunil Hadap, Dave Eberle, Pascal Volino, Ming C. Lin, Stephane Redon, Christer Ericson
2004 Proceedings of the conference on SIGGRAPH 2004 course notes - GRAPH '04  
The proponents and expert practitioners from academia and industry will cover widely accepted and proved methodologies in detail.  ...  Course Abstract This course will primarily cover widely accepted and proved methodologies in collision detection.  ...  -Relies on the properties of the Minkowski difference of A and B • Not enough time to go into full detail -Just a brief description • Minkowski sum -The sweeping of one convex object with another Christer  ... 
doi:10.1145/1103900.1103915 dblp:conf/siggraph/HadapEVLRE04 fatcat:dwo7ebg7k5codaqw5xd6zdy4qm

Active zones in CSG for accelerating boundary evaluation, redundancy elimination, interference detection, and shading algorithms

Jaroslaw R. Rossignac, Herbert B. Voelcker
1988 ACM Transactions on Graphics  
or linear space transformations.  ...  This insight was precisely formulated in my influential paper on Active Zones, which has lead to a generation of simpler and more efficient approaches to the design, editing, evaluation, and rendering  ...  I have further expanded this approach to convex combinations of more than two shapes and have demonstrated its power by creating Bezier curves in the space of polyhedra.  ... 
doi:10.1145/49155.51123 fatcat:psnn6mwnrbhjlndd2bu6vatavi

Gross motion planning---a survey

Yong K. Hwang, Narendra Ahuja
1992 ACM Computing Surveys  
This paper surveys the work on gross-motionplanning, including motion planners for point robots, rigid robots, and manipulators in stationary, time-varying, constrained, and movable-object environments.The  ...  Motlonplanning lsoneofthe mostimportant areasofrobotics research The complexity of the motion-planning problem has hindered the developmentof practical algorithms.  ...  ACM Computmg Surveys, Vol. 24, No. 3, September ACKNOWLEDGMENTS This  ... 
doi:10.1145/136035.136037 fatcat:ylshsgnr5jhkje2uruafaf7bpa

Voronoi diagrams---a survey of a fundamental geometric data structure

Franz Aurenhammer
1991 ACM Computing Surveys  
ACM Computing Surveys, Vol. 23, No. 3, September  ...  Next, we study the duality of (order-1) power diagrams and convex hulls [Aurenhammer 1987al. Duality is usually defined for convex polyhedra. Let Z and Z' be two convex polyhedra in R'+ 1.  ...  Answering Crum's problem, Dewdney and Vranch [1977] exhibit an arbitrarily large set of Voronoi polyhedra in R 3 each pair of which shares a facet.  ... 
doi:10.1145/116873.116880 fatcat:a6vg5x4mj5fnnckqcrksfwlh2i

Three-dimensional object recognition

Paul J. Besl, Ramesh C. Jain
1985 ACM Computing Surveys  
This paper proposes a precise definition of the 3-D object recognition problem, discusses basic concepts associated with this problem, and reviews the relevant literature.  ...  A general-purpose computer vision system must be capable of recognizing threedimensional (3-D) objects.  ...  Because the extended Gaussian image uniquely determines convex polyhedra [Minkowski 18971, this technique appears to be ideal for convex object recognition without occlusion.  ... 
doi:10.1145/4078.4081 fatcat:fan2tkkvq5gg5h5crwvr27puiy

Learning Capacity in Simulated Virtual Neurological Procedures

Mattia Samuel Mancosu, Silvester Czanner, Martin Punter
2020 Journal of WSCG  
ACKNOWLEDGMENTS The authors acknowledge the support of the NSERC/Creaform Industrial Research Chair on 3-D Scanning for conducting the work presented in this paper.  ...  This work was partially supported by a grant of Ministry of Research and Innovation, CNCS -UEFISCDI, project number PN-III-P4-ID-PCE-2016-0842, within PNCDI III.  ...  The second approach for calculating Minkowski sums for non-convex polyhedra is to determine the convolution of two polyhedra, which is a superset of the Minkowski sum.  ... 
doi:10.24132/csrn.2020.3001.13 fatcat:uytlm7nytrhmnk553ellfhl54a

Partial surface and volume matching in three dimensions

G. Barequet, M. Sharir
1997 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this problem we are given two objects in 3-space, each represented as a set of points, and the goal is to find a rigid motion of one object which makes a sufficiently large portion of its boundary lying  ...  The algorithm steps through a sequence of rotations, in a steepest-descent style, and uses a novel technique for scoring the match for any fixed rotation.  ...  -Israeli Binational Science Foundation, and by the Fund for Basic Research administered by the Israeli Academy of Sciences.  ... 
doi:10.1109/34.615444 fatcat:oyn4twjpkjd3zawebm4zizrzra

Simplification and Compression of 3D Scenes [article]

Jarek Rossignac
1997 Eurographics State of the Art Reports  
The geometric complexity of 3D models used in scientific, industrial, medical, or military applications significantly exceeds the complexity of what can be rapidly downloaded over the internet and of what  ...  This situation is not likely to change, because the need for higher levels of accuracy in the 3D models and the complexity of the industrial and scientific 3D data sets increase at a much faster rate than  ...  Simplicial and other complexes A k-simplex is the convex hull of k+1 linearly independent points in E 3 .  ... 
doi:10.2312/egt.19971010 fatcat:2swtn4jzs5atxiwmv33rvguhue

Computational Symmetry in Computer Vision and Computer Graphics

Yanxi Liu
2008 Foundations and Trends in Computer Graphics and Vision  
In the arts and sciences, as well as in our daily lives, symmetry has made a profound and lasting impact.  ...  Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences.  ...  Thanks also go to Jingchen Liu, Kyle Brocklehurst, and Seungkyu Lee for collecting citations on symmetry related papers, and Jingchen Liu for creating Figure 1  ... 
doi:10.1561/0600000008 fatcat:t4x5zq3n5jcjnktzlft63eblnm

Tropical Ehrhart Theory and Tropical Volume [article]

Georg Loho, Matthias Schymura
2019 arXiv   pre-print
We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes.  ...  We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.  ...  Recent advances on the complexity of linear programming using tropical geometry [3] demonstrated a fruitful use of metric estimates for tropical polyhedra.  ... 
arXiv:1908.07893v1 fatcat:ifa63e7tcfd6lhmnwytbve5dmq

Tropical Ehrhart theory and tropical volume

Georg Loho, Matthias Schymura
2020 Research in the Mathematical Sciences  
We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes.  ...  We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.  ...  The authors were supported by the Swiss National Science Foundation (SNSF) within the project Convexity, geometry of numbers, and the complexity of integer programming (Nr. 163071) .  ... 
doi:10.1007/s40687-020-00228-1 pmid:33029581 pmcid:PMC7510937 fatcat:2xvrwj7khzdcfkmff5ne4v2t7m
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