Efficiently approximating the minimum-volume bounding box of a point set in three dimensions

Keywords

Bounding overwatch, Volume (thermodynamics), Minimum bounding box, Mathematics, Point (geometry)

References

• Solving geometric problems with the rotating calipersGodfried T. Toussaint — 1983
• Covering a set of points by two axis-parallel boxesSergei Bespamyatnikh, Michael Segal — 2000
• Direct spatial search on pictorial databases using packed R-treesNick Roussopoulos, Daniel B. Leifker — 1985
• OBBTree: a hierarchical structure for rapid interference detectionS. Gottschalk, Ming C. Lin, Dinesh Manocha — 1996
• BOXTREE: A Hierarchical Representation for Surfaces in 3DGill Barequet, Bernard Chazelle, Leonidas Guibas — 1996
• Approximating shortest paths on a convex polytope in three dimensionsPankaj K. Agarwal, Sariel Har-Peled, Micha Sharir — 1997
• Approximating the Diameter of a Set of Points in the Euclidean SpaceÖmer Eğeci̇oğlu, Bahman Kalantari — 1989
• Inner and outerj-radii of convex bodies in finite-dimensional normed spacesPeter Gritzmann, Victor Klee — 1992
• An object centered hierarchical representation for 3D objects: The prism treeJean Ponce, Olivier Faugeras — 1987
• Output-sensitive results on convex hulls, extreme points, and related problemsTimothy M. Chan — 1995
• Applications of random sampling in computational geometry, IIKenneth L. Clarkson — 1988
• Approximate Shortest Paths and Geodesic Diameter on a Convex Polytope in Three DimensionsSariel Har-Peled — 1999
• New applications of random sampling in computational geometryKenneth L. Clarkson — 1987
• A LOWER BOUND FOR THE VOLUME OF STRICTLY CONVEX BODIES WITH MANY BOUNDARY LATTICE POINTSGeorge E. Andrews — 1963
• Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPsJames T. Klosowski, Martin Held, Joseph S. B. Mitchell — 1998
• The R+-Tree: A Dynamic Index for Multi-Dimensional ObjectsTimos Sellis, Nick Roussopoulos, Christos Faloutsos — 1987
• Approximate shortest paths and geodesic diameters on convex polytopes in three dimensionsSariel Har-Peled — 1997
• The R*-tree: an efficient and robust access method for points and rectanglesNorbert Beckmann, Hans‐Peter Kriegel, Ralf Schneider — 1990
• FastMap: a fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasetsChristos Faloutsos, King-Ip Lin — 1995
• Collision Detection for Interactive Graphics ApplicationsPhilip M. Hubbard — 1995

Cited by

• Game Engine Gems 2Eric Lengyel — 2011
• Design of CF for Automotive Body Parts Based on Artificial IntelligentMomang Bastian Wibar, N. M. N. M. Zuki — 2014
• Algorithms for continuous queries: A geometric approachAlbert Yu — 2013
• Theoretical and experimental aspects of ray shootingAllen Y. Chang — 2004
• Clustering and reconstructing large data setsJoseph S. B. Mitchell, Piyush Kumar — 2004
• Intégration CAO / calcul par reconstruction du modèle CAO à partir des résultats éléments finisBorhen Louhichi, Lilia Romdhane — 2008
• Experimental Study of Bounding Box AlgorithmsDarko Dimitrov, Mathias Holst, Christian Knauer — 2016
• SHREC'12 Track: 3D Mesh SegmentationGuillaume Lavoué, Jean‐Philippe Vandeborre, Halim Benhabiles — 2012
• High throughput patient-specific orthopaedic analysis: development of interactive tools and application to graft placement in anterior cruciate ligament reconstructionA. Ramme — 2012
• Approximate Minimum Volume Enclosing Ellipsoids Using Core SetsPiyush Kumar, E. Alper Yıldırım — 2003
• Inference and experimental design for percolation and random graph models.Andrei Iu. Bejan — 2010
• Computing Diameter in the Streaming and Sliding-Window ModelsJoan Feigenbaum, Sampath Kannan, Jian Zhang — 2002
• Geometric Approximation AlgorithmsSariel Har-Peled — 2011
• Modélisation mécanique intégrant des champs répulsifs pour la génération de trajectoires 5 axes hors collisionVirgile Lacharnay — 2014
• Management and visualisation of non-linear history of polygonal 3D modelsJozef Doboš — 2015
• Automated grasping for articulated structures using evolutionary learning algorithms.Ralf Globisch — 2008
• Enabling heterogeneous data integration and biomedical event prediction through ICT: the test case of cancer reoccurrence.Marco Picone, Sebastian Steger, Konstantinos Exarchos — 2011
• A literature review of bounding volumes hierarchy focused on collision detectionSimena Dinas, José María Bañón — 2015
• Geometric Avatar ProblemsMario E. Consuegra, Giri Narasimhan — 2013
• Penetration Depth of Two Convex Polytopes in 3DPankaj K. Agarwal, Leonidas Guibas, Sariel Har-Peled — 2000

Related papers

• Enhancing Bounding Volumes using Support Plane Mappings for Collision DetectionAthanasios Vogiannou, Κωνσταντίνος Μουστάκας, Dimitrios Tzovaras — 2010
• Algorithm of the Bounding Box Based on the OBBChao-Yang Geng, Min Liu — 2012
• A Method to Generate the Minimum Bounding Boxes for Shape-Arbitrary ObjectsHua Chen — 2010
• Fast Projected Area Computation for Three-Dimensional Bounding BoxesDieter Schmalstieg, Robert F. Tobler — 1999
• Temporally consistent caption detection in videos using a spatiotemporal 3D methodDongqing Zhang, Sitaram Bhagavathy, Joan Llach — 2009
• Bounding-box Centralization for Improving SiamFC++Huapeng Dong, Jiamin Jiao, Yong Bai — 2021
• Stability analysis of kinetic oriented bounding boxesWouter Meulemans, Kevin Verbeek, Jules Wulms — 2019
• Swift Interference Checking Based on Envelops Bounding Box DecompositionGao Feng — 2000