On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra Algorithms and implementation
PurposeContact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called ent...
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| Vydáno v: | Engineering computations Ročník 37; číslo 1; s. 54 - 72 |
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Emerald Group Publishing Limited
16.01.2020
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| ISSN: | 0264-4401, 1758-7077 |
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| Abstract | PurposeContact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking.Design/methodology/approachIn this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted.FindingsNumerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small.Originality/valueThe equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies. |
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| AbstractList | PurposeContact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking.Design/methodology/approachIn this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted.FindingsNumerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small.Originality/valueThe equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies. |
| Author | Tan, Yuanqiang Feng, Y.T. |
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| Cites_doi | 10.1016/j.cma.2011.02.010 10.1109/56.2083 10.1145/361002.361007 10.1108/02644400410519785 10.1016/j.cad.2007.05.017 10.1145/235815.235821 10.1016/0148-9062(88)92293-0 10.1002/nme.502 10.1007/BF02712873 10.1680/geot.1979.29.1.47 10.1080/10867651.1999.10487502 |
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| References | (key2020020312132506800_ref015) 1997 (key2020020312132506800_ref008) 2002; 55 (key2020020312132506800_ref014) 2018 key2020020312132506800_ref017 (key2020020312132506800_ref019) 2013 (key2020020312132506800_ref007) 1979; 29 (key2020020312132506800_ref016) 2004 (key2020020312132506800_ref020) 1999; 4 (key2020020312132506800_ref021) 2001 (key2020020312132506800_ref006) 1988; 25 (key2020020312132506800_ref005) 1995 (key2020020312132506800_ref013) 2004; 24 (key2020020312132506800_ref010) 2012; 205-208 (key2020020312132506800_ref001) 1996; 22 (key2020020312132506800_ref003) 1997 (key2020020312132506800_ref011) 1988; 4 (key2020020312132506800_ref002) 1975; 18 (key2020020312132506800_ref004) 1996; 16 (key2020020312132506800_ref022) 2004; 21 (key2020020312132506800_ref023) 2006 (key2020020312132506800_ref012) 2007; 39 (key2020020312132506800_ref018) 2013 (key2020020312132506800_ref009) 2004; 21 |
| References_xml | – volume: 205-208 start-page: 169 year: 2012 ident: key2020020312132506800_ref010 article-title: Energy-conserving contact interaction models for arbitrarily shaped discrete elements publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/j.cma.2011.02.010 – ident: key2020020312132506800_ref017 – volume-title: Handbook of Discrete and Computational Geometry: Geometric Data Structures and Searching year: 2018 ident: key2020020312132506800_ref014 article-title: Chapter 39. Collision and proximity queries – volume: 4 start-page: 193 issue: 2 year: 1988 ident: key2020020312132506800_ref011 article-title: A fast procedure for computing the distance between complex objects in three-dimensional space publication-title: IEEE Journal on Robotics and Automation doi: 10.1109/56.2083 – volume: 18 start-page: 509 issue: 9 year: 1975 ident: key2020020312132506800_ref002 article-title: Multidimensional binary search trees used for associative searching publication-title: Communications of the ACM doi: 10.1145/361002.361007 – volume-title: Computational Contact Mechanics year: 2006 ident: key2020020312132506800_ref023 – volume-title: Frontiers of Discontinuous Numerical Methods and Practical Simulation in Engineering and Disaster Prevention year: 2013 ident: key2020020312132506800_ref019 article-title: Basic theory of two dimensional and three dimensional contacts – volume: 21 start-page: 265 issue: 2/3/4 year: 2004 ident: key2020020312132506800_ref009 article-title: A 2D polygon/polygon contact model: algorithmic aspects publication-title: Engineering Computations doi: 10.1108/02644400410519785 – volume-title: The Combined Finite-Discrete Element Method year: 2004 ident: key2020020312132506800_ref016 – volume: 39 start-page: 929 issue: 11 year: 2007 ident: key2020020312132506800_ref012 article-title: Exact and efficient construction of Minkowski sums of convex polyhedra with applications publication-title: Computer-Aided Design doi: 10.1016/j.cad.2007.05.017 – volume: 22 start-page: 469 issue: 4 year: 1996 ident: key2020020312132506800_ref001 article-title: The quickhull algorithm for convex hulls publication-title: ACM Transactions on Mathematical Software doi: 10.1145/235815.235821 – year: 1997 ident: key2020020312132506800_ref015 article-title: Fast and robust polyhedral collision detection – start-page: 189 volume-title: ACM International 3D Graphics Conference year: 1995 ident: key2020020312132506800_ref005 article-title: I-COLLIDE: an interactive and exact collision detection system for large scale environments – volume: 21 start-page: 215 issue: 2/3/4 year: 2004 ident: key2020020312132506800_ref022 article-title: A contact algorithm for partitioning N arbitrary sized objects publication-title: Engineering Computations – volume: 24 start-page: 165 issue: 2 year: 2004 ident: key2020020312132506800_ref013 article-title: Performance comparisons of tree based and cell based contact detection algorithms publication-title: Engineering Computations – volume-title: Game Developers Conference year: 2001 ident: key2020020312132506800_ref021 article-title: Proximity queries and penetration depth computation on 3d game objects – start-page: 3112 volume-title: International Conference Robotics and Automation year: 1997 ident: key2020020312132506800_ref003 article-title: Enhancing GJK: Computing minimum and penetration distances between convex polyhedra – volume: 25 start-page: 107 issue: 3 year: 1988 ident: key2020020312132506800_ref006 article-title: Formulation of a three-dimensional distinct element model – part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks publication-title: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts doi: 10.1016/0148-9062(88)92293-0 – volume: 55 start-page: 159 issue: 2 year: 2002 ident: key2020020312132506800_ref008 article-title: An augmented spatial digital tree algorithm for contact detection in computational mechanics publication-title: International Journal for Numerical Methods in Engineering doi: 10.1002/nme.502 – start-page: 253 volume-title: Proceedings of the 47th US Rock Mechanics/Geo-Mechanics Symposium year: 2013 ident: key2020020312132506800_ref018 article-title: Basic Equations of Two and Three Dimensional Contacts – volume: 16 start-page: 361 issue: 4 year: 1996 ident: key2020020312132506800_ref004 article-title: Optimal output-sensitive convex hull algorithms in two and three dimensions publication-title: Discrete and Computational Geometry doi: 10.1007/BF02712873 – volume: 29 start-page: 47 issue: 1 year: 1979 ident: key2020020312132506800_ref007 article-title: A discrete numerical model for granular assemblies publication-title: Géotechnique doi: 10.1680/geot.1979.29.1.47 – volume: 4 start-page: 7 issue: 2 year: 1999 ident: key2020020312132506800_ref020 article-title: A fast and robust GJK implementation for collision detection of convex objects publication-title: Journal of Graphics Tools doi: 10.1080/10867651.1999.10487502 |
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| SubjectTerms | Algorithms Computer graphics Deformation analysis Discrete element method Energy conservation Equivalence Mathematical models Performance evaluation Polygons Polyhedra Robotics |
| Subtitle | Algorithms and implementation |
| Title | On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra |
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