Efficient Collision Detection Using Bounding Volume Hierarchies of K
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Tree Code for Collision Detection of Large Numbers of Particles
Tree Code for Collision Detection of Large Numbers of Particles Application for the Breit-Wheeler Process [preprint] O. Jansen, E. d’Humi`eres, X. Ribeyre, S. Jequier, V.T. Tikhonchuk Univ. Bordeaux/CNRS/CEA, Centre Lasers Intenses et Applications [email protected] August 4, 2016 Abstract Collision detection of a large number N of particles can be challenging. Directly testing N particles for 2 collision among each other leads to N queries. Especially in scenarios, where fast, densely packed particles interact, challenges arise for classical methods like Particle-in-Cell or Monte-Carlo. Modern collision detec- tion methods utilising bounding volume hierarchies are suitable to overcome these challenges and allow a detailed analysis of the interaction of large number of particles. This approach is applied to the analysis of the collision of two photon beams leading to the creation of electron-positron pairs. Keywords tree code; collision detection; QED; Breit-Wheeler process; pair creation; astronomy 1 Introduction Modelling a large number of particles often is a challenge in physics. Many-body problems are well known in astronomy, plasma physics, solid state physics and other disciplines. In astronomy a common way to overcome the challenge of simulating a many-body problem, like the movement of stars of one galaxy under each others gravitational force, is to use the Barnes-Hut (BH) method [1]. In a BH simulation space is partitioned in an hierarchic octree structure. The tree branches grow towards successive smaller volumes of space in such way as to include at maximum one particle (star) in each leaf node, while still covering the entirety of the simulation domain. -
Efficient Algorithms for Two-Phase Collision Detection
MERL { A MITSUBISHI ELECTRIC RESEARCH LABORATORY http://www.merl.com Ecient Algorithms for Two-Phase Collision Detection Brian Mirtich TR-97-23 Decemb er 1997 Abstract This article describ es practical collision detection algorithms for rob ot motion planning. Attention is restricted to algorithms that handle rigid, p olyhedral ge- ometries. Both broad phase and narrow phase detection strategies are discussed. For the broad phase, an algorithm using axes-aligned b ounding b oxes and a hi- erarchical spatial hash table is describ ed. For the narrow-phase, the Lin-Canny algorithm is presented. Alternatives to these algorithms are also discussed. Fi- nally, the article describ es a scheduling paradigm for managing collision checks that can further reduce computation time. Pointers to downloadable software are included. To appear in Practical Motion Planning in Rob otics: Current Approaches and Future Directions, K. Gupta and A.P. del Pobil, editors. This work may not b e copied or repro duced in whole or in part for any commercial purp ose. Permission to copy in whole or in part without payment of fee is granted for nonpro t educational and research purp oses provided that all such whole or partial copies include the following: a notice that such copying is by p er- mission of Mitsubishi Electric Information Technology Center America; an acknowledgment of the authors and individual contributions to the work; and all applicable p ortions of the copyright notice. Copying, repro duction, or republishing for any other purp ose shall require a license with payment of fee to Mitsubishi Electric Information Technology Center America. -
Fast Oriented Bounding Box Optimization on the Rotation Group SO(3, R)
Fast oriented bounding box optimization on the rotation group SO(3; R) CHIA-TCHE CHANG1, BASTIEN GORISSEN2;3 and SAMUEL MELCHIOR1;2 1Universite´ catholique de Louvain, Department of Mathematical Engineering (INMA) 2Universite´ catholique de Louvain, Applied Mechanics Division (MEMA) 3Cenaero An exact algorithm to compute an optimal 3D oriented bounding box was published in 1985 by Joseph O’Rourke, but it is slow and extremely hard C b to implement. In this article we propose a new approach, where the com- Xb putation of the minimal-volume OBB is formulated as an unconstrained b b optimization problem on the rotation group SO(3; R). It is solved using a hybrid method combining the genetic and Nelder-Mead algorithms. This b b method is analyzed and then compared to the current state-of-the-art tech- b b X b niques. It is shown to be either faster or more reliable for any accuracy. Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Compu- b b b tational Geometry and Object Modeling—Geometric algorithms; Object b b representations; G.1.6 [Numerical Analysis]: Optimization—Global op- eξ b timization; Unconstrained optimization b b b b General Terms: Algorithms, Performance, Experimentation b Additional Key Words and Phrases: Computational geometry, optimization, b ex b manifolds, bounding box b b ∆ξ ∆η 1. INTRODUCTION This article deals with the problem of finding the minimum-volume oriented bounding box (OBB) of a given finite set of N points, 3 denoted by R . The problem consists in finding the cuboid, Fig. 1. Illustration of some of the notation used throughout the article. -
An Optimal Solution for Implementing a Specific 3D Web Application
IT 16 060 Examensarbete 30 hp Augusti 2016 An optimal solution for implementing a specific 3D web application Mathias Nordin Institutionen för informationsteknologi Department of Information Technology Abstract An optimal solution for implementing a specific 3D web application Mathias Nordin Teknisk- naturvetenskaplig fakultet UTH-enheten WebGL equips web browsers with the ability to access graphic cards for extra processing Besöksadress: power. WebGL uses GLSL ES to communicate with graphics cards, which uses Ångströmlaboratoriet Lägerhyddsvägen 1 different Hus 4, Plan 0 instructions compared with common web development languages. In order to simplify the development process there are JavaScript libraries handles the Postadress: Box 536 751 21 Uppsala communication with WebGL. On the Khronos website there is a listing of 35 different Telefon: JavaScript libraries that access WebGL. 018 – 471 30 03 It is time consuming for developers to compare the benefits and disadvantages of all Telefax: these 018 – 471 30 00 libraries to find the best WebGL library for their need. This thesis sets up requirements of a Hemsida: specific WebGL application and investigates which libraries that are best for http://www.teknat.uu.se/student implmeneting its requirements. The procedure is done in different steps. Firstly is the requirements for the 3D web application defined. Then are all the libraries analyzed and mapped against these requirements. The two libraries that best fulfilled the requirments is Three.js with Physi.js and Babylon.js. The libraries is used in two seperate implementations of the intitial game. Three.js with Physi.js is the best libraries for implementig the requirements of the game. -
Mathematical Approaches for Collision Detection in Fundamental Game Objects
Mathematical Approaches for Collision Detection in Fundamental Game Objects Weihu Hong1 , Junfeng Qu2, Mingshen Wu3 1 Department of Mathematics, Clayton State University, Morrow, GA, 30260 2 Department of Information Technology, Clayton State University, Morrow, GA, 30260 3Department of Mathematics, Statistics, and Computer Science, University of Wisconsin-Stout, Menomonie, WI 54751 Otherwise, a lot of false alarm will be introduced in collision Abstract – This paper presents mathematical solutions for detection as show in Figure 1, where two objects, one circle computing whether or not fundamental objects in game and one pentagon, are not collided at all even the represented development collide with each other. In game development, sprites collide each other. detection of collision of two or more objects is often brought up. By categorizing most fundamental boundaries in game object, this paper will provide some mathematical fundamental methods for detection of collisions between objects identified. The approached methods provide more precise and efficient solutions to detect collisions between most game objects with mathematical formula proposed. Keywords: Collision detection, algorithm, sprite, game object, game development. 1 Introduction Figure 1. Collision detection based on Boundary The goal of collision detection is to automatically report a geometric contact when it is about to occur or has actually occurred. It is very common in game development that objects in the game science controlled by game player might collide each other. Collision detection is an essential component in video game implementation because it delivers events in the game world and drives game moving though game paths designed. In most game developing environment, game developers relies on written APIs to detect collisions in the game, for example, XNA Game Studio from Microsoft, Cocoa from (a) (b) Apple, and some other software packages developed by other parties. -
Opencl Accelerated Rigid Body and Collision Detection
OpenCL accelerated rigid body and collision detection Erwin Coumans Advanced Micro Devices Robotics: Science and Systems Conference 2011 Overview • Intro • GPU broadphase acceleration structures • GPU convex contact generation and reduction • GPU BVH acceleration for concave shapes • GPU constraint solver Robotics: Science and Systems Conference 2011 Industry view PS3, Xbox 360, x86, PowerPC, PC, iPhone, Android Havok, PhysX Cell, ARM Bullet, ODE, Newton, PhysBAM, Box2D OpenCL, CUDA Hardware Platform C++ APIs and Implementations Custom in-house Rockstar, Epic physics engines EA, Disney Games Industry Content Creation Maya, 3ds Max, Houdini, LW, Game and Film Tools Cinema 4D Sony Imageworks physics Simulation Movie Industry Blender Data PDI Dreamworks representation Academia, Universities Conferences, binary .hkx, ILM, Disney Presentations .bullet format Stanford, UNC FBX, COLLADA GDC, SIGGRAPH etc. Robotics: Science and Systems Conference 2011 Our open source work • Bullet Physics SDK, http://bulletphysics.org • Sony Computer Entertainment Physics Effects • OpenCL/DirectX11 GPU physics research Robotics: Science and Systems Conference 2011 OpenCL™ • Open development platform for multi-vendor heterogeneous architectures • The power of AMD Fusion: Leverages CPUs and GPUs for balanced system approach • Broad industry support: Created by architects from AMD, Apple, IBM, Intel, NVIDIA, Sony, etc. AMD is the first company to provide a complete OpenCL solution • Kernels written in subset of C99 Robotics: Science and Systems Conference 2011 Particle -
Parallel Construction of Bounding Volumes
SIGRAD 2010 Parallel Construction of Bounding Volumes Mattias Karlsson, Olov Winberg and Thomas Larsson Mälardalen University, Sweden Abstract This paper presents techniques for speeding up commonly used algorithms for bounding volume construction using Intel’s SIMD SSE instructions. A case study is presented, which shows that speed-ups between 7–9 can be reached in the computation of k-DOPs. For the computation of tight fitting spheres, a speed-up factor of approximately 4 is obtained. In addition, it is shown how multi-core CPUs can be used to speed up the algorithms further. Categories and Subject Descriptors (according to ACM CCS): I.3.6 [Computer Graphics]: Methodology and techniques—Graphics data structures and data types 1. Introduction pute [MKE03, LAM06]. As Sections 2–4 show, the SIMD vectorization of the algorithms leads to generous speed-ups, A bounding volume (BV) is a shape that encloses a set of ge- despite that the SSE registers are only four floats wide. In ometric primitives. Usually, simple convex shapes are used addition, the algorithms can be parallelized further by ex- as BVs, such as spheres and boxes. Ideally, the computa- ploiting multi-core processors, as shown in Section 5. tion of the BV dimensions results in a minimum volume (or area) shape. The purpose of the BV is to provide a simple approximation of a more complicated shape, which can be 2. Fast SIMD computation of k-DOPs used to speed up geometric queries. In computer graphics, A k-DOP is a convex polytope enclosing another object such ∗ BVs are used extensively to accelerate, e.g., view frustum as a complex polygon mesh [KHM 98]. -
Bounding Volume Hierarchies
Simulation in Computer Graphics Bounding Volume Hierarchies Matthias Teschner Outline Introduction Bounding volumes BV Hierarchies of bounding volumes BVH Generation and update of BVs Design issues of BVHs Performance University of Freiburg – Computer Science Department – 2 Motivation Detection of interpenetrating objects Object representations in simulation environments do not consider impenetrability Aspects Polygonal, non-polygonal surface Convex, non-convex Rigid, deformable Collision information University of Freiburg – Computer Science Department – 3 Example Collision detection is an essential part of physically realistic dynamic simulations In each time step Detect collisions Resolve collisions [UNC, Univ of Iowa] Compute dynamics University of Freiburg – Computer Science Department – 4 Outline Introduction Bounding volumes BV Hierarchies of bounding volumes BVH Generation and update of BVs Design issues of BVHs Performance University of Freiburg – Computer Science Department – 5 Motivation Collision detection for polygonal models is in Simple bounding volumes – encapsulating geometrically complex objects – can accelerate the detection of collisions No overlapping bounding volumes Overlapping bounding volumes → No collision → Objects could interfere University of Freiburg – Computer Science Department – 6 Examples and Characteristics Discrete- Axis-aligned Oriented Sphere orientation bounding box bounding box polytope Desired characteristics Efficient intersection test, memory efficient Efficient generation -
Graphics Pipeline and Rasterization
Graphics Pipeline & Rasterization Image removed due to copyright restrictions. MIT EECS 6.837 – Matusik 1 How Do We Render Interactively? • Use graphics hardware, via OpenGL or DirectX – OpenGL is multi-platform, DirectX is MS only OpenGL rendering Our ray tracer © Khronos Group. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. 2 How Do We Render Interactively? • Use graphics hardware, via OpenGL or DirectX – OpenGL is multi-platform, DirectX is MS only OpenGL rendering Our ray tracer © Khronos Group. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/. • Most global effects available in ray tracing will be sacrificed for speed, but some can be approximated 3 Ray Casting vs. GPUs for Triangles Ray Casting For each pixel (ray) For each triangle Does ray hit triangle? Keep closest hit Scene primitives Pixel raster 4 Ray Casting vs. GPUs for Triangles Ray Casting GPU For each pixel (ray) For each triangle For each triangle For each pixel Does ray hit triangle? Does triangle cover pixel? Keep closest hit Keep closest hit Scene primitives Pixel raster Scene primitives Pixel raster 5 Ray Casting vs. GPUs for Triangles Ray Casting GPU For each pixel (ray) For each triangle For each triangle For each pixel Does ray hit triangle? Does triangle cover pixel? Keep closest hit Keep closest hit Scene primitives It’s just a different orderPixel raster of the loops! -
A New Fast and Robust Collision Detection and Force Computation Algorithm Applied to the Physics Engine Bullet: Method, Integration, and Evaluation
Conference and Exhibition of the European Association of Virtual and Augmented Reality (2014) G. Zachmann, J. Perret, and A. Amditis (Editors) A New Fast and Robust Collision Detection and Force Computation Algorithm Applied to the Physics Engine Bullet: Method, Integration, and Evaluation Mikel Sagardia †, Theodoros Stouraitis‡, and João Lopes e Silva§ German Aerospace Center (DLR), Institute of Robotics and Mechatronics, Germany Abstract We present a collision detection and force computation algorithm based on the Voxelmap-Pointshell Algorithm which was integrated and evaluated in the physics engine Bullet. Our algorithm uses signed distance fields and point-sphere trees and it is able to compute collision forces between arbitrary complex shapes at simulation frequencies smaller than 1 msec. Utilizing sphere hierarchies, we are able to rapidly detect likely colliding areas, while the point trees can be used for processing colliding regions in a level-of-detail manner. The integration into the physics engine Bullet was performed inheriting interface classes provided in that framework. We compared our algorithm with Bullet’s native GJK, GJK with convex decomposition, and GImpact, varying the resolution and the scenarios. Our experiments show that our integrated algorithm performs with similar computation times as the standard collision detection algorithms in Bullet if low resolutions are chosen. With high resolutions, our algorithm outperforms Bullet’s native implementations and objects behave realistically. Categories and Subject Descriptors (according to ACM CCS): Computing Methodologies [I.3.5]: Computational Geometry and Object Modeling—Geometric algorithms, Object hierarchies; Computing Methodologies [I.3.7]: Three-Dimensional Graphics and Realism—Animation, Virtual reality. 1. Introduction The physics library Bullet [Cou14] provides with several collision detection implementations able to handle simple Methods that perform collision detection and force compu- geometries and a powerful rigid body dynamics framework. -
Parallel Reinsertion for Bounding Volume Hierarchy Optimization
EUROGRAPHICS 2018 / D. Gutierrez and A. Sheffer Volume 37 (2018), Number 2 (Guest Editors) Parallel Reinsertion for Bounding Volume Hierarchy Optimization D. Meister and J. Bittner Czech Technical University in Prague, Faculty of Electrical Engineering Figure 1: An illustration of our parallel insertion-based BVH optimization. For each node (the input node), we search for the best position leading to the highest reduction of the SAH cost for reinsertion (the output node) in parallel. The input and output nodes together with the corresponding path are highlighted with the same color. Notice that some nodes might be shared by multiple paths. We move the nodes to the new positions in parallel while taking care of potential conflicts of these operations. Abstract We present a novel highly parallel method for optimizing bounding volume hierarchies (BVH) targeting contemporary GPU architectures. The core of our method is based on the insertion-based BVH optimization that is known to achieve excellent results in terms of the SAH cost. The original algorithm is, however, inherently sequential: no efficient parallel version of the method exists, which limits its practical utility. We reformulate the algorithm while exploiting the observation that there is no need to remove the nodes from the BVH prior to finding their optimized positions in the tree. We can search for the optimized positions for all nodes in parallel while simultaneously tracking the corresponding SAH cost reduction. We update in parallel all nodes for which better position was found while efficiently handling potential conflicts during these updates. We implemented our algorithm in CUDA and evaluated the resulting BVH in the context of the GPU ray tracing. -
Hierarchical Bounding Volumes Grids Octrees BSP Trees Hierarchical
Spatial Data Structures HHiieerraarrcchhiiccaall BBoouunnddiinngg VVoolluummeess GGrriiddss OOccttrreeeess BBSSPP TTrreeeess 11/7/02 Speeding Up Computations • Ray Tracing – Spend a lot of time doing ray object intersection tests • Hidden Surface Removal – painters algorithm – Sorting polygons front to back • Collision between objects – Quickly determine if two objects collide Spatial data-structures n2 computations 3 Speeding Up Computations • Ray Tracing – Spend a lot of time doing ray object intersection tests • Hidden Surface Removal – painters algorithm – Sorting polygons front to back • Collision between objects – Quickly determine if two objects collide Spatial data-structures n2 computations 3 Speeding Up Computations • Ray Tracing – Spend a lot of time doing ray object intersection tests • Hidden Surface Removal – painters algorithm – Sorting polygons front to back • Collision between objects – Quickly determine if two objects collide Spatial data-structures n2 computations 3 Speeding Up Computations • Ray Tracing – Spend a lot of time doing ray object intersection tests • Hidden Surface Removal – painters algorithm – Sorting polygons front to back • Collision between objects – Quickly determine if two objects collide Spatial data-structures n2 computations 3 Speeding Up Computations • Ray Tracing – Spend a lot of time doing ray object intersection tests • Hidden Surface Removal – painters algorithm – Sorting polygons front to back • Collision between objects – Quickly determine if two objects collide Spatial data-structures n2 computations 3 Spatial Data Structures • We’ll look at – Hierarchical bounding volumes – Grids – Octrees – K-d trees and BSP trees • Good data structures can give speed up ray tracing by 10x or 100x 4 Bounding Volumes • Wrap things that are hard to check for intersection in things that are easy to check – Example: wrap a complicated polygonal mesh in a box – Ray can’t hit the real object unless it hits the box – Adds some overhead, but generally pays for itself.