Offline Model Simplification for Interactive Rigid Body Dynamics Simulations Satyandra K. Gupta University of Maryland, College Park


 Arleen Goodman
 2 years ago
 Views:
Transcription
1 NSF GRANT # NSF PROGRAM NAME: Engineering Design Offline Model Simplification for Interactive Rigid Body Dynamics Simulations Satyandra K. Gupta University of Maryland, College Park Atul Thakur University of Maryland, College Park Abstract: Rigid body dynamics simulations require use of accurate computation of contacts among bodies. Often collision detection algorithms are used for determining the contact between moving bodies. Mechanical parts have a large number of features and hence collision detection with the detailed part models often slows down the rigid body dynamics simulations. In many simulation scenarios, all the parts participating in the simulation are known in advance. In such cases, the simulation context (i.e., a priori knowledge of parts) can be exploited to simplify the part geometries such that the contact points among parts do not change. For example, parts with significant concavities may have regions on their boundaries that will be inaccessible to other parts in the simulation and hence contact points cannot lie on such inaccessible regions. Removing such regions from the parts can simplify the model and hence speed up the simulation. In this paper, we describe an offline simplification algorithm that performs part simplification based on accessibility considerations. Our algorithm ensures that the potential contact points among parts do not change as a result of the simplification process and hence it preserves the underlying physics. 1. Introduction: Rigid body dynamics simulations are nowadays used in a wide variety of virtual environment based applications ranging from entertainment (computer games, 3Dmovies, etc.), defense (ground vehicle simulations, explosive ordnance disposal robot simulation, flight simulations, etc.), healthcare (surgical simulation, drug disposal using needle steering, etc.), manufacturing (assembly simulation), etc. Many of the applications also need simulation of compliant parts in addition to rigid body simulations especially in healthcare and manufacturing applications. Such compliance is often modeled using rigid bodies connected by springs (i.e. by pseudorigid bodies) which intrinsically use the rigid body simulations. Thus, the rigid body dynamics simulation could be applied to a variety of applications involving both rigid as well as compliant parts. In a rigid body simulator, the major computational effort is spent on computing the contact points at each time step. Often collision detection algorithms are used for computing the contact points. Since the mechanical parts have large number of features, the collision detection of the detailed part models slows down the rigid body dynamics simulation. Hence, simplification of geometric models can improve the performance of dynamics simulation. To simplify a geometric model, many techniques involving vertex, edge and face decimation have been reported [1, 2]. A recent survey on model simplification techniques for physics based simulations can be found in [3]. One of the main limitations from the point of view of dynamics simulation of these techniques is that the shape of the simplified model is different than the original model. This is undesirable in case of rigid body dynamics simulation as its fidelity depends upon the accuracy of the contact points returned by collision detection engine. Thus, one of the main constraints for model simplification in case of rigid body dynamics simulation is that the potential contact points of colliding models should be preserved (remain unaltered) after simplification. The potential contact points depend upon the collision context (i.e., which parts are colliding). In many problems of dynamics simulations the collision context is known in advance or could be easily determined as the parts and their initial configurations are known beforehand and the underlying physics could be used to predict part configuration at each time step. This opens up a possibility of storing and retrieving multiple representations of parts based on collision contexts, where each representation can be simplified for the given collision context. This scheme is promising as memory is relatively inexpensive compared to the real time computation of contact points for fully featured part models. We plan to utilize the collision context to generate physics preserving simplified models. Our idea is to simplify models with respect to each other in an offline manner, i.e. before the simulation is performed in such a way that possible contact points are preserved using part accessibility considerations. We developed an algorithm to implement and test this idea
2 and the details of the algorithm are presented in the following section. 2. Problem Statement and Solution Approach: Given a pair of boundary representation models A and B, generate simplified boundary representation models A s and B s such that the set of contact points obtained under any arbitrary rigid body collision between A and B is same as the set of contact points obtained by collision between and A s and B s. Our approach to solve this problem is mainly based on the fact that in a pair of parts colliding with each other there are some regions that are never accessed and should be removed from the models representing the parts for collision computations. Our algorithm for simplification of given model A with respect to B consists of the following three main steps: Step 1: Construction of the Connected Convex Edge Set (CCES) graph for A. We extract the convex edges of A and determine the sets of connected convex edges (CCES) in this step. The CCES thus determined represents the artifacts in the model representing cavity openings and protrusions. After this we find out the connectivity in terms of accessibility between the CCESs of the model and construct a graph whose nodes store the CCES and the edges store the connectivity information between the CCESs. The process of CCES construction is shown in Fig. 1. Step 2: Construction of approximate Part Section Signature (PSS) for B. We represent the part B with a 2D curve called PSS, which gives the minimum circular hole diameter (D) in which the part B can enter till a given distance (δ). The distance (δ) is represented along the X axis and minimum hole diameter (D) is plotted along the Yaxis of the PSS. Part B and the PSS construction procedure are shown in Fig. 2. The ideal PSS can be constructed by scanning infinite directions of approach which is not practical and thus we scan finite number of directions δ ( 1 α ) and introduce an estimation factor equal to D, where α is the discritization angle. We multiply this factor with the approximate part section signature obtained by discrete directions to estimate the lower bound on the PSS as shown in Fig. 2 (d) by the broken line. Step 3: Model simplification of A with respect to B. In this step, the CCES graph of A is traversed in depthfirst manner to determine which nodes (CCES) are inaccessible. To determine whether the part B enters a given opening of A (represented by a node of CCES graph of A), the bounding circle of the opening represented by the node is compared with the minimum bounding cylinder of B for the depth of the node. If the minimum bounding cylinder radius of B is found to be greater than radius of node's bounding circle, the children nodes of the node are considered to be inaccessible. The faces related to inaccessible CCES nodes are then removed from A and the simplified model A s is generated. Above steps are repeated by swapping A and B to generate B s. Fig. 3. shows the simplified models of A and B with respect to each other. Fig. 1. Construction of CCES graph of Part Model A 3. Implementation and Testing: We developed a prototype software implementation of the contact preserving model simplification algorithm discussed in this paper. The programming platform was chosen as VC++ (version 8) using ACIS modeling kernel on Windows XP operating system. We used CGAL library (version 3.3.1) for bounding circles and convex hull computations. To test the results of model simplification, we built a virtual environment consisting of an articulated mobile (wheeled) robot that picks and places parts. We selected Open Dynamics (version 0.10) physics engine for doing physics based modeling and simulation of the virtual environment [4]. We devised the test wherein the robot is used to pick up a geometrically complex part in an environment containing other geometrically complex parts and to move it to another place. We tested the simulation performance with the simplified parts obtained by using the techniques discussed in this paper. Our algorithm takes BRep model (ACIS SAT) file as input and after simplification generates output in the same format.
3 a. Part Model A b. Part Section variation along d1 c. Part Section variation along d2 d. Part Section signature of B Fig. 2. Construction of Part Section Signature of Part B
4 Fig. 3. Simplified models A s and B s with respect to each other Since most of the simulation engines take triangulated data as input, we chose ACIS relative precision to be for triangulating both the unsimplified input and the simplified output models for the purpose of comparison. We obtained the test models from an online repository [5]. We obtained the simplification results as shown in Fig. 4. The figure shows the reduction in file size and triangle count of simplified and unsimplified models. For the reported test part models we found that the reduction in number of triangle count ranges from 6% to 55% depending on part complexity and collision context. We then tested the simplified models in OpenDynamics Physics engine. We created a wheeled robot with two serially connected, articulated arms in the simulation world. At the end of the articulator, there is a gripper to lift parts. There are several objects spread in the virtual world. The task of the robot is to pick an object and place it at another location moving through the space. We performed the pickandplace experiment with unsimplified and simplified models and monitored the frame rates using Fraps [6]. The screen shots of the simulation using simplified and unsimplified parts are shown in Fig. 5. The improvement in the frame rate was found to be about 35%. Fig. 5. Rigid body dynamics simulation with simplified and unsimplified models Fig. 4. Results obtained by simplification of various parts with respect to each other 4. Conclusion: We introduced the concept of contact preserving model simplification by using part accessibility considerations for accelerating the collision queries in rigid body dynamics simulations. The accuracy of rigid body simulation depends upon the accuracy of the contact points generated by the underlying collision detection engine. Our offline approach gets rid of faces not playing any role in collision while retaining all the faces which might possibly affect the results of collision query. Our main contributions are as follows:
5 i. We introduced the concept of accessibility based on the part section signature and openings. ii. We developed and implemented a new offline algorithm for contact preserving model simplification for rigid body dynamics simulation. iii. We demonstrated performance gains in a typical rigid body dynamics simulation scenario when our offline model simplification approach is used. A limitation of this work is the conservative approximation of approaching parts with bounding cylinders that sets an upper bound on the part crosssection, which can simplify the other parts relative to the approaching part but might leave some faces which should be removed. This way, we guarantee that the part is never oversimplified. Also, using this approach the number of models needed to be stored for the given n models in a scene is n 2 for the worst case. However, in practical situations, number of models needed to be stored can be further reduced based on part similarity and the collision context. 10. References: [1] P. Cignoni, C. Montani, and R. Scopigno. A comparison of mesh simplification algorithms, Computers & Graphics, 22(1):37 54, [2] D. P. Luebke. A developer s survey of polygonal simplification algorithms, IEEE Computer Graphics Applications, 21(3):24 35, [3] A. Thakur, A. G. Banerjee, and S. K. Gupta. A survey of CAD model simplification techniques for physicsbased simulation applications, Computer Aided Design, 41(2):6580, [4] Opendynamics rigid body dynamics engine, November [5] 3d part repository, September [6] Frame rate monitoring, September
Computational Geometry. Lecture 1: Introduction and Convex Hulls
Lecture 1: Introduction and convex hulls 1 Geometry: points, lines,... Plane (twodimensional), R 2 Space (threedimensional), R 3 Space (higherdimensional), R d A point in the plane, 3dimensional space,
More informationBernice E. Rogowitz and Holly E. Rushmeier IBM TJ Watson Research Center, P.O. Box 704, Yorktown Heights, NY USA
Are Image Quality Metrics Adequate to Evaluate the Quality of Geometric Objects? Bernice E. Rogowitz and Holly E. Rushmeier IBM TJ Watson Research Center, P.O. Box 704, Yorktown Heights, NY USA ABSTRACT
More informationConstrained Tetrahedral Mesh Generation of Human Organs on Segmented Volume *
Constrained Tetrahedral Mesh Generation of Human Organs on Segmented Volume * Xiaosong Yang 1, Pheng Ann Heng 2, Zesheng Tang 3 1 Department of Computer Science and Technology, Tsinghua University, Beijing
More informationSolid Edge ST3 Advances the Future of 3D Design
SUMMARY AND OPINION Solid Edge ST3 Advances the Future of 3D Design A Product Review White Paper Prepared by Collaborative Product Development Associates, LLC for Siemens PLM Software The newest release
More informationParallel Simplification of Large Meshes on PC Clusters
Parallel Simplification of Large Meshes on PC Clusters Hua Xiong, Xiaohong Jiang, Yaping Zhang, Jiaoying Shi State Key Lab of CAD&CG, College of Computer Science Zhejiang University Hangzhou, China April
More informationFaculty of Computer Science Computer Graphics Group. Final Diploma Examination
Faculty of Computer Science Computer Graphics Group Final Diploma Examination Communication Mechanisms for Parallel, Adaptive LevelofDetail in VR Simulations Author: Tino Schwarze Advisors: Prof. Dr.
More informationEfficient Storage, Compression and Transmission
Efficient Storage, Compression and Transmission of Complex 3D Models context & problem definition general framework & classification our new algorithm applications for digital documents Mesh Decimation
More information6.1 Application of Solid Models In mechanical engineering, a solid model is used for the following applications:
CHAPTER 6 SOLID MODELING 6.1 Application of Solid Models In mechanical engineering, a solid model is used for the following applications: 1. Graphics: generating drawings, surface and solid models 2. Design:
More informationMultiresolution 3D Rendering on Mobile Devices
Multiresolution 3D Rendering on Mobile Devices Javier Lluch, Rafa Gaitán, Miguel Escrivá, and Emilio Camahort Computer Graphics Section Departament of Computer Science Polytechnic University of Valencia
More informationSolving Geometric Problems with the Rotating Calipers *
Solving Geometric Problems with the Rotating Calipers * Godfried Toussaint School of Computer Science McGill University Montreal, Quebec, Canada ABSTRACT Shamos [1] recently showed that the diameter of
More informationIntroduction to Computer Graphics
Introduction to Computer Graphics Torsten Möller TASC 8021 7787822215 torsten@sfu.ca www.cs.sfu.ca/~torsten Today What is computer graphics? Contents of this course Syllabus Overview of course topics
More informationSimplification of Nonconvex Tetrahedral Meshes
Simplification of Nonconvex Tetrahedral Meshes Martin Kraus and Thomas Ertl Visualization and Interactive Systems Group, Institut für Informatik, Universität Stuttgart, Breitwiesenstr. 20 22, 70565 Suttgart,
More informationAn Overview of the Finite Element Analysis
CHAPTER 1 An Overview of the Finite Element Analysis 1.1 Introduction Finite element analysis (FEA) involves solution of engineering problems using computers. Engineering structures that have complex geometry
More informationSurface Reconstruction from a Point Cloud with Normals
Surface Reconstruction from a Point Cloud with Normals Landon Boyd and Massih Khorvash Department of Computer Science University of British Columbia,2366 Main Mall Vancouver, BC, V6T1Z4, Canada {blandon,khorvash}@cs.ubc.ca
More informationComputer Aided Systems
5 Computer Aided Systems Ivan Kuric Prof. Ivan Kuric, University of Zilina, Faculty of Mechanical Engineering, Department of Machining and Automation, Slovak republic, ivan.kuric@fstroj.utc.sk 1.1 Introduction
More informationArrangements And Duality
Arrangements And Duality 3.1 Introduction 3 Point configurations are tbe most basic structure we study in computational geometry. But what about configurations of more complicated shapes? For example,
More informationSegmentation of building models from dense 3D pointclouds
Segmentation of building models from dense 3D pointclouds Joachim Bauer, Konrad Karner, Konrad Schindler, Andreas Klaus, Christopher Zach VRVis Research Center for Virtual Reality and Visualization, Institute
More information3D POINT CLOUD CONSTRUCTION FROM STEREO IMAGES
3D POINT CLOUD CONSTRUCTION FROM STEREO IMAGES Brian Peasley * I propose an algorithm to construct a 3D point cloud from a sequence of stereo image pairs that show a full 360 degree view of an object.
More informationComputer Graphics AACHEN AACHEN AACHEN AACHEN. Public Perception of CG. Computer Graphics Research. Methodological Approaches          
Public Perception of CG Games Computer Graphics Movies Computer Graphics Research algorithms & data structures fundamental continuous & discrete mathematics optimization schemes 3D reconstruction global
More informationAlgorithms for RealTime Tool Path Generation
Algorithms for RealTime Tool Path Generation Gyula Hermann John von Neumann Faculty of Information Technology, Budapest Polytechnic H1034 Nagyszombat utca 19 Budapest Hungary, hermgyviif.hu Abstract:The
More informationUSING TRIANGULATIONS IN COMPUTER SIMULATIONS OF GRANULAR MEDIA
USING TRIANGULATIONS IN COMPUTER SIMULATIONS OF GRANULAR MEDIA DIDIER MÜLLER, THOMAS M. LIEBLING EPFLDMA, 1015 Lausanne, Switzerland ABSTRACT The distinct element method used to simulate behavior of granular
More informationEngineering Geometry
Engineering Geometry Objectives Describe the importance of engineering geometry in design process. Describe coordinate geometry and coordinate systems and apply them to CAD. Review the righthand rule.
More informationA Generalized Marching Cubes Algorithm Based On NonBinary Classifications
KonradZuseZentrum fu r Informationstechnik Berlin Takustraße 7 D14195 BerlinDahlem Germany HANSCHRISTIAN HEGE DETLEV STALLING MARTIN SEEBASS MALTE ZOCKLER A Generalized Marching Cubes Algorithm Based
More informationA Fuzzy System Approach of Feed Rate Determination for CNC Milling
A Fuzzy System Approach of Determination for CNC Milling Zhibin Miao Department of Mechanical and Electrical Engineering Heilongjiang Institute of Technology Harbin, China email:miaozhibin99@yahoo.com.cn
More informationEveryday Mathematics. Grade 3 GradeLevel Goals. 3rd Edition. Content Strand: Number and Numeration. Program Goal Content Thread Grade Level Goal
Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 33, 58 84, 87 16, 49
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 68 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationGeometric Constraints
Simulation in Computer Graphics Geometric Constraints Matthias Teschner Computer Science Department University of Freiburg Outline introduction penalty method Lagrange multipliers local constraints University
More informationIntersection of a Line and a Convex. Hull of Points Cloud
Applied Mathematical Sciences, Vol. 7, 213, no. 13, 51395149 HIKARI Ltd, www.mhikari.com http://dx.doi.org/1.12988/ams.213.37372 Intersection of a Line and a Convex Hull of Points Cloud R. P. Koptelov
More informationCAD Import Module and LiveLink for CAD V4.3a
CAD Import Module and LiveLink for CAD V4.3a LiveLink for AutoCAD, LiveLink for Creo Parametric, LiveLink for Inventor, LiveLink for Pro/ENGINEER, LiveLink for Solid Edge, LiveLink for SolidWorks, LiveLink
More informationDesign of a Universal Robot Endeffector for Straightline Pickup Motion
Session Design of a Universal Robot Endeffector for Straightline Pickup Motion Gene Y. Liao Gregory J. Koshurba Wayne State University Abstract This paper describes a capstone design project in developing
More informationThe Basics of FEA Procedure
CHAPTER 2 The Basics of FEA Procedure 2.1 Introduction This chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique. A spring
More informationBachelor of Games and Virtual Worlds (Programming) Subject and Course Summaries
First Semester Development 1A On completion of this subject students will be able to apply basic programming and problem solving skills in a 3 rd generation objectoriented programming language (such as
More informationWhite Paper. Cloth Simulation. February 2007 WP03018001_v01
White Paper Cloth Simulation February 2007 WP03018001_v01 White Paper Document Change History Version Date Responsible Reason for Change _v01 CZ, TS Initial release Go to sdkfeedback@nvidia.com to provide
More informationEveryday Mathematics. Grade 4 GradeLevel Goals CCSS EDITION. Content Strand: Number and Numeration. Program Goal Content Thread GradeLevel Goal
Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.12 Grade 6 Math : SubClaim A The student solves problems involving the Major Content for grade/course with
More information3D SCANNING: A NEW APPROACH TOWARDS MODEL DEVELOPMENT IN ADVANCED MANUFACTURING SYSTEM
3D SCANNING: A NEW APPROACH TOWARDS MODEL DEVELOPMENT IN ADVANCED MANUFACTURING SYSTEM Dr. Trikal Shivshankar 1, Patil Chinmay 2, Patokar Pradeep 3 Professor, Mechanical Engineering Department, SSGM Engineering
More informationThe Effects of Wheelbase and Track on Vehicle Dynamics. Automotive vehicles move by delivering rotational forces from the engine to
The Effects of Wheelbase and Track on Vehicle Dynamics Automotive vehicles move by delivering rotational forces from the engine to wheels. The wheels push in the opposite direction of the motion of the
More informationEveryday Mathematics. Grade 4 GradeLevel Goals. 3rd Edition. Content Strand: Number and Numeration. Program Goal Content Thread GradeLevel Goals
Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation
More informationModel Repair. Leif Kobbelt RWTH Aachen University )NPUT $ATA 2EMOVAL OF TOPOLOGICAL AND GEOMETRICAL ERRORS !NALYSIS OF SURFACE QUALITY
)NPUT $ATA 2ANGE 3CAN #!$ 4OMOGRAPHY 2EMOVAL OF TOPOLOGICAL AND GEOMETRICAL ERRORS!NALYSIS OF SURFACE QUALITY 3URFACE SMOOTHING FOR NOISE REMOVAL 0ARAMETERIZATION 3IMPLIFICATION FOR COMPLEXITY REDUCTION
More informationOptical Digitizing by ATOS for Press Parts and Tools
Optical Digitizing by ATOS for Press Parts and Tools Konstantin Galanulis, Carsten Reich, Jan Thesing, Detlef Winter GOM Gesellschaft für Optische Messtechnik mbh, Mittelweg 7, 38106 Braunschweig, Germany
More informationA HYBRID GROUND DATA MODEL TO SUPPORT INTERACTION IN MECHANIZED TUNNELING
A HYBRID GROUND DATA MODEL TO SUPPORT INTERACTION IN MECHANIZED TUNNELING F. HEGEMANN P. MANICKAM K. LEHNER M. KÖNIG D. HARTMANN Department of Civil and Environmental Engineering, RuhrUniversity of Bochum,44780
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More informationCHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.
TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has
More informationRobot TaskLevel Programming Language and Simulation
Robot TaskLevel Programming Language and Simulation M. Samaka Abstract This paper presents the development of a software application for Offline robot task programming and simulation. Such application
More informationImproved Billboard Clouds for Extreme Model Simplification
Improved Billboard Clouds for Extreme Model Simplification I.T. Huang, K. L. Novins and B. C. Wünsche Graphics Group, Department of Computer Science, University of Auckland, Private Bag 92019, Auckland,
More informationLecture 7  Meshing. Applied Computational Fluid Dynamics
Lecture 7  Meshing Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (20022006) Fluent Inc. (2002) 1 Outline Why is a grid needed? Element types. Grid types.
More informationAn Instructional Aid System for Driving Schools Based on Visual Simulation
An Instructional Aid System for Driving Schools Based on Visual Simulation Salvador Bayarri, Rafael Garcia, Pedro Valero, Ignacio Pareja, Institute of Traffic and Road Safety (INTRAS), Marcos Fernandez
More informationGenetic Algorithms commonly used selection, replacement, and variation operators Fernando Lobo University of Algarve
Genetic Algorithms commonly used selection, replacement, and variation operators Fernando Lobo University of Algarve Outline Selection methods Replacement methods Variation operators Selection Methods
More informationUnit 1: Integers and Fractions
Unit 1: Integers and Fractions No Calculators!!! Order Pages (All in CC7 Vol. 1) 31 Integers & Absolute Value 191194, 203206, 195198, 207210 32 Add Integers 33 Subtract Integers 215222 34 Multiply
More informationVolumes of Revolution
Mathematics Volumes of Revolution About this Lesson This lesson provides students with a physical method to visualize dimensional solids and a specific procedure to sketch a solid of revolution. Students
More informationRobotics ABB Robotics Laser Cutting Software High precision laser cutting made easy  Greater manufacturing flexibility at lower capital investment
Robotics ABB Robotics Laser Cutting Software High precision laser cutting made easy  Greater manufacturing flexibility at lower capital investment Robotic laser cutting Overview Allows for the increased
More informationCATIA Drafting TABLE OF CONTENTS
TABLE OF CONTENTS Introduction...1 Drafting...2 Drawing Screen...3 Pulldown Menus...4 File...4 Edit...5 View...6 Insert...7 Tools...8 Drafting Workbench...9 Views and Sheets...9 Dimensions and Annotations...10
More informationQuestions: Does it always take the same amount of force to lift a load? Where should you press to lift a load with the least amount of force?
Lifting A Load 1 NAME LIFTING A LOAD Questions: Does it always take the same amount of force to lift a load? Where should you press to lift a load with the least amount of force? Background Information:
More informationComputer Graphics. Geometric Modeling. Page 1. Copyright Gotsman, Elber, Barequet, Karni, Sheffer Computer Science  Technion. An Example.
An Example 2 3 4 Outline Objective: Develop methods and algorithms to mathematically model shape of real world objects Categories: WireFrame Representation Object is represented as as a set of points
More informationPath Tracking for a Miniature Robot
Path Tracking for a Miniature Robot By Martin Lundgren Excerpt from Master s thesis 003 Supervisor: Thomas Hellström Department of Computing Science Umeå University Sweden 1 Path Tracking Path tracking
More informationFactoring Patterns in the Gaussian Plane
Factoring Patterns in the Gaussian Plane Steve Phelps Introduction This paper describes discoveries made at the Park City Mathematics Institute, 00, as well as some proofs. Before the summer I understood
More informationHIGHPERFORMANCE INSPECTION VEHICLE FOR RAILWAYS AND TUNNEL LININGS. HIGHPERFORMANCE INSPECTION VEHICLE FOR RAILWAY AND ROAD TUNNEL LININGS.
HIGHPERFORMANCE INSPECTION VEHICLE FOR RAILWAYS AND TUNNEL LININGS. HIGHPERFORMANCE INSPECTION VEHICLE FOR RAILWAY AND ROAD TUNNEL LININGS. The vehicle developed by Euroconsult and Pavemetrics and described
More informationVisualizing Data: Scalable Interactivity
Visualizing Data: Scalable Interactivity The best data visualizations illustrate hidden information and structure contained in a data set. As access to large data sets has grown, so has the need for interactive
More informationVRSPATIAL: DESIGNING SPATIAL MECHANISMS USING VIRTUAL REALITY
Proceedings of DETC 02 ASME 2002 Design Technical Conferences and Computers and Information in Conference Montreal, Canada, September 29October 2, 2002 DETC2002/ MECH34377 VRSPATIAL: DESIGNING SPATIAL
More informationIndustrial Robotics. Training Objective
Training Objective After watching the program and reviewing this printed material, the viewer will learn the basics of industrial robot technology and how robots are used in a variety of manufacturing
More informationCurrent Standard: Mathematical Concepts and Applications Shape, Space, and Measurement Primary
Shape, Space, and Measurement Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two and threedimensional shapes by demonstrating an understanding of:
More informationMean Value Coordinates
Mean Value Coordinates Michael S. Floater Abstract: We derive a generalization of barycentric coordinates which allows a vertex in a planar triangulation to be expressed as a convex combination of its
More informationCATIA V5 Tutorials. Mechanism Design & Animation. Release 18. Nader G. Zamani. University of Windsor. Jonathan M. Weaver. University of Detroit Mercy
CATIA V5 Tutorials Mechanism Design & Animation Release 18 Nader G. Zamani University of Windsor Jonathan M. Weaver University of Detroit Mercy SDC PUBLICATIONS Schroff Development Corporation www.schroff.com
More informationWe can display an object on a monitor screen in three different computermodel forms: Wireframe model Surface Model Solid model
CHAPTER 4 CURVES 4.1 Introduction In order to understand the significance of curves, we should look into the types of model representations that are used in geometric modeling. Curves play a very significant
More informationReal Time Simulation for OffRoad Vehicle Analysis. Dr. Pasi Korkealaakso Mevea Ltd., May 2015
Real Time Simulation for OffRoad Vehicle Analysis Dr. Pasi Korkealaakso Mevea Ltd., May 2015 Contents Introduction Virtual machine model Machine interaction with environment and realistic environment
More informationThis article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
IEEE/ACM TRANSACTIONS ON NETWORKING 1 A Greedy Link Scheduler for Wireless Networks With Gaussian MultipleAccess and Broadcast Channels Arun Sridharan, Student Member, IEEE, C Emre Koksal, Member, IEEE,
More informationProgramming ABB Industrial Robot for an Accurate Handwriting
Programming ABB Industrial Robot for an Accurate Handwriting ABIGO IZABO 1, TARIG FAISAL 1* MAHMUD IWAN 1, H M A A ALASSADI 2, HANIF RAMLI 2 1 Faculty of Engineering, Technology & Built Environment, UCSI
More informationWORK SCHEDULE: MATHEMATICS 2007
, K WORK SCHEDULE: MATHEMATICS 00 GRADE MODULE TERM... LO NUMBERS, OPERATIONS AND RELATIONSHIPS able to recognise, represent numbers and their relationships, and to count, estimate, calculate and check
More informationShortest Path Algorithms
Shortest Path Algorithms Jaehyun Park CS 97SI Stanford University June 29, 2015 Outline Cross Product Convex Hull Problem Sweep Line Algorithm Intersecting Halfplanes Notes on Binary/Ternary Search Cross
More informationSolved with COMSOL Multiphysics 4.3
Vibrating String Introduction In the following example you compute the natural frequencies of a pretensioned string using the 2D Truss interface. This is an example of stress stiffening ; in fact the
More informationIn mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target
More informationNumerical Analysis of Independent Wire Strand Core (IWSC) Wire Rope
Numerical Analysis of Independent Wire Strand Core (IWSC) Wire Rope Rakesh Sidharthan 1 Gnanavel B K 2 Assistant professor Mechanical, Department Professor, Mechanical Department, Gojan engineering college,
More informationHonors Geometry Final Exam Study Guide
20112012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.
More informationManual for simulation of EB processing. Software ModeRTL
1 Manual for simulation of EB processing Software ModeRTL How to get results. Software ModeRTL. Software ModeRTL consists of five thematic modules and service blocks. (See Fig.1). Analytic module is intended
More informationTopological Data Analysis Applications to Computer Vision
Topological Data Analysis Applications to Computer Vision Vitaliy Kurlin, http://kurlin.org Microsoft Research Cambridge and Durham University, UK Topological Data Analysis quantifies topological structures
More informationList of Problems Solved Introduction p. 1 Concept p. 1 Nodes p. 3 Elements p. 4 Direct Approach p. 5 Linear Spring p. 5 Heat Flow p.
Preface p. v List of Problems Solved p. xiii Introduction p. 1 Concept p. 1 Nodes p. 3 Elements p. 4 Direct Approach p. 5 Linear Spring p. 5 Heat Flow p. 6 Assembly of the Global System of Equations p.
More informationANALYTICAL AND EXPERIMENTAL EVALUATION OF SPRING BACK EFFECTS IN A TYPICAL COLD ROLLED SHEET
International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, JanFeb 2016, pp. 119130, Article ID: IJMET_07_01_013 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1
More informationINTERNATIONAL JOURNAL OF COMPUTER ENGINEERING & TECHNOLOGY (IJCET)
INTERNATIONAL JOURNAL OF COMPUTER ENGINEERING & TECHNOLOGY (IJCET) International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 6367(Print), ISSN 0976 6367(Print) ISSN 0976 6375(Online)
More informationINTERSECTION OF LINE SEGMENTS IN A DISCRETE DOMAIN
INTERSECTION OF LINE SEGMENTS IN A DISCRETE DOMAIN Marcel Lourenço de Luna André Kubagawa Sato Marcos de Sales Guerra Tsuzuki Rogério Yugo Takimoto Thiago de Castro Martins Computational Geometry Laboratory,
More informationMine & IED Roller Solutions Route Clearance, AntiTank, Dismounted, Area Clearance
Mine & IED Roller Solutions Route Clearance, AntiTank, Dismounted, Area Clearance Mine & IED Rollers RCRA Route Clearance Roller Advanced RCRB Route Clearance Roller Basic Dismounted Protection Roller
More informationVolumetric Meshes for Real Time Medical Simulations
Volumetric Meshes for Real Time Medical Simulations Matthias Mueller and Matthias Teschner Computer Graphics Laboratory ETH Zurich, Switzerland muellerm@inf.ethz.ch, http://graphics.ethz.ch/ Abstract.
More informationVirtual CRASH 3.0 Staging a Car Crash
Virtual CRASH 3.0 Staging a Car Crash Virtual CRASH Virtual CRASH 3.0 Staging a Car Crash Changes are periodically made to the information herein; these changes will be incorporated in new editions of
More informationAdaptive Tolerance Algorithm for Distributed TopK Monitoring with Bandwidth Constraints
Adaptive Tolerance Algorithm for Distributed TopK Monitoring with Bandwidth Constraints Michael Bauer, Srinivasan Ravichandran University of WisconsinMadison Department of Computer Sciences {bauer, srini}@cs.wisc.edu
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationA Strategy for Teaching Finite Element Analysis to Undergraduate Students
A Strategy for Teaching Finite Element Analysis to Undergraduate Students Gordon Smyrell, School of Computing and Mathematics, University of Teesside The analytical power and design flexibility offered
More informationPHOTOGRAMMETRIC TECHNIQUES FOR MEASUREMENTS IN WOODWORKING INDUSTRY
PHOTOGRAMMETRIC TECHNIQUES FOR MEASUREMENTS IN WOODWORKING INDUSTRY V. Knyaz a, *, Yu. Visilter, S. Zheltov a State Research Institute for Aviation System (GosNIIAS), 7, Victorenko str., Moscow, Russia
More informationCAD and Creativity. Contents
CAD and Creativity K C Hui Department of Automation and Computer Aided Engineering Contents Various aspects of CAD CAD training in the university and the industry Conveying fundamental concepts in CAD
More informationApplication Report. Propeller Blade Inspection Station
34935 SE Douglas Street, Suite, Snoqualmie, WA 9874 Ph: 4253965577 Fax: 425396586 Application Report Propeller Blade Inspection Station Prepared By Kyle Johnston, Ph. D. Metron Systems Inc.5.5 3 2.5
More information567 Meshes. Nima Aghdaii Hamid Younesy Hao Zhang
5 Meshes Nima Aghdaii Hamid Younesy Hao Zhang Graphics, Usability and Visualization (GrUVi) Lab School of Computing Science Simon Fraser University Figure 1: A triangle mesh (left) with low and highvalence
More informationDMU Viewer CATIA V5R19 TABLE OF CONTENTS
TABLE OF CONTENTS Introduction...1 DMU Viewer...1 Product Structure Introduction...3 Pull Down Menus...4 Start...4 File...5 Edit...6 View...9 Insert...12 Tools...13 Analyze...16 Window...17 Help...18 Product
More informationIncremental Expansion of Manufacturing Knowledge Base
ABSTRACT Incremental Expansion of Manufacturing Knowledge Base Sanjeewa Gamaralalage, Dusan Sormaz Department of Industrial and Systems Engineering Ohio University Athens, Ohio45701 Email: sg110610@ohio.edu,
More informationThe Influence of Aerodynamics on the Design of HighPerformance Road Vehicles
The Influence of Aerodynamics on the Design of HighPerformance Road Vehicles Guido Buresti Department of Aerospace Engineering University of Pisa (Italy) 1 CONTENTS ELEMENTS OF AERODYNAMICS AERODYNAMICS
More informationFRACTURE is commonplace in crashes and explosions,
30 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 20, NO. 1, JANUARY 2014 Fast Collision Detection for Fracturing Rigid Bodies Loeiz Glondu, Sara C. Schvartzman, Maud Marchal, Georges Dumont,
More informationSeminar. Path planning using Voronoi diagrams and BSplines. Stefano Martina stefano.martina@stud.unifi.it
Seminar Path planning using Voronoi diagrams and BSplines Stefano Martina stefano.martina@stud.unifi.it 23 may 2016 This work is licensed under a Creative Commons AttributionShareAlike 4.0 International
More informationStudy of Analysis System for Bridge Test
Study of Analysis System for Bridge Test Chen Ke, Lu JianMing, Research Institute of Highway, 100088, Beijing, China (chenkezi@163.com, lujianming@263.net) Summary Analysis System for Bridge Test (Chinese
More informationPrentice Hall Mathematics: Course 1 2008 Correlated to: Arizona Academic Standards for Mathematics (Grades 6)
PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). Strand 1: Number Sense and Operations Every student should understand and use all concepts and
More informationArchitecture for Direct ModeltoPart CNC Manufacturing
Architecture for Direct ModeltoPart CNC Manufacturing Gilbert Poon, Paul J. Gray, Sanjeev Bedi Department of Mechanical Engineering, University of Waterloo Waterloo, Ontario, N2L 3G1, Canada and Daniel
More informationBehavioral Animation Modeling in the Windows Environment
Behavioral Animation Modeling in the Windows Environment MARCELO COHEN 1 CARLA M. D. S. FREITAS 1 FLAVIO R. WAGNER 1 1 UFRGS  Universidade Federal do Rio Grande do Sul CPGCC  Curso de Pós Graduação em
More informationMathematics on the Soccer Field
Mathematics on the Soccer Field Katie Purdy Abstract: This paper takes the everyday activity of soccer and uncovers the mathematics that can be used to help optimize goal scoring. The four situations that
More informationSOFA an Open Source Framework for Medical Simulation
SOFA an Open Source Framework for Medical Simulation J. ALLARD a P.J. BENSOUSSAN b S. COTIN a H. DELINGETTE b C. DURIEZ b F. FAURE b L. GRISONI b and F. POYER b a CIMIT Sim Group  Harvard Medical School
More information