CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Lecture VIII Deformable Bodies CS274: Computer Animation and Simulation.

Slides:



Advertisements
Similar presentations
Steady-state heat conduction on triangulated planar domain May, 2002
Advertisements

Modeling of Neo-Hookean Materials using FEM
Surface Flattening in Garment Design Zhao Hongyan Sep. 13, 2006.
CSE554Extrinsic DeformationsSlide 1 CSE 554 Lecture 9: Extrinsic Deformations Fall 2012.
CSE554Extrinsic DeformationsSlide 1 CSE 554 Lecture 10: Extrinsic Deformations Fall 2014.
Beams and Frames.
Meshless Elasticity Model and Contact Mechanics-based Verification Technique Rifat Aras 1 Yuzhong Shen 1 Michel Audette 1 Stephane Bordas 2 1 Department.
A Bezier Based Approach to Unstructured Moving Meshes ALADDIN and Sangria Gary Miller David Cardoze Todd Phillips Noel Walkington Mark Olah Miklos Bergou.
Dynamic Real-Time Deformations using Space & Time Adaptive Sampling Gilles Debunne Marie-Paule Cani Gilles Debunne Marie-Paule Cani Mathieu Desbrun Alan.
Overview Class #6 (Tues, Feb 4) Begin deformable models!! Background on elasticity Elastostatics: generalized 3D springs Boundary integral formulation.
Advanced Computer Graphics (Fall 2010) CS 283, Lecture 23: Physical Simulation 2 Ravi Ramamoorthi Most slides.
Finite Element Method Introduction General Principle
ECIV 720 A Advanced Structural Mechanics and Analysis Solid Modeling.
MECH303 Advanced Stresses Analysis Lecture 5 FEM of 1-D Problems: Applications.
Finite Element Method in Geotechnical Engineering
ECIV 720 A Advanced Structural Mechanics and Analysis Lecture 10: Solution of Continuous Systems – Fundamental Concepts Mixed Formulations Intrinsic Coordinate.
1cs533d-winter-2005 Notes  Some example values for common materials: (VERY approximate) Aluminum: E=70 GPa =0.34 Concrete:E=23 GPa =0.2 Diamond:E=950.
Physically-Based Simulation of Objects Represented by Surface Meshes Matthias Muller, Matthias Teschner, Markus Gross CGI 2004.
Introduction to Non-Rigid Body Dynamics A Survey of Deformable Modeling in Computer Graphics, by Gibson & Mirtich, MERL Tech Report Elastically Deformable.
1cs533d-term Notes. 2 Poisson Ratio  Real materials are essentially incompressible (for large deformation - neglecting foams and other weird composites…)
ECIV 720 A Advanced Structural Mechanics and Analysis Lecture 12: Isoparametric CST Area Coordinates Shape Functions Strain-Displacement Matrix Rayleigh-Ritz.
MCE 561 Computational Methods in Solid Mechanics
Forces. Normal Stress A stress measures the surface force per unit area.  Elastic for small changes A normal stress acts normal to a surface.  Compression.
Computer graphics & visualization Rigid Body Simulation.
Computer Animation Rick Parent Computer Animation Algorithms and Techniques Physically Based Animation.
Review (2 nd order tensors): Tensor – Linear mapping of a vector onto another vector Tensor components in a Cartesian basis (3x3 matrix): Basis change.
Lecture VII Rigid Body Dynamics CS274: Computer Animation and Simulation.
A Survey on FFD Reporter: Gang Xu Mar 15, Overview Volumn-based FFD Surface-based FFD Curve-based FFD Point-based FFD Accurate FFD Future Work Outline.
Analytical Vs Numerical Analysis in Solid Mechanics Dr. Arturo A. Fuentes Created by: Krishna Teja Gudapati.
Motion and Stress Analysis by Vector Mechanics Edward C. Ting Professor Emeritus of Applied Mechanics Purdue University, West Lafayette, IN National Central.
Chapter 9: Differential Analysis of Fluid Flow SCHOOL OF BIOPROCESS ENGINEERING, UNIVERSITI MALAYSIA PERLIS.
CS 551/651 Advanced Computer Graphics Warping and Morphing Spring 2002.
School of Civil EngineeringSpring 2007 CE 595: Finite Elements in Elasticity Instructors: Amit Varma, Ph.D. Timothy M. Whalen, Ph.D.
Mesh Deformation Based on Discrete Differential Geometry Reporter: Zhongping Ji
The Finite Element Method A Practical Course
Haptics and Virtual Reality
1 20-Oct-15 Last course Lecture plan and policies What is FEM? Brief history of the FEM Example of applications Discretization Example of FEM softwares.
1 LES of Turbulent Flows: Lecture 6 (ME EN ) Prof. Rob Stoll Department of Mechanical Engineering University of Utah Spring 2011.
Dr. Wang Xingbo Fall , 2005 Mathematical & Mechanical Method in Mechanical Engineering.
Computer Animation Algorithms and Techniques Chapter 4 Interpolation-based animation.
FLUID PROPERTIES Independent variables SCALARS VECTORS TENSORS.
1 Haptic Systems Mohsen Mahvash Lecture 9 20/1/06.
David Levin Tel-Aviv University Afrigraph 2009 Shape Preserving Deformation David Levin Tel-Aviv University Afrigraph 2009 Based on joint works with Yaron.
MECH4450 Introduction to Finite Element Methods Chapter 3 FEM of 1-D Problems: Applications.
CHAP 3 WEIGHTED RESIDUAL AND ENERGY METHOD FOR 1D PROBLEMS
© 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the.
CS274 Spring 01 Lecture 7 Copyright © Mark Meyer Lecture VII Rigid Body Dynamics CS274: Computer Animation and Simulation.
M. Zareinejad
Advanced Computer Graphics Spring 2014 K. H. Ko School of Mechatronics Gwangju Institute of Science and Technology.
Basic Geometric Nonlinearities Chapter Five - APPENDIX.
Honours Graphics 2008 Session 9. Today’s focus Physics in graphics Understanding:
Purdue Aeroelasticity
Solid object break-up Ivan Dramaliev CS260, Winter’03.
1 CHAP 3 WEIGHTED RESIDUAL AND ENERGY METHOD FOR 1D PROBLEMS FINITE ELEMENT ANALYSIS AND DESIGN Nam-Ho Kim.
11 Energy Methods.
11 Energy Methods.
Chapter 4 Fluid Mechanics Frank White
Continuum Mechanics (MTH487)
Boundary Element Method
Finite Element Method in Geotechnical Engineering
Mechanics of Solids I Energy Method.
Continuum Mechanics (MTH487)
روش عناصر محدود غیرخطی II Nonlinear Finite Element Procedures II
Materials Science & Engineering University of Michigan
Introduction to Non-Rigid Body Dynamics
Advanced Computer Graphics Spring 2008
Introduction to Non-Rigid Body Dynamics
(deformacija objektov)
CSE 554 Lecture 10: Extrinsic Deformations
Presentation transcript:

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Lecture VIII Deformable Bodies CS274: Computer Animation and Simulation

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Overview Deformable Bodies Many objects are not rigid  jello  mud  gases/liquids  etc. Two main techniques:  Geometric deformations  Physically-based methods

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Geometric Deformations Deform the object’s geometry directly Two main techniques:  control point / vertex manipulation  space warping

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Control Point / Vertex Manipulation Edit the surface vertices or control points directly

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Space Warping Deform the object by deforming the space it is in Two main techniques:  Nonlinear Deformation  Free Form Deformation (FFD) Independent of object representation

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Nonlinear Global Deformation Objects are defined in a local object space Deform this space using a combination of:  Non-uniform Scaling  Tapering  Twisting  Bending

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Nonlinear Global Deformation

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Nonlinear Global Deformation Good for modeling [Barr 87] Animation is harder

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Free Form Deformation (FFD) Deform space by deforming a lattice around an object The deformation is defined by moving the control points Imagine it as if the object were encased in rubber

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Free Form Deformation (FFD) The lattice defines a Bezier volume Compute lattice coordinates Alter the control points Compute the deformed points

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer FFD Example

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer FFD Example

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer FFD Animation Animate a reference and a deformed lattice referencedeformedmorphed

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer FFD Animation Animate the object through the lattice referencedeformedmorphed

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Extended Free Form Deformations Extended FFDs:  noncubical lattice  arbitrary parameterization Dirichlet FFDs:  use Delaunay triangulation of the control points as the lattice  use Sibson coordinates as the lattice coordinates

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Factor Curves Modify the transformation applied to the object based on where and when it is applied

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Factor Curves Scripted animation can lead to complex motions (depending on animator skill) Deformations can be nested

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Physically-Based Deformations Deform the object according to physical laws Two main techniques:  mass-spring systems  finite element methods

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Connect the particles with springs:  structural springs  shear springs  bending springs  etc. Mass-Spring Systems Treat the object as a collection of particles Simulate using standard particle dynamics

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Finite Element Methods Mass-Spring systems are not very realistic We need:  more accurate physical laws  error control Finite Element Methods (FEM) offer a way to solve the physical equations we wish to simulate.

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Elastic Models Deformations and forces are related by: deformation energy density and dampening

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Elastic Models Deformation energy approximated by: Simulate using finite elements/finite differences 1 st Fundamental Form2 nd Fundamental Form measures curvaturemeasures length

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Green Deformation Model Relates the stress and strain: Simulate using finite elements/finite differences

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Green Deformation Model Stress Tensor: Strain Tensor: represents the force distribution within an object

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Finite Element Methods We need a way to solve the equations Finite Element Method:  discretize the object into elements  represent the solution as a sum of basis functions  compute the solution such that the residual is orthogonal to a set of test functions Example:

CS274 Spring 01 Lecture 8 Copyright © Mark Meyer Weak Form Sometimes we need to solve: But our basis functions may not have second derivatives?!? Integration by parts can move derivatives to the test functions!! This is known as the weak form.