290-072: Physically Based Modeling, Simulation and
"We hope that, since the endless complexity
and variety of natural phenomenon are caused by few basic elements and
laws, their visual simulation can be achieved using few basic primitives
and algorithms. We are still far from that goal, but then again we do not
have as many processors or as much time as nature does."
- A. Fournier and W. T. Reeves
in Guest Editors' Introduction: Special Issue on the Modeling of Natural
Phenomena, ACM TRANSACTIONS ON GRAPHICS, July 1987
Gain Basic Skills for Implementing Physically Based
In this course, we will study various techniques to simulate the mechanical
behavior of objects. This course is targeted at students who
have a background in graphics and numerical computing, but not much in
physical simulation. At the end of this course, you will learn about implementing
a basic simulation program that produces interesting results and verify
You will learn three basic components in physically based simulation;
geometry, physics, and numerical computing.
Acquire Broad Perspective on Simulation Techniques
Many different kinds of physical phenomena and simulation techniques
will be explained. The relationship between different techniques
will be made clear so that you can picture a global map of research areas.
After taking this class, you should be able to assess the complexity of
a particular simulation problem, and understand related work in that area.
Get Inspired to Pursue Advanced Research
In your course project, you will have the option of exploring any idea(s).
Many course projects from the last offering resulted in conference publications
(these include ACM SIGGRAPH Conference, ACM Symposium on Interactive
3D Graphics, Computer Animation, Eurographics
Conference and Workshop, ACM Symposium on Solid Modeling, etc.)
as well as dissertation topic.
LIST OF TOPICS
Collision Detection, Distance Computation, and Contact
The problem of checking whether two geometric objects overlap or not is
called collision detection.
Because of its complexity, collision detection is often the
bottleneck in physical simulation systems. We will also discuss more
complex problems such as distance computation (computing distance
between two objects), and contact determination or intersection computation
( finding the first contact point of two moving objects).
The followings are some of results in UNC research group. Please look at:
This shows a hand interacting with hundreds of objects in a kitchen architectural
environment. Note we detect the exact contact points (the hand's fingers
turning red indicates contact).
This shows a composite mpeg of the previous sections. It goes over the
convex polytope distance tracking algorithm (Lin-Canny), multiple moving
bodies algorithm, and non-convex collision detection algorithm. All the
simulations in this segment were recoreded in real time.
Simulation of objects with no spatial extent. Most of basic concepts and
mathematical and numerical techniques (error estimation, ODE, and DAE)
of physically based simulation will be illustrated by using particle dynamics.
Definition of particle system is not very clear. In physically based modeling,
it is often an application of particle dynamics.
Rigid Body Dynamics
Simulation of "hard" objects. This is the core of the course.
Simulation of deformable objects.
Facial Animation by Finite Element Method
Research Group, University of Auckland
Highly Deformable Objects
Finite Element Analysis of
Large Elastic Deformation
and Volume Preserving
Computer Science Department, UNC-CH
Space Time Constraints
Michael Kass, Andrew
Using a force feedback device, users can touch and feel virtual objects.
Computing feedback force in virtual environment is called force display
or force rendering. This technology involves far more than physically
based simulation. The designer of a force feedback system must be
familiar with mechanical engineering, control theory, and human factor.
The application of this technology in computer graphics, especially
in geometric modeling, has great potential. See an interesting example:
Liquid (Computer and Information Science Department, UPENN)
Various Numerical and Geometric Methods
Differential Equation Related Topics
Ordinary Differential Equation (ODE)
Differential-Algebraic Equation (DAE)
Initial / Boundary Value Problem
Finite Difference Method (FDM)
Finite Element Method (FEM)
Computational Geometry Related Topics