CS497JCH Advanced Surface Modeling

CS 497, Fall 2000
Prof. John C. Hart

Advanced Surface Modeling

Section JCH, #08907
12:30 - 1:45 p.m., Tu/Th, 106B3 Engineering Hall

This course will develop the tools necessary for interrogation and display of advanced non-parametric surface representations, focusing on implicit surfaces, subdivision surfaces and level sets. These surface representations are procedural, which means they are well-defined surfaces somewhere in space but one has to use the procedure to figure out where they are. Implicit surfaces are surfaces where a function over space is equal to a fixed isovalue. Subdivision surfaces are smooth surfaces that result from subdividing the polygons in a given mesh. Level sets are advancing fronts that develop over time depending on local and global effects.

These surface models have applications in computer graphics, computer vision, computer-aided geometric design, scientific computing/visualization, computational biology and computational fluid dynamics. Concepts will include analytic/procedural/sampled representations, mesh data structures/operations, constrained dynamics, differential geometry, surface topology, and initial-value/boundary-value problems. Students completing this course will have acquired the background and domain knowledge necessary to contribute new ideas to this field.

Course Goals

To learn about this category of geometric surface representation.
To develop a freely-available library package for using these representations.

Class Project

We will be cooperatively build a new freely-available class library to support advanced surface research. Individual homework and project assignments will be assigned as new member functions of this library.

This library is built on libgm.
Documentation: Class Hierarchy and Technical Paper.
Current library is available at http://sourceforge.net/projects/surface
Links to download WinCVS and a Win32 SSH program. You will need to set the variable CVS_RSH to "ssh" and make sure that the directory with ssh.exe (and the dll's) is in your PATH. Set the CVSROOT in the WinCVS system to point to: "loginname@cvs.yourproject.sourceforge.net:/cvsroot/yourproject". You can use "anonymous" as your login name to download (e.g. checkout) code but you must have an approved login to upload (e.g. commit) code. More info on WinCVS, CVS and SourceForge.

Prerequisites

Familiarity with:

3-D graphics and
numerical methods.

Project

The course project will consist of member functions for these advanced surface classes. The member functions that will be assigned, integrated and tested by the instructor. Collaboration and teamwork will be encouraged since each student will be assigned unique coding assignments.

Outline

Tools for visualizing surfaces during development

OpenGL
VRML
the Crossroads file translator

Implicit surfaces

Polygonizing implicit surfaces

Notes
Interval analysis
Jules Bloomenthal's polygonizer (updated for OpenGL compile with -DUSEGLUT)

Particle systems constrained to implicit surfaces

Notes on dynamic constraints (by Andrew Witkin)
Using particles to sample and control implicit surfaces (presented by Ed Bachta)
Mpeg video of particle system on implicit surface
Hans Pedersen's code for modeling implicit surfaces with a particle system (uses X-windows, OpenGL and XForms)

Meshing and surface topology

Notes

Fitting data with implicit surfaces

A-Patches (in implicit surfaces book)
Variational implicit surfaces (presented by Bill Nagel)

Mesh compression

Progressive Meshes (presented by Steve Zelinka)
No class on Thursday, 12 Oct. 2000

Subdivision surfaces

Curves (Schroeder, Caltech)
Surfaces (Zorin, NYU)
Zoo (Zorin, NYU)
Java demos: Chaikin's corner cutting, 4-point piecewise interpolation.

Applications of subdivision surfaces

Efficient, fair interpolation using catmull-clark surfaces (10/31)
Subdivision surfaces in character animation and notes (presented by Lennie Brown, 11/2)
Exact Evaluation of Subdivision Surfaces (11/7) and notes.
MAPS: Multiresolution Adaptive Parameterization of Surfaces and notes (presented by Jeff Decker, 11/9)
Displacement mapping (presented by Nate Carr, 11/14)

Level sets

Introduction and applications in computer graphics
Level set methods
Fast marching methods
Applications in advanced rocketry (Jim Jiao)

Books

Jules Bloomenthal (Ed.). Introduction to Implicit Surfaces. Morgan Kaufmann Publishers, August 1997, ISBN: 155860233X.
Peter Schroeder and Denis Zorin (Eds.). Subdivision for Modeling and Animation.

Zorin/Schroeder's SIGGRAPH 99 Course Notes, August 1999. (Contains Jos Stam's notes on exact evaluation.)
Zorin/Schroeder's SIGGRAPH 2000 Course Notes, July 2000. (Contains better introductory material.)
Joe Warren's manuscript "Subdivision Methods for Geometric Design."
Brian Sharp's Gamasutra article "Subdivision Surface Theory" for game developers.
Kenneth Joy's Online Geometric Modeling Notes contains some nice detailed info on subdivs.

James Albert Sethian. Level Set Methods and Fast Marching Methods (Second Edition). Cambridge University Press, June 1999, ISBN: 0521645573.

Sethian's web site with movies and java demos.
Ross Whitaker's VISPACK that contains level set code.
A fast marching method for finding the closest point to a curve or surface.