Lectures and Readings

This is a preliminary schedule of lectures. Required reading materials and some additional papers will be handed out in class.

Lecture 1, September 9 Introduction and overview

Applications of geometric modeling: animation, cinematic special effects, mechanical CAD, visualization of scientific data, 3D on the Web.
Overview of the class.

Lecture 2, September 16 Spline curves

Parameteric curves. Spline curves. Bezier form: quadratic and cubic curves.  Blossoming.

[Farin], Chapter 3, 4.1-4.6,7.1-7.7

Additional reading on splines:

Hans-Peter Seidel, An introduction to polar forms IEEE Transaction on Computer Graphics, 1, 1993, pp. 38-46
Carl deBoor B-spline basics Fundamental Developments of Computer-Aided Geometric Modeling, Les Piegl (ed.), Academic Press (London) 1993; 27--49;
Lyle Ramshaw Blossoming: A Connect-the-Dots Approach to Splines,SRC Research Report 19, 19987, and Blossoms are polar forms , SRC Report 34, 1989
Stephen Mann, ``Algorithms from Blossoms,'' Research Report CS-96-29, Computer Science Department, University of Waterloo (October 1996).
[Joy] Bezier Curves and Patches , B-Spline Curves and Patches

Lecture 3, September 23 Spline curves

Properties of Bezier curves. Bernstein polynomials. Blossoming.
[Farin], Chapter 3, 4.1-4.6,7.1-7.7

Additional reading

[Joy] Bezier Curves and Patches

Lecture 4, September 30  Spline curves

Constructing B-splines with blossoming. Bezier and deBoor control points. NURBS.

[Farin] Ch. 10
[Joy]  B-Spline Curves and Patches

Lecture 5, October 7 Spline surfaces; subdivision curves

Tensor product patches. Trimming curves.

Uniform B-splines. Two-scale relation.
Subdivision as a generalization of splines. Subdivision rules for cubic and quadratic splines.

[Farin] Chapter 16.1-16.4, 17.1, 17.2, 17.10
[Warren] , Chapter 1,2
[Siggraph] Chapter 2.

Additional reading

J. Miller. Sculptured surfaces in solid models: issues and alternative approaches. IEEE Transactions on Computer Graphics and Applications, 6(12), pp. 37--48, 1986
A. Rockwood and K. Heaton and T. Davis, Real-time rendering of Trimmed Surfaces, SIGGRAPH `89

[Joy] Subdivision/Refinement
G. Chaikin. An algorithm for high-speed curve generation. Computer Graphics and Image Processing, 3, pp. 346-349, 1974

Lecture 6, October 14 Subdivision curves

Four-point rule. Convergence and smoothness analysis. Generating functions. Difference schemes.
[Siggraph] Chapter 3.

Additional reading
N. Dyn, J. Gregory and D. Levin. A four-point interpolatory subdivision scheme for curve design. Computer-Aided Geometric Design 4, pp. 257-268, 1987
G. Deslauriers, S. Dubuc. Symmetric Iterative Interpolation Processes, CONAP, 5(1), pp. 49-68, 1989

Lecture 7, October 21 Subdivision surfaces

More on generating functions and difference schemes.

Subdivision rules for tensor product splines. Subdivision rules for triangular splines. Loop subdivision scheme.
[Siggraph] Chapter 3.

Additional reading
[Joy] Subdivision/Refinement
C. Loop. Smooth subdivision surfaces based on triangles. MS thesis. University of Utah, 1987.

Lecture 8, October 28 Subdivision surfaces and variatinal surfaces

What is a smooth surface? Subdivision matrices for surface schemes.
[Siggraph] Chapter 3 Lecture 9, November 4 Subdivision surfaces Surface subdivision schemes: Catmull-Clark, Doo-Sabin, Butterfly. Analysis of smoothness and construction of subdivision schemes. Subdivision rules for boundaries and creases. Introducing features into subdivision surfaces.
[Siggraph] Chapter 3.

Additional reading
[Joy] Subdivision/Refinement
E. Catmull and J. Clark. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design 10, 1978, 350-355
D. Doo. A subdivision algorithm for smoothing down irregularly shaped polyhedrons. In Proced. Int'l Conf. Ineractive Techniques in Computer Aided Design (1978), pp. 157-165. Bologna, Italy, IEEE Computer Soc.
D. Doo and M. Sabin. Behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design 10 (Sept. 1978), 356-360
N. Dyn, D. Levin and C. Micchelli. Using parameters to increase smoothness of curves and surfaces generated by subdivision. Computer-Aided Geometric Design 7, pp. 129-140, 1990
U. Reif. A Unified approach to subdivision algorithms near extraordinary points, Computer-Aided Geometric Design 12, pp. 153-174, 1995

H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer and W. Stuetzle. Piecewise Smooth Surface Reconstruction. SIGGRAPH 95 Conference Proceedings, pp. 173--182
[Siggraph] Chapter 8,10.
T. DeRose, M. Kass, T. Truong. Subdivision Surfaces in Character Animation. SIGGRAPH 98 Conference Proceedings pp. 85--94

Lecture 10, November 11 Multiresolution representations

Multiresolution representatons related to subdivision. Brief introduction to wavelets. Burt-Adelson pyramid. Multiresolution representations of surfaces. Wavelet-based representation. Pyramid-based representation. Hierarchical splines.
[Siggraph] Chapter 6,7.

Lecture 11, November 18 Mesh simplification

Mesh simplification algorithms. Progressive mesh representation. Mesh simplification algorithms: vertex decimation, vertex clustering, edge contraction. View-dependent simplification.

Carl Erikson, Polygonal Simplification: An Overview, Technical Report TR96-016, University of North Carolina, Chapel Hill, 1996.
Hugues Hoppe, Progressive Meshes, SIGGRAPH 96.

Additional reading
Greg Turk, Re-Tiling Polygonal Surfaces, SIGGRAPH '92 Proceedings.
William J. Schroeder, Jonathan Zarge, and William Lorensen, Decimation of Triangle Meshes, SIGGRAPH 92 Proceedings
J. Rossignac and P. Borrel, Multi-resolution 3D approximations for rendering complex scenes (vertex clustering).
Michael Garland and Paul Heckbert, Surface Simplification Using Quadric Error Metrics, SIGGRAPH '97 Proceedings
Jonathan Cohen et al., Simplification Envelopes, SIGGRAPH '96.
Multiresolution Surface Modeling Course Notes, SIGGRAPH `97.

Lecture 12, November 25 Mesh smoothing and compression

Mesh smoothing, frequency analysis on meshes. Approaches to mesh compression. Connectivity and geometry compression. Progressive transmission.

G. Taubin A Signal Processing Approach to Fair Surface Design IBM Technical Report
G. Taubin, T. Zhang and G. Golub, Optimal Surface Smoothing as Filter Design. Proc. of the Fourth European Conference on Computer Vision, vol.1, pp. 283 - 292, 1996. Also available as an IBM Technical Report
Gabriel Taubin and Jarek Rossignac, Geometry Compression through Topological Surgery, ACM Transactions On Graphics, v. 17, n. 4, p. 84-115, 1998
VRML 2.0 binary format proposal based on this paper
Michael Deering. Geoemtry Compression. SIGGRAPH '95 Proceeedings. pp. 13-19 Java3D geometry compression specs based on this paper

Lecture 13, December 2 Volume and solid representations

Binary space partition trees and their applications. Constructive solid geometry. Voxel-based representations.

B. Naylor. Tutorial on BSP trees.
A. Kaufman, D. Cohen and R. Yagel, Volume Graphics, IEEE Computer, Vol. 26, No. 7, July 1993, pp. 51-64.

Additional reading

H. Fuchs, Z. Kedem and B. Naylor, "On Visible Surface Generation by A Priori Tree Structures" SIGGRAPH '80, pp124-133.
BSP tree FAQ
R. Westermann, T. Ertl, A Multiscale Approach to Integrated Volume Segmentation and Rendering Eurographics 1997, Conference Proceedings

Lecture 14, December 9 Image-based representations

Image-based representations. Light fields. Combining light fields and geometry. Extracting geometry from images.

Shenchang Eric Chen and Lance Williams, View Interpolation for Image Synthesis, SIGGRAPH `93.
Leonard McMillan and Gary Bishop, Plenoptic Modeling: An Image-Based Rendering System, SIGGRAPH `95.
Michael Cohen's Talk for the SIGGRAPH `97 Panel on Image-Based Rendering

Marc Levoy and Pat Hanrahan, Light Field Rendering, SIGGRAPH '96
Steven J. Gortler, Radek Grzeszczuk, Richard Szeliski, and Michael J. Cohen, The Lumigraph, SIGGRAPH '96

Finals week

Projects due!

© Denis Zorin, 1998