Overview of the class.

slides

[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

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

**Additional reading**

[Joy] Bezier Curves and Patches

[Farin] Ch. 10

[Joy]
B-Spline Curves and Patches

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

[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

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.

[Siggraph]

[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

[Siggraph]

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.

**Reading**

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

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

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

© Denis Zorin, 1998