Annotated Bibliography

Introduction to Implicit Surfaces, Edited by Jules Bloomenthal 1997.

This book is more than just implicit surfaces: it covers topics such as solids, rendering, surface tiling (turning an implicit surface into a mesh polygon mesh), and spatial subdivision. It does not assume previous familiarity with topics in representing surfaces. Of particular interest for this lecture was Chapter 4, "Surface Tiling".

Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide, Gerald Farin 1993 (3rd ed.).

The subtitle ``A Practical Guide'' is a little deceiving. This mathematics-heavy book covers the fundamentals of parametric surfaces, i.e., spline curves and surfaces. The fundamentals cover among other things, (building from spline curves in 2D and working up to surfaces in 3D) continuity and basis functions, and the matrix formulation of spline surfaces. I did not make very much use of this book in preparation for this lecture.

Computer Graphics: Principles and Practice (2nd edition in C), Foley, van Dam, Feiner, Hughes 1996.

This is just your everyday computer graphics textbook, albeit 1147 pages long, so it convers a great many different topics. Of interest for this lecture was Chapters 11 and 12. However, I did not find too much useful material in this textbook for this lecture -- the mathematical discussion of parametric curves is nice (but mostly omitted from this lecture).

The Visualization Toolkit: An Object-Oriented Approach to 3D Graphics, Will Schroeder, Ken Martin, Bill Lorenson 1998 (2nd Edition).

This is ``officially'' the user manual to the Visualization Toolkit Library software package, but covers much more detail than an average user manual, explaining to the non-computer graphics community what the software does. The toolkit has the Marching Cubes Algorithm already implemented, and its operation is described in chapter 6. The Visualization Toolkit is installed on Athena -- you can access it using ``add vtk''. However Professor Teller warns that the learning curve on this package is quite steep.

``Approximation Hierarchies and S-bounds'', in proceedings of ``Symposium on Solid Modeling Foundations and CAD/CAM Applications'' , Stephen Cameron 1991.

This paper describes boundary hierarchies, a technique in which a complicated CSG solid is represented by a hierarchy is simpler bounding objects. It's running example is from robotics: determining quickly whether a robot will intersect its environment. It gives some nice diagrams where the simpler bounding objects are convex hulls of parts of the robot.

SIGGRAPH 98 Conference Proceedings.

The proceedings from recent SIGGRAPH Computer Graphics conferences make good coffee-table reading material, as they are usually filled with page after page of pretty pictures. Just avoid the silly by by the Media Lab. The 1998 conference had a special session on "Surfaces", which was of interest to this talk. The papers of interest were

``Non-uniform Recursive Subdivision Surfaces'', by Sederberg, et al.
``Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values'', by Stam
``Subdivision Surfaces in Character Animation'', by De Rose, et al. This paper by authors from PIXAR describes the animation of the chess-playing old man Geri from the animated short ``Geri's Game''.

http://www.multires.caltech.edu/teaching/courses/subdivision/ Web search terms (Robust Hyperlink): "dforsey midedge surflab dzorin louns kobbelt lounsbery catmull" (*)

This website was the best introduction to subdivision surfaces. This website is an online repository of a special course on Subdivision Surfaces that was taught at the 1998 SIGGRAPH Conferences. Select the "actual course notes" link (it's 26MB) unzip it, and read Denis Zorin's chapter 3 on subdivision surfaces.

http://www.pixar.com/products/renderman/prman/subdivs.html Web search terms (Robust Hyperlink): "catmull mtor prman bicubic quadrilaterals polyhedron nurbs interpolates interpolate" (*)

This is a non-mathematical summary of a paper presented by the PIXAR authors in SIGGRAPH 98. It gives a brief introduction to Subdivision Surfaces.

http://graphics.lcs.mit.edu/classes/6.838/S98/meetings/m7/start.html Web Search terms (Robust Hyperlink): "morcrette brep geodesics voxels amram defs repr curvature csg breadth" (*)

This was the previous 6.838 presentation of this topic. It contains some material left out of this lecture. Some of the sections are no longer available, and some of the links are out of date.

http://graphics.cs.ucdavis.edu/CAGDNotes/Doo-Sabin/Doo-Sabin.html Web search terms (Robust Hyperlink): "biquadratic polyhedrons nonplanar midpoints chaikin proced sabin repetitively meshes" (*)

This is just one page in a website of "On-line Geometric Modeling Notes". This specific page covers the Doo-Sabin scheme of subdivision surfaces. It does require some previous familiarity with the material: I found it difficult to understand as introductory reading. Because it is just a set of hyperlinked notes, there is no good ``starting page'' and order to read them.

http://www-2.cs.cmu.edu/~ph/heckbert.html Web search terms (Robust Hyperlink): "stenedge zonohedron stahovich zonohedra ikonas hiddenline ribelles obfuscators heckbert quadric" (*)

This is Paul Heckbert's home page at CMU. Of particular interest for this lecture is his paper, which describes the particle method of enumerating points on an implicit surface.

``Using Particles to Sample and Control Implicit Surfaces'', Andy Witkin and Paul Heckbert, SIGGRAPH '94

Heckbert has a wealth of other graphics related material on his page.

http://research.microsoft.com/~cloop/ Web search terms (Robust Hyperlink): "cloop bicubic quartic chebyshev multiresolution topological curvature bezier smoothness eigenvalues" (*)

This is Charles Loop's homepage. Loop's master's thesis is on subdivision surfaces, and describes Loop's subdivision scheme.

http://www.slicerdicer.com/gallery.html

Images of volumetric data were borrowed from this page.