Topics in Computer Graphics

Monday 5:00 pm-7:00 pm

719 Broadway, room 1221 (changed to 1202 until further notice).

Denis Zorin, office hours: Monday 1-3 pm and by appointment


This course surveys several topics in geometric modeling. The following topics will be covered: spline curves and surfaces, subdivision surfaces, mesh processing, surface parameterization and reconstruction of surfaces.


Mathematics: linear algebra, calculus.
Computer Science: solid programming ability in at least one language (Java, C++, C). An introductory graduate class in computer graphics is recommended.


Project. The grade will be primarily based on the course project. A list of suggested projects will be provided; however, students may choose their own project. In either case, the intended project should be discussed with the instructor.
Written assignments. There will be one or two short written assignments.
Paper presentation. Each student is required to present a paper. Presentations should be 30 min. long + 10 min for questions and discussion. The presenter should prepare slides for the presentation, which should be sent to the instructor for review no later than Friday before the presentation.
Scribing. Each student serves as a scribe for one lecture. Scribes are expected to take detailed notes and produce a typeset version of the notes to be distributed to the class. Detailed instructions for notes and LaTeX templates are here

Reading materials

The course will be based on a collection of papers and notes. Links to relevant materials on the Web will be added to the list of lectures below.

Project ideas


October 21 A detailed description of the proposed project.

November 18 Progress report.

Finals week Projects due.


September 9    Introduction; basic differential geometry.
Scribe: Elif Tosun. Lecture notes (PDF).
September 16 Spline curves. Bezier curves and B-splines. Blossoming.
Scribe: Kranthi K. Gade. Lecture notes (PDF).

Reading: H.-P. Seidel, An introduction to polar forms IEEE Transaction on Computer Graphics,1, 1993, pp. 38-46
Lyle Ramshaw Blossoming: A Connect-the-Dots Approach to Splines,SRC Research Report 19, 19987, and Blossoms are polar forms , SRC Report 34, 1989

September 23 Spline surfaces. Blossoming in two dimensions. NURBS.
Scribe: Zhihua Wang. Lecture notes (PDF).
September 30 Subdivision curves and surfaces I. Subdivision curves; Subdivision for splines. Catmull-Clark subdivision.
Scribe: Chris DeCoro. Lecture notes (PDF).

Reading: D. Zorin, P. Schröder, A. DeRose, L. Kobbelt, A. Levin, W. Sweldens. Subdivision for Modeling and Animation

Paper: A. DeRose, M. Kass, T. Tuong. Subdivision surfaces in character animation.
Presenter: Chris DeCoro.

October 7 Subdivision surfaces II. Loop subdivision, subdivision matrix, limit positions and tangents.

Reading: SIGGRAPH course notes.
Paper: H. Biermann, A. Levin, D. Zorin. Piecewise smooth subdivision surfaces with normal control.
Presenter: Steven Gutstein.

October 14 Operations on parameteric surfaces: trimming, intersection.

Mesh simplification. Classification of methods. Edge, vertex, face decimation. Error metrics. Topology preserving and nonpreserving simplification.
Scribe: Feng Ning. Lecture notes (PDF).
Additional Reading: N. Litke, A. Levin, P. Schröder Trimming for Subdivision Surfaces.

October 21 Paper presentations.

Paper: M. Hohmeyer. Robust and efficient surface intersection for solid modeling, Ch. 3, Loop detection.
Presenter: Zhongshan Zhang. Paper: S. Zelinka and Garland. Surface simplification using quadric error metrics.
Presenter: Dazhi Xie.

October 28No Class
November 4 Mesh smoothing. Discrete Laplacian and related smoothing methods. Discrete curvature and geodesics.
Scribe: Zhongshan Zhang. Lecture notes (PDF).

Paper: M. Desbrun, M. Meyer, P. Schröder. Implicit fairing of arbitrary meshes using diffusion and curvature flow.
Presenter: Feng Ning.

November 11 Mesh parameterization. Floater parametrization. Distortion measures. Harmonic and conformal maps.
Scribe: Steven Gutstein. Lecture notes (PDF).

Paper: M.S. Floater. One-to-one piecewise linear mappings over triangulations.
Presenter: Elif Tosun.
M. Floater. Parametrization and smooth approximation of surface triangulations.
M. Desbrun, M. Meyer, P. Alliez. Intrinsic Parameterizations of Surface Meshes.

November 18 Surfaces from volume data. Marching cubes. Dual methods. Distance functions.
Scribe: Chien-Yu Hung. Lecture notes (PDF).

Paper: L. Kobbelt, M. Botsch, U. Schwanecke, H.-P. Seidel. Feature sensitive surface extraction from volume data.
Presenter: Chien-Yu Hung.

November 25Surfaces from point clouds. Vornoi diagrams, medial axes. Crust algorithm.
Scribe: Xie Dazhi

Paper: H. Edelsbrunner. Surface reconstruction by wrapping finite point sets in space.
Presenter: Kranthi K. Gade.

December 2Mesh reparameterization.
Scribe: Oleg Kim.

Paper: I. Guskov, K. Vidimce, W. Sweldens, P. Schröder. Normal meshes.
Presenter: Zhihua Wang.

December 9 Implicit surfaces. Paper: Chandrajit Bajaj. Introduction to Implicit Surfaces, Ch. 3: Implicit Surface Patches. (available from instructor).
Presenter: Oleg Kim.

Denis Zorin