Topics in Computer Graphics

Wed. 7:00 pm-9:00 pm

719 Broadway, room 1221.

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

Description

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

Prerequisites

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.

Requirements

Project. The grade will be primarily based on homeworks and a 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. Working in groups is encouraged.
Written assignments. There will be two 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 Monday before the presentation.

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

Links to software

Deadlines

February 25 A detailed description of the proposed project.

March 31Progress report.

Finals weekProject reports due.

Homework

Splines and Subdivision. . Due March 24.

Lectures

Several files with slides are zipped PostScript files (due to problems with PDF conversion). TO view postscript files, you can use gsview.

January 28	Spline curves. Bezier curves and B-splines. Blossoming. Lecture notes 1 (PDF) Lecture notes 2 (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
February 4	Spline surfaces. Blossoming in two dimensions. NURBS. Lecture notes 3(PDF).
February 11	Subdivision curves and surfaces I. Subdivision curves; Subdivision for splines. Catmull-Clark subdivision. Lecture notes 4(PDF). slides (zipped PS). Reading: D. Zorin, P. Schröder, A. DeRose, L. Kobbelt, A. Levin, W. Sweldens. Subdivision for Modeling and Animation Paper 1: A. DeRose, M. Kass, T. Tuong. Subdivision surfaces in character animation. Presenter: Geoffrey Catto.
February 18	Subdivision surfaces II. Loop subdivision, subdivision matrix, limit positions and tangents. Reading: SIGGRAPH course notes. slides (zipped PS). Paper 2: H. Biermann, A. Levin, D. Zorin. Piecewise smooth subdivision surfaces with normal control. Presenter: Koray Kavukcuoglu.
February 25	Operations on parameteric surfaces: trimming, intersection. Mesh simplification. Classification of methods. Edge, vertex, face decimation. Error metrics. Topology preserving and nonpreserving simplification. Lecture notes 6 (PDF). Additional Reading: N. Litke, A. Levin, P. Schröder Trimming for Subdivision Surfaces. Paper 3: S. Zelinka and Garland. Surface simplification using quadric error metrics. Presenter: Eric Olstad.
March 3	Paper presentations. Paper 4: T. W. Sederberg et al. T-splines and T-NURCCs. Presenter: Christopher Logie. Paper 5: X. Decoret et al. Billboard clouds for extreme model simplification. Presenter: Sung Hee Lee
March 10	Mesh smoothing. Discrete Laplacian and related smoothing methods. Discrete curvature and geodesics. Lecture notes 8 (PDF). Paper 6: M. Desbrun, M. Meyer, P. Schröder. Implicit fairing of arbitrary meshes using diffusion and curvature flow. Presenter: Soren Roth
March 17	Spring recess
March 24	Mesh parameterization. Floater parametrization. Distortion measures. Harmonic and conformal maps. Lecture notes 9 (PDF). Paper 7: M.S. Floater. One-to-one piecewise linear mappings over triangulations. Presenter: Yanjun Wang. Paper 8: M. Desbrun, M. Meyer, P. Alliez. Intrinsic Parameterizations of Surface Meshes. Presenter: Raia Hadsell Reading: M. Floater. Parametrization and smooth approximation of surface triangulations.
March 31	Surfaces from volume data. Marching cubes. Dual methods. Distance functions. Lecture notes (PDF). Paper 9: L. Kobbelt, M. Botsch, U. Schwanecke, H.-P. Seidel. Feature sensitive surface extraction from volume data. Presenter: Chieh-Chung Lee. Ensuring consistent topology of marching cubes surfaces: J.-O. Lachaud. Topologically Defined Iso-surfaces. E. V. Chernyaev. Marching Cubes 33: Construction of Topologically Correct Isosurfaces.
April 7	Surfaces from point clouds. Vornoi diagrams, medial axes. Crust algorithm. Paper 10: Nina Amenta, Sunghee Choi and Ravi Kolluri. The power crust. Presenter: Kevin Casey
April 14	Mesh reparameterization. Paper 11: I. Guskov, K. Vidimce, W. Sweldens, P. Schröder. Normal meshes. Presenter: Shoumen Saha.
April 21	Implicit surfaces, radial basis functions. Paper 12: Y. Ohtake et al. Multi-level partition of unity implicits. Presenter: Adrian Secord.
April 28	Paper presentations. Paper 13: Ken Museth et al. Level set surface editing operators. Presenter: Jason Reisman. Paper 14: S. Frisken et al. Adaptively sampled distance fields: a general representation of shape for computer graphics. Presenter: Yotam Gingold.
May 5 Project presentations.

Denis Zorin