Digital Geometry Processing
(MATH6419P.01, 2024 Spring)

Introduction

This course will introduce the basic mathematical foundation of 3D surfaces from the perspective of discrete differential geometry. In detail, we will introduce the complete geometric processing pipeline, including mesh representation, mesh smoothing, mesh parameterization, mesh deformation, mesh repairing, mesh mapping, remeshing, mesh simplification, and direction field generation. We will learn the representation method, data structure, modeling method, shape editing and analysis method of polygon mesh in the computer by many programming tasks.

Course Info

• Instructors: Qing Fang
• Date and time: Wednesday, 2:00pm–3:30pm / Friday, 3:55pm-6:10pm.
• Location: Room 5304, East Campus, USTC.

Schedule

• 28 Feb(Wed)— Overview and mesh.
• 01 Mar(Fri)— Delaunay Triangulations and Voronoi Diagram.
• 06 Mar(Wed)— Surface Reconstruction I.
• 08 Mar(Fri)— Surface Reconstruction II.
• 13 Mar(Wed)— Differential Curves.
• 15 Mar(Fri)— Differential Surfaces.
• 20 Mar(Wed)— Mesh Smoothing.
• 22 Mar(Fri)— Mesh Smoothing I.
• 27 Mar(Wed)— Mesh Smoothing II.
• 29 Mar(Fri)— Mesh Smoothing III.
• 03 Apr(Wed)— Deformation I.
• 07 Apr(Sun)— Deformation II.
• 10 Apr(Wed)— Cubic Stylization and Polycube.
• 12 Apr(Fri)— Geodesic Distance.
• 17 Apr(Wed)— Spectral Mesh Processing.
• 19 Apr(Fri)— Vector Fields.
• 24 Apr(Wed)— Conformal Parameterization I.
• 26 Apr(Wed)— Conformal Parameterization II.

Assignments

1.Surface Simplification Using Quadric Error Metrics(slide).
Deadline: 23:59 2024/3/10.

2.Poisson Surface Reconstruction(slide).
Deadline: 23:59 2024/3/24.

3.A Local/Global Approach to Mesh Parameterization(slide).
Deadline: 23:59 2024/3/31.

4.Cubic Stylization(slide).
Deadline: 23:59 2024/4/17.

5.You Can Find Geodesic Paths in Triangle Meshes by Just Flipping Edges(slide).
Deadline: 23:59 2024/5/01.

6.Spectral Mesh Simplification(slide).
Deadline: 23:59 2024/5/10.

7.Designing N-polyvector Fields with Complex Polynomials.
Deadline: 23:59 2024/5/24.

8.Discrete Calabi Flow: A Unified Conformal Parameterization Method.
Deadline: 23:59 2024/6/09.

Survey and presentation.
Time: 2024/5/08 - 2024/5/31.