Welcome to CSE 274 "Selected topic in computer graphics" — Discrete Differential Geometry.
Visit Canvas (for all info including Zoom links), Gradescope (HW submission) and Piazza (Q&A).
Week  Tuesday  Thursday  

1  1/10: Introduction, Houdini

1/12: Triangle meshes, Euler characteristics  
2  1/17: Half edges, introduction to Laplacian  1/19: Discrete Laplacian


3  1/24: Discrete exterior calculus (DEC)

1/26: Dirichlet principle, Vectors and covectors


4  1/31: Vectors and covectors

2/2: Exterior calculus  
5  2/7: Exterior calculus  2/9: Exterior calculus  
6  2/14: Differential geometry of curves

2/16: Differential geometry of curves


7  2/21: Differential geometry of surfaces  2/23: Differential geometry of surfaces  
8  2/28: Differential geometry of surfaces  3/2: Vector field design, gauge theory  
9  3/7: Vector field design, gauge theory

3/9: Vector field design, gauge theory  
10  3/14: Hodge decomposition

3/16: Hodge decomposition


Final  3/21: No class

3/23: No class  
Spring break 
Discrete Differential Geometry introduces the mathematics and algorithms for digital geometry processing and simulation problems. Think of it as applied differential geometry for computer graphics and computational mathematics.
What is discrete differential geometry? In the traditional approach for many computational and engineering problems, one (1) derives the governing equation with multivariable calculus on a coordinate system; (2) applies a generic discretization scheme (finite difference/finite element) to approximate the solution. This direction becomes extremely tedious as the domain of the problem becomes a more general shape (as often encountered in computer aided designs and computer graphics), where no natural coordinate system may fit the geometry featured in the problem. Also, discretization schemes based on approximation theory don't usually preserve the structures (e.g. conservation laws) of the underlying physical or geometric system.
Discrete differential geometry takes a different route. Starting from the modeling stage (deriving governing equation) all the way to algorithmic stage, we use the language of geometry. It bypasses any artificial coordinate systems, and only speaks about relationships between points, lines, surfaces, and the field defined on top of them. During discretization, we directly find the discrete analogs of these relation, preserving as many differential geometry theorems as possible.
Some highlight:
There is no quiz or exam. The grades are made of the following HWs and project:
We will post some related papers here for further reading