Welcome to CSE 270 "Discrete Differential Geometry"
Week  Tuesday (Lecture)  Wednesday (Discussion)  Thursday (Lecture) 

1  1/9: Introduction, Houdini

1/10 Houdini rendering tips Möbius transform, digital asset 
1/11: Triangle meshes, Euler characteristics

2  1/16: Half edges, introduction to Laplacian

1/17 Level sets on surfaces Area using hedge data struct Numpy slicing 
1/18: Discrete Laplacian, Discrete exterior calculus (DEC)

3  1/23: Discrete exterior calculus (DEC)  1/24 Wave equation vector field visualization 
1/25: Vectors, covectors, differential 
4  1/30: Differential  1/31 Boundary conditions on Poisson equation 
2/1: Exterior calculus

5  2/6: Exterior calculus  2/7  2/8: Finite Element Exterior calculus 
6  2/13: Differential geometry of curves  2/14 Curvature domain processing 
2/15: Differential geometry of curves

7  2/20: Differential geometry of surfaces  2/21 Minimal surface 
2/22: Differential geometry of surfaces 
8  2/27: Differential geometry of surfaces

2/28  2/29: Vector field design, gauge theory

9  3/5: Vector field design, gauge theory  3/6 Stripe patterns on surfaces stripe_pattern.hipnc 
3/7: Vector field design, Hodge decomposition 
10  3/12: Hodge decomposition  3/13 No discussion 
3/14: Optimal transport

Final  3/19: No class

3/20: No class  3/21: 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 highlights:
There is no quiz or exam. The grades are made of the following HWs: