## CSE 274 (FA 2020)

Welcome to CSE 274, Advanced Topics in Computer Graphics — Discrete Differential Geometry.

The course provides an introduction to discrete differential geometry and its applications in geometric modeling and analysis. The contents include the smooth and discrete theory of curves, surfaces, exterior calculus, the Hodge theory, and the vector bundle theory. The theories are explained alongside with applications including numerical methods for differential equations on manifolds, surface texturing, shape analysis and vector field designs. The course also covers the basics of the graphics software Houdini FX.

### Course Logistics

The main course information, Zoom links are on the UCSD Canvas.
• Instructor: Albert Chern (office hour: Thu 17:00–18:00)
• Time: MWF 17:00–17:50 (remote)
• Grade: 90% Homework (including theory and implementation) + 10% Participation
• We recommend the implementation part of the the homework be done via the Houdini software.
• Use Piazza for Q&A discussion.

### Schedule

• 10/2 (Fri) Introduction to Discrete Differential Geometry.
• 10/5 (Mon) Intro to Houdini. (HW0 available)
• 10/9 (Fri): Plane curves.
• 10/12 (Mon): Discrete plane curves. (HW0 due)(HW1 available)
• 10/14 (Wed): Space curves.
• 10/16 (Fri): Space curves.
• 10/19 (Mon): Topology of surfaces.
• 10/21 (Wed): Discrete surface theory/smooth surface theory.
• 10/23 (Fri): Smooth surface theory.
• 10/26 (Mon): Smooth surface theory. (HW1 due)
• 10/28 (Wed): Discrete Laplacian / Discrete exterior calculus. (HW2 available)
• 10/30 (Fri): Exterior calculus.
• 11/2 (Mon): (Discrete) exterior calculus.
• 11/4 (Wed): PDEs on manifolds.
• 11/6 (Fri): PDEs on manifolds.
• 11/9 (Mon): Exterior calculus.
• 11/11 (Wed): Holiday
• 11/13 (Fri): Lie derivative, codifferential, Laplacian, calculus of variations. (HW2 due)
• 11/16 (Mon): Integral geometry. (HW3 available)
• 11/18 (Wed): Integral Geometry continued.
• 11/20 (Fri): Hodge Decomposition, Homology Theory.
• 11/23 (Mon): Morse theory, Vector bundle, Poincaré–Hopf.
• 11/25 (Wed): More connections.
• 11/27 (Fri): Thanksgiving
• 11/30 (Mon): (HW3 due)
• 12/2 (Wed): More $$U(1)$$ gauge theory in graphics.
(Stripe pattern, polyvector field and quad meshing, vortex detection, Ginzburg–Landau systems)
• 12/4 (Fri):
• 12/7 (Mon):
• 12/9 (Wed):(HW4 due)
• 12/11 (Fri):

The last few buffer lectures may cover additional topics in graphics such as conformal geometry processing, geometric fluid dynamics, etc.