Instructor Introduction

Three Major Course Components

• Assignments & lectures on foundational material
  • Slides posted online
  • Lectures recorded and linked on Piazza
  • May work in pairs on assignments, if desired
• Research paper presentations by students followed by discussion (exact form subject to change)
  • Non-presenters required to submit a brief (2-3 sentence) summary, and participate in discussion on Piazza
  • Presenters will lead in-class discussion
• Project/Exam (TBD)
  • To be done in teams of up to 3
  • Papers can provide inspiration; project could be an implementation or extension of one of these, or application of existing implementations to a new domain
  • Complexity of project may be adjusted to student level

Geometry - γεωμετρία

geo = earth

Geometry - γεωμετρία

geo = earth

Geometry - γεωμετρία

metria = measure

A little bit of History

Images from Wikipedia

A little bit of History

Classic Geometry was based on compass-and-straightedge construction

Images from Wikipedia

A little bit of History

Images from Wikipedia

A little bit of History

• Modern Geometry joins classic geometry and algebra/calculus
• Analytic Geometry = Geometry with coordinates and equations
• Add in ability to compute, and Geometry Processing results
• “science of shape”:
  • length
  • area
  • volume
  • angle
  • curvature
  • deformation
  • …

A little bit of History

Our goal is complex geometry for simulation and animation

3D Scanning

Cultural Heritage

© Digital Michelangelo Project

Urban Modeling

Automotive Industry

Digital Avatars

© ICT

Computational Fabrication

Course Content

Course Content

Course Content

Course Content

Course Content

Detailed Course Information

• Attending class
  • Lecture: 9:30 AM - 10:45 AM, Tuesdays and Thursdays, CAS 226, Zoom link
  • In-person attendance is encouraged, if you are healthy
  • Lectures and discussions will be recorded
  • If virtual, I will ask that videos be on, to encourage participation
  • Please bring materials for virtual participation, even if you participate in person
• Office hours
  • 10-noon, Fridays, MCS 209, Zoom link
  • Can schedule separate meetings if there are conflicts

Detailed Course Information

• Piazza will serve as the main resource center for the course
  • Main hub for discussion
  • Course syllabus, tentative schedule, growing paper list already up
  • Links to recordings & slides
• Gradescope for turning in assignments
  • Weekly assignments
  • Paper summaries
  • Project-related hand-ins

Weekly Assignments

• Programming in C++ within the Open Flipper framework
• Skeleton code will be provided, so some experience with C++ is helpful, but you do not need to be an expert
• Some have theory components
• Assigned on Thursdays, due on Friday of following week
• Handed in on Gradescope and graded during a demo session on Friday, during office hours ideally
• Mini-lab sessions on Tuesdays during first half of class

Paper Readings & Discussion (may change)

• 30 minutes for student presentation of the paper in question
  • May use publicly available slides/media (with proper attribution)
• 30 minutes for discussion in breakout groups
  • Presenter to float around and help guide discussion
• Non-presenters:
  • required to submit a brief (2-3 sentence) summary on Gradescope
  • post a discussion question on Piazza, and respond substantively to another question

Project/Exam (time-dependent)

• To be done alone or in teams of up to 3
• Papers can provide inspiration; project could be an implementation or extension of one of these, or application of existing implementations to a new domain
• Brief project proposal required
• Final project presentation to be done at the end
• Complexity of project may be adjusted to student level

Tentative Schedule

See doc

Recommended Prerequisites

• Working knowledge of programming and data structures (CAS CS 111 and CS 112, or equivalent). The most useful languages/platforms are C++ and Matlab, but you can use any language you like for your final project.
• A strong foundation in linear algebra (CAS CS 132 or MA 242 or equivalent).
• A strong foundation in multivariable calculus (MA 225 or equivalent)
• Additional background in differential geometry or topology could be quite helpful, but is not necessary, as projects may be tailored towards students’ level of knowledge.
• Project may be tailored to you’re level of preparation. If you’re unsure, feel free to talk to me.

How to use our HTML slides

• Use the keys left/right to navigate through the slides.
• Click page number (bottom right) to open navigation menu.
• Press f/ESC to enter/leave fullscreen mode
• Double-click an item (e.g. an image) to zoom in/out.
• If the whiteboard icon is highlighted red () something was written to the virtual whiteboard. Click the icon to show/hide the whiteboard.
• Use Chrome/Chromium or Firefox 👍. Do not use Safari, it cannot handle WebGL demos 👎.

Slide Acknowledgements

Other resources (even courses!)

• Polygon Mesh Processing by Kobbelt et al.
• Numerical Algorithms: Methods for Computer Vision, Machine Learning and Graphics by Justin Solomon
• Libigl - a header-only C++ geometry processing library
• David Bommes’s course @ Uni Bern
• Justin Solomon’s course @ MIT
• Keenan Crane’s course @ CMU
• Alec Jacobson’s course @ UToronto