• geo = earth

• metria = measure

• Earliest recorded beginnings of geometry:
  • 3000 B.C. by Indus Valley civilization (north India) and Babylonina People

• Our Goal: complex geometry

• “science of shape”
• measurements
  • length
  • area
  • volume
  • angle
  • curvature
  • deformation
  • …
• analytic and/or constructive
• visual nature often allows for intuitive arguments!
  • typically first a picture then a formal algebraic proof

• Cultural Heritage

• Automotive Industry

• Digital Avatars

• Digital Avatars

• Surgery Simulation

• Urban Modeling

• A revolution in materials and fabrication
  • 3D printing, laser cutting, CNC machining, robotic fabrication, etc.
  • digital & smart materials
• An opportunity for graphics research
  • new and complex materials & geometries
  • rapid prototyping and industrial production of custom models
  • intuitive user interfaces for computational, material-aware design
  • data-driven modeling and machine learning
  • control strategies robotic fabrication and assembly
  • fully digital workflow, from design, visualization, simulation, to fabrication

• Additive Manufacturing

• Core Questions
  • What is geometry and where is it used?
  • How can we represent geometry?
  • Which structural properties do we need in practice? (raw geometry vs. practically useful)
  • What kind of basic operations can we perform to process geometry?
  • How can we go from physical to digital?
  • How can we go from digital to physical?
  • What advanced operations can be perform to manipulate geometry?
  • How can we efficiently implement geometry processing algorithms?

• At the end of the course you will be able to:
  • Explain and contrast fundamental geometry representations
  • Explain and apply concepts from discrete differential geometry
  • Analyze the 3D content creation pipeline and understand its limitations
  • Implement and evaluate basic geometry processing algorithms, such as smoothing, remeshing, deformation
  • Implement algorithms for advanced modeling
  • Create digital 3D models from photographs and process the acquired raw geometry to build physical prototypes
  • Coordinate a team during a software project

• Programming and written exercises
  • implement fundamental algorithms for geometry analysis, smoothing, remeshing, editing
• Must be done in groups of 3
• All deadlines are strict!
  • Zero points when submitted after the deadline
  • Don’t wait until the last minute but submit version early. Can always be replaced by final version before deadline
  • Contact me early in case of military service, sick leave, etc.

• Each assignment is worth 10 points
• Admission to final exam requires 50% of total points
• Final exam determines grade
• Exams cover material from lectures and practical assignments
• Zero tolerance for cheating!

… know how to express love with equations

… be able to untangle messy curves

… know why this can be made from a single sheet of paper

… know why this cannot be made from a single sheet of paper

… understand why at any time there is at least one point on the planet where there is no ground wind (and what that has to do with geometry)

… be able to figure out if the universe is flat (well, sort of)

… know how to properly eat pizza

… know a lot more about soccer balls

… be able to play games with funky dice

… know what the Fourier transform of a bunny looks like

… know how to skin a cow

… be able to make a Dino hatch from an egg

… have seen some very unique geometric objects

… understand why it’s hard to scan something

… understand why it’s hard to 3D print something

… (hopefully) appreciate the beauty of geometry