What will we Learn in This class?
How to think about shape…
- mathematically (differential geometry)
- computationally (geometry processing)
Central Theme: link these two perspectives
What is Differential Geometry?
Language for talking about locel properties of shape
- How fast are we traveling along a curve?
- How much does the surface bend at a point?
- etc
And their connection to global properties of shape
- so-called “local-global” relationships.
What is Discrete Differential Geometry
Also a language describing local properties of shape
- infinity no longer allowed
- No longer talk about derivatives, infinitesimals…
- Everything expressed in terms of lengths, angles…
- Surprisinglt little is lost!
- Faithfully captures many fundamental ideas
How can we get there?
A common “game” is played in DDG to obtain discrete definitions:
- Write down several equivalent definitions in the smooth setting
- Apply each smooth definition to an object in the discrete setting
- Determine which properties are captured by each resulting **inequivalent ** discrete definition.