Discrete Differential Geometry

What it is about

You learn the fundamentals of the differential geometry of curves and surfaces in a discrete framework. The focus is on structurally analogous concepts (e.g. discrete tangents, normals, curvature) and not on numerical approximation. In the end you will be able to treat discrete analogues of smooth curves and surfaces as well as their invariants in a structural and analytical way.

What you will be able to do

• Understand discrete tangent and normal concepts
• Apply curvature concepts for polygonal curves and polyhedral surfaces
• Utilize Euler-type theorems and flow concepts in discrete models
• Analyze parametrizations and 3D compatibility of discrete surfaces
• Describe properties of special classes of surfaces (e.g. discrete minimal surfaces) and their transformations

What the module consists of

• VorlesungConveying the content in lecture with illustrative examples and discussion
• ÜbungProblem sets with solutions for independent checking and deepening, initially guided, later increasingly independent or in small groups

Teaching method

• Vorlesungfor introduction, illustration and discussion of the concepts
• Übung mit Aufgabenblätternfor self-check and deepening of methods and concepts; transition from guided to independent work