Geometric Data Analysis and Processing

• select and use surface representations for tasks involving geometric data
• compute differential geometric properties using the Laplace Beltrami operator for triangle meshes
• polygonize implicit surfaces
• represent functions on meshes using basis functions and perform interpolation
• simplify polygonal meshes
• smooth and remove noise from polygonal meshes
• register point clouds
• triangulate 2D point sets using Delaunay triangulation
• parameterize 3D surfaces
• use the volume representation to process geometric data
• use computer graphics to visualize geometric data effectively

The following topics are discussed:
– Several surface representations, for instance, meshes, distance fields (signed and unsigned), skeletal and medial representations, tetrahedral and hexahedral grids, point clouds, etc.
– Spectral analys of triangle meshes using methods that are analogous to Fourier analysis.
– Differential geometry properties of discrete surface representations.
– Primitive operations on meshes.
– Simplification and optimization of meshes.
– Registration of point clouds using the ICP method.
– Triangulation and manipulation of triangulations.
– Basis functions and of scattered data.
– Approaching geometry processing and analysis through programming.
– Using computer graphics to make geometric data more accessible.

01002/01004/01005/01006/02002/02631/02632/02633, Knowledge of a programming language such as Python and a good understanding of basic calculus and linear algebra including eigenvalue problems. Knowledge of Fourier series (introduced in Advanced Engineering Math 2) is an advantage.

Lectures and databar exercises.