Geometric Data Analysis and Processing

• select and use surface representations such as point clouds, triangle meshes and implicit surfaces for tasks involving geometric data
• compute geometric and differential geometric properties of triangle meshes
• use tools from linear algebra for reconstruction and manipulation of surfaces
• polygonize implicit surfaces
• simplify, optimize, and remove noise from 3D triangle meshes
• perform spectral analysis of triangle meshes using the Laplace-Beltrami operator and apply it to smoothing, parametrization and more
• detect and classify features in point clouds and register point clouds
• triangulate 2D point sets using Delaunay triangulation
• reconstruct triangle meshes from 3D point clouds
• compute basic topological features such as genus from polygonal meshes
• represent 3D surfaces as skeletons or medial surfaces

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.
– Geometric and 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 scattered data interpolation. Representation of surfaces as implicit surfaces or height maps via basis functions.
– Approaching geometry processing and analysis through programming.
– The use of methods from linear algebra such as linear system solving (including the Singular Value Decomposition) for tasks in geometry reconstruction and manipulation.
– Computation of topological characteristics using the Euler-Poincare formula.
– Using computer graphics to make geometric data more accessible.

• 36 – 49 (Thurs 13-17)

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.