Geometric Modeling

Modul	INF-MSc-505
Vorlesung	Dienstag, 14-16 Uhr, OH16 205
Übung	Dienstag, 16-18 Uhr, OH16 205
Lehrende:r	Mario Botsch
Tutor:innen	Gerrit Nolte Sven Wagner
Evaluation	letzte Lehrevaluation

Course Content

After digital audio, images, and videos, virtual 3D models can be seen as the next step in digital multimedia content. Digital geometric models are ubiquitous – for example, in computer games, computer-generated movies, computer-aided design (CAD), numerical simulations, and many other applications. In most cases, discrete polygon meshes – particularly triangle meshes – are the preferred surface representation, as their conceptual simplicity allows for efficient processing of geometric datasets.

In this course, we will discuss the various stages of the geometry processing pipeline. We begin with 3D scanning methods, which produce a high-resolution point cloud that is then converted into a triangle mesh in the next step. The resulting triangle mesh is then optimized according to various criteria: mesh smoothing removes measurement noise, mesh simplification reduces the number of triangles while preserving the shape as much as possible, remeshing improves the shape of triangles and thereby the numerical stability of many geometric algorithms. Mesh parameterization computes a two-dimensional UV layout for texturing. Mesh deformation allows modification of the geometric shape. We will also discuss statistical morphable models, which are trained from several instances of the same class of models (e.g., faces or human bodies). To solve these practical problems, we will also learn the necessary theoretical foundations – for example, (discrete) differential geometry and the solution of (discrete) differential equations on triangle meshes.

To support understanding, the most important methods and algorithms will be implemented in programming exercises.

Prerequisites

• Basic knowledge in linear algebra and calculus is requried (really!).
• Our basic course Computer Graphics is recommended, but not strictly required.
• The programming exercises are done in C++. We will have a C++ crash course at the beginning.

Course Material

• Lecture slides are provided here as HTML slides, as this allows the integration of interactive content such as videos and demo apps. Additionally, the slides are also available as (non-interactive) PDF documents. Access credentials will be sent via LSF email.
• Video recordings will be integrated into the HTML slides.
• After the lecture period ends, the HTML slides and lecture videos will also be available as an Electron app for archiving and offline access.
• The lecture is based on this book (available as a PDF): Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, Bruno Levy: Polygon Mesh Processing, AK Peters, 2010.