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Graphics & Geometry Group Graphics & Geometry

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
Teaser image for Geometric Modeling

Prof. Botsch has a sabbatical in summer 2025 👍. To be able to still offer this course, we will organize it as inverted classroom. Lecture material (including pre-recorded videos) will be provided on the weekend, and we will Q&A, quizzes, theoretical exercises, and programming exercises on Tuesdays, 14:15–17:45.

Attention: Please note that dates, times, and rooms in LSF are not (yet) up to date.

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

Course Material