Geometric meshes: modeling and processing 2014
Instructors:
Leila De Floriani - DIBRIS Univ. Genova
Enrico Puppo - DIBRIS Univ. Genova
Period:
September, 8-12, 2014 - 4 hours per day: 10-12 - 14-16
Location:
Valletta Puggia - Room 711 Mon.-Wed. - Room 217 Thu.-Fri.
Number of hours:
20
Summary:
Geometric meshes play a fundamental role in Computer Graphics, CAD, scientific visualization, spatial data processing, Finite Element Methods and engineering in general. Geometric meshes provide a finite, discrete representation the geometry and topology of complex shapes and domains, and can be used for a number of applications. This course provides an introduction to geometric meshes and related
modeling and computational issues. We will discuss relevant issues in designing geometric and topological data structures that are efficient (in time and space) and effective (for specific applications). We will review recent contributions on compact representations for structured, unstructured and hierarchical meshes in two, three and higher dimensions, and how they effectively exploit properties of the meshing domain to achieve their efficiency. Next we will explore some problems in geometry processing, showing how classical mathematical concepts from the continuum can be effectively and efficiently discretized on geometric meshes. To this purpose, we will focus on the case of surfaces embedded in 3D space and we will show computational techniques for analyzing and manipulating such surfaces.
Prerequisites:
Basic geometry and linear algebra; elementary data structures (graphs, trees)
Syllabus:
Preliminaries (E. Puppo)
• Elements of combinatorial topology
• Elements of discrete differential geometry
Processing (E. Puppo)
• Analysis of discrete surfaces
• Smoothing and fairing
• Mesh parametrization
• Mesh simplification
Modeling (L. De Floriani)
• A taxonomy of data structures for mesh representation
• Representations for polygonal, triangle and tetrahedral meshes
• Dimension-independent representations for cell and simplicial complexes
• Hierarchical representations: mesh hierarchies and spatial indexes
Final exam:
Either a small project, or a seminar on the subject of the course.
