80412 - Geometric Modeling (2017/2018)
General information
80412 - Geometric Modeling (GM, 6 CFU), first semester, years: 1°, 2°
LM.
Course content
Background Notions
- notions on analysis of algorithms
- graphs: data structures and traversal algorithms
- Abstract and Euclidean cell and simplicial complexes: review
Models of discrete geometric shapes
- mathematical shape models
- representing shapes through simplicial and cell complexes
- boundary representations
- combinatorial shape characterization
- constriction of discrete shape models: Delaunay triangulation
Representations for cell and simplicial complexes
- topological entities and relations
- data structures for 2D shapes discretized as cell complexes
- data structures for simplicial complexes in two, three and higher dimensions
- operators for manipulating cell and simplicial complexes; Euler operators
Discrete differential geometry
- parametric representation of lines and surfaces: tangent vector ad plane,normal Jacobian matrix, Gauss map, directional derivatives
- First and second fundamental forms
- principal curvatures, shape operator, curvature tensor, lines of curvature, umbilicals
- Laplace-Beltrami operator
- discrete estimation of differential properties on meshes
Geometry processing
- Smoothing
- Fairing
- Parametrization
- Simplification
Language
English
Teacher
Enrico Puppo
Teaching style
In presence
Attendance
Suggested