AIMS AND CONTENT

LEARNING OUTCOMES

Learning theoretical foundations, techniques and methodologies for the representation and manipulation of solid objects, 2D and 3D scalar surfaces and fields. Representations of solid objects based on contour, based on decompositions, constructive; Representations of surfaces and scalar fields by triangular and tetrahedric grids; Multi-resolution techniques; Morphological modeling of shapes and scalar fields. Reference applications: computer graphics, scientific visualization, CAD systems, geographic information systems, virtual reality.

TEACHING METHODS

In presence

SYLLABUS/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

TEACHERS AND EXAM BOARD

Exam Board

ENRICO PUPPO (President)

PAOLA MAGILLO

FRANCESCA ODONE

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

GEOMETRIC MODELING

EXAMS

EXAM DESCRIPTION

Oral.