CODE 80412 ACADEMIC YEAR 2018/2019 CREDITS 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR INF/01 TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB 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 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 Curves and surfaces Piecewise polynomial curves: definitions and properties Basic algorithms for manipulating curves and surfaces Interpolation and approximation Subdivision curves and surfaces: definitions and properties Subivision schemes in 2D and 3D Geometry processing Smoothing Fairing Parametrization Simplification TEACHERS AND EXAM BOARD ENRICO PUPPO Ricevimento: Appointment by email to enrico.puppo@unige.it During class period appointments for groups can be set by posting on the course forum on AulaWeb. CHIARA EVA CATALANO Exam Board ENRICO PUPPO (President) CHIARA EVA CATALANO FRANCESCA ODONE LESSONS LESSONS START The class will start according to the academic calendar. Class schedule GEOMETRIC MODELING EXAMS EXAM DESCRIPTION Oral.
