Alberto Paoluzzi, Department of Computer Science and Automation, Roma Tre University <paoluzzi@dia.uniroma3.it>
The course aims to develop the ability of (a) producing geometric models of highly complex components and structures, both natural and manmade, and (b) understanding the design and development process of computeraided modeling and simulation. The course offers some background about the geometric and mathematical techniques required, and provides some insight into the main topics of computer techniques, including computer graphics, geometric computing and computational geometry. The theory is carefully linked to practice by implementing several graphical models in a modern programming environment based on Python.

Monday, Feb 13, 2012, 10:00 AM, Room: Teacher’s (DIA 2.21)

Monday, Feb 20, 2012, 10:00 AM, Room: Teacher’s (DIA 2.21)

Monday, Feb 27, 2012, 10:00 AM, Room: Teacher’s (DIA 2.21)

Monday, Feb 27, 2012, 10:00 AM, Room: CAD Lab (DIA 2.08)
Course program
FIRST TERM
Equivalence with the course of ComputerAided Design (DM 509)
Introduction to the language Python, the PLaSM language, the PyPlasm module.
Vector spaces, convex sets, simplicial complexes and polyhedral complexes, fields, differential operators.
Affine transformations, graphical primitives, hierarchical structure, the 3D pipeline, projections, texture mapping, 3D reconstruction
Curves, surfaces, solids. Parametric representations. Rational and polynomial maps. Tensor product rectangular Patches. Multivariate simplicial decompositions. Transfinite Geometric Modeling.
SECOND TERM
Equivalence with the course of Computer Graphics (DM 509)
Introduction to the use of crossplatform Python binding to OpenGL and related APIs. Elements of shader programming / buffer / texture model of OpenGL.
Intersection of segments in one and more dimensions. Convex hull. Triangulations. Dual complexes.
Simplicial complexes, complexes of cells. Chains and cochains. Boundary and coboundary Operators. Sparse Matrix Representation. Hierarchical triangulations. Characteristics Operations.
Reconstruction of the imperial palaces on the Palatine; Rome’s underground system modeling; development of the parametric model of a shopping center.
Teaching materials

Alberto Paoluzzi, "Geometric Programming for ComputerAided Design", Wiley, 2003
Exam

9 credits: 60 hours of lectures, 30 hours of lab work.

Grade: project 40%; graphics programming test 60%