Teachings

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Professor
GREGORIO FRANZONI (Tit.)
Period
First Semester 
Teaching style
Convenzionale 
Lingua Insegnamento
ITALIANO 



Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/65]  MATHEMATICS [65/00 - Ord. 2012]  PERCORSO COMUNE 6 48

Objectives

- KNOWLEDGE AND UNDERSTANDING
The main subject of this course is the geometry of curves, surfaces and other geometrical objects, with a focus on creating a link between the academic/theoretical point of view and the technological/application one, meant as computer visualization and 3D printing.

- APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course the student will be able to produce computer images of mathematical objects and 3D models suitable to be 3D printed.

- MAKING JUDGEMENTS
Being able to understand whether or not a 3D model is suitable to be visualized and/or physically printed.

- COMMUNICATION SKILLS
Being able to describe the geometrical and topological properties of the geometrical objects by using the correct terminology.

- LEARNING SKILLS
Being able to elaborate strategies suited to solve exercises and problems in space geometry and topology autonomously. Being able to read and understand a text of advanced space geometry and a software manual referred to scientific visualization or CAGD software.

Prerequisites

- basic concepts of analytic geometry in 2 and 3 dimensions and of linear algebra: vector spaces, linear applications, matrices;
- basic concepts of topology;
- basic concepts of algebraic and parametrized curves and surfaces

Contents

Recall of plane curves, space curves, surfaces. Computer representation of curves, surfaces and other mathematical objects. Rapid prototyping and 3D printing: introduction; birth and evolution of different technologies; materials; application fields. 3D printing of mathematical objects. From the mathematical description of curves and surfaces to their polygonal/polyhedral models. Basic elements of computational geometry. Polyhedral representation of a surface. Thickening. Managing self intersections and singularities. Managing non-orientable objects. Checking and repairing solid models. 3D printing of sample objects.

Teaching Methods

Frontal lesson on the blackboard and multimedia presentations

Verification of learning

The exam consists in preparing a project in which the student designs and creates a model for a mathematical object or chosen from some of the teacher's proposals.

Texts

- R.Caddeo, A.Grey, Curve e superfici con Mathematica, Cuec.
- Introductory notes to the Rinoceros software provided by the teacher

More Information

Our University provides support for students with specific learning disability (SLD). Those interested can find more informations at this link: http://corsi.unica.it/matematica/info-dsa/.

Questionnaire and social

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