### Teachings

Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
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