# Curve and Surface Design

## You are here

Credits
6
Types
Elective
Requirements
This subject has not requirements, but it has got previous capacities
Department
MAT
Optional course that aims at presenting an introduction to the main topics in curve and surface design for graphics and CAD/CAM. The different types of curves and surfaces will be introduced, together with their main properties and some implementation aspects. The course has a practical component that will consist in carrying out a number of lab assignments to become familiar with the implementation and properties of the different curves and surfaces.

## Teachers

### Person in charge

• Rodrigo Ignacio Silveira ( )

## Weekly hours

Theory
2
Problems
0
Laboratory
2
Guided learning
0
Autonomous learning
6

## Competences

### Transversal Competences

#### Reasoning

• G9 [Avaluable] - Capacity of critical, logical and mathematical reasoning. Capacity to solve problems in her study area. Abstraction capacity: capacity to create and use models that reflect real situations. Capacity to design and perform simple experiments and analyse and interpret its results. Analysis, synthesis and evaluation capacity.
• G9.2 - Analysis and synthesis capacity, capacity to solve problems in its field, and to interpret the results in a critical way. Abstraction capacity: capacity to create and use models which reflect real situations. Capacity to design and perform simple experiments and to analyse and interpret their results in a critical way.

## Objectives

1. Know the main types of curves used in graphics and CAD/CAM
Related competences: G9.1, G3.1, G3.2, G9.2,
2. Become familiar with practical aspects in the implementation of algorithms for curves
Related competences: G7.1, G9.1, G9.3, G3.1, G3.2, G9.2,
3. Know some of the types of surfaces used in graphics and CAD/CAM
Related competences: G9.1, G3.1, G3.2, G9.2,
4. Become familiar with practical aspects in the implementation of algorithms for surfaces
Related competences: G7.1, G9.1, G9.3, G3.1, G3.2, G9.2,

## Contents

1. Fundamentals
Basic notions of vector and affine spaces. Parametrizations of affine varieties.
2. Parametrizing curves
How to mathematically describe a curve. Tangent vector, normal vector, osculating plane and curvature. Conics.
3. Interpolating curves
Piecewise linear interpolation. Polynomial interpolation. Uniform and non-uniform polynomial parametric interpolation. Hermite (cubic) interpolation. Spline interpolation.
4. Approximating curves
Bézier curves. B-Splines. Considerations on the efficiency of the computation of the curves.
5. Surfaces: parametrization and approximation
Methods to model a surface. Quadric surfaces. Vector normal to a surface at a point. Bézier surfaces. NURBS surfaces.

## Activities

Activity Evaluation act

### Theory

Lectures about the different types of curves and surfaces
Objectives: 1 3
Contents:
Theory
29h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
15h

### Lab work

Implementation of some of the topics covered in the theory lectures
Objectives: 2 4
Contents:
Theory
0h
Problems
0h
Laboratory
27h
Guided learning
0h
Autonomous learning
65h

### Exam

Objectives: 1 2 3 4
Contents:
Theory
1h
Problems
0h
Laboratory
3h
Guided learning
0h
Autonomous learning
10h

## Teaching methodology

The course has a theoretical and a practical part. The theory lectures will introduce the main mathematical concepts related to the different types of curves and surfaces. The students will get familiar with the practical aspects of these different topics by carrying out a number of practical, implementation-based assignments.

## Evaluation methodology

The course will be graded based on:
- Handing-in the practical assigments that will be carried out during the lab sessions (50% of the final grade).
- A final exam, covering theory and practice (50% of the final grade).

## Previous capacities

- English
- Basic knowledge of JavaScript