Curve and Surface Design

Credits
6
Types
Elective
Requirements
This subject has not requirements , but it has got previous capacities
Department
MAT
Web
https://dccg.upc.edu/courses-dcs/
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

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

    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).

    Bibliography

    Basic

    Complementary

    Previous capacities

    - English
    - Basic knowledge of JavaScript