Curve and Surface Design

• Weekly hours
• Competences
• Objectives
• Contents
• Activities
• Teaching methodology
• Evaluation methodology
• Bibliography
• Previous capacities

Teachers

Person in charge

• Rodrigo Ignacio Silveira ( )

Weekly hours

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

Teaching methodology

Evaluation methodology

Bibliography

Basic:

• Curves and surfaces for computer graphics - Salomon, D, Springer, 2006. ISBN: 0387241965
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991004086549706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Curves and surfaces for CAGD: a practical guide - Farin, G.E, Morgan Kaufmann : Academic Press, 2002. ISBN: 9781558607378
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991000682539706711&context=L&vid=34CSUC_UPC:VU1&lang=ca

Complementary:

• A practical guide to splines - De Boor, C, Springer-Verlag , 2001. ISBN: 0387953663
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991002495629706711&context=L&vid=34CSUC_UPC:VU1&lang=ca

Previous capacities