Geometric modeling

Fecha: Vie, Ene 29 - Vie, Feb 19 2021

Hora: 10:00

Ubicación: Online

Ponentes: Michael Barton (BCAM)

DATES: January 29 and February 5, 12 and 19, 2021 (4 sessions)
TIME: 10:00 - 12:00 (a total of 10 hours)

Geometric modeling and computer-aided design (CAD) are fundamental disciplines to represent real-life objects in digital world. We will discuss mathematical tools for geometric modeling, particularly focusing on problems appearing in computer numerically controlled (CNC) machining. We introduce basics of projective and differential geometry, and discuss suitable parametric representations of curves and surfaces (B-zier, B-spline, NURBS).

1. Projective geometry (homogenous coordinates, projective extension of an affine space, linear collineation in 2D, double ratio, Placker coordinates, Klein quadric)
2. Parametric curves and surfaces (Frenet frame, curvature, torsion, principal curvatures, first and second fundamental form, Meusnier´s theorem)
3. B-zier and B-spline curves and surfaces (Bernstein basis, control points, geometric continuity)

- Calculus
- Linear Algebra

- Farin, G., Hoschek J., and Kim M.-S. Handbook of computer aided geometric design. Elsevier, 2002.
- Cohen, E., Riesenfeld R., and Elber G. Geometric Modeling with Splines, AK Peters, Ltd., 2001.
- Pottmann, H. and Wallner, J., 2009. Computational line geometry. Springer Science & Business Media.

*Registration is free, but mandatory before January 25th (extended deadline). To sign-up go to and fill the registration form.





Ponentes confirmados:

Michael Barton (BCAM)