Geometric modeling

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

ABSTRACT:
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).

PROGRAMME:
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)


PREREQUISITIES:
- Calculus
- Linear Algebra

REFERENCES:
- 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 https://forms.gle/FBC6edL5eJYewTcM6 and fill the registration form.

• BCAM_UPV/EHU_Course_2020_01_22