**April 21, 2020 at 10:30 - April 30, 2020**
- BCAM

**Michael Barton (BCAM)**

**DATES:** April 21st, 24th, 28th and 30th (4 sessions)

**TIME:** 10:30 - 12:30 (a total of 10 hours)

**LOCATION:** BCAM Seminar room

**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. We discuss suitable parametric representations of curves and surface (Bézier, B-spline, NURBS).

**PROGRAMME:**
**1. **Projective geometry (homogenous coordinates, projective extension of an affine space, linear collineation 2D, double ratio, Plücker coordinates, Klein quadric)

**2. **Parametric curves and surfaces (Frenet frame, curvature, torsion, principal curvatures)

**3. **Bézier and B-spline curves and surfaces (Bernstein basis, control points, geometric continuity)

**PREREQUISITES:**
Basic knowledge of calculus and linear algebra.

**REFERENCES: **
• Farin, G., Hoschek J., and Kim M.-S.. Handbook of computer aided geo- metric design. Elsevier, 2002.

• Cohen, E., Riesenfeld R., and Elber G. Geometric Modeling with Splines, AK Peters, Ltd., 2001.

** *Registration is free, but mandatory before 17th April.** To sign-up go to

https://forms.gle/DmT2SzscyF9mX8zH7 and fill the registration form.