Geometric modelling of curved objects

DATES: April 30th and May 3rd, 7th and 10th, 2019 - Tuesdays and fridays (4 sessions)
TIME: 10:00 - 12:30 (a total of 10 hours)
LOCATION: BCAM Seminar room

Geometric modelling and computer-aided design (CAD) are fundamental disciplines to represent real-life objects in the digital world. In this course, we will discuss mathematical concepts of geometric modelling, particularly focusing on problems appearing in computer numerically controlled (CNC) machining.

We introduce the basics of differential geometry of curves and surfaces and discuss their suitable parametric representations (B-zier, B-spline, NURBS). The second part of the course will focus on rigid body transformations in 3D and associated vector fields of instantaneous motions.

PROGRAMME:

1. Parametric curves and surfaces (Frenet frame, curvature, torsion, principal curvatures)
2. B-zier and B-spline curves and surfaces (Bernstein basis, control points, geometric continuity)
3.Spatial kinematics (rigid body motion, instantaneous motion, velocity field, Study quadric)
4. Approximation and interpolation of free-form geometry (Hermite and Lagrange interpolation, spline fitting)


PREREQUISITES:
- 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.

*Registration is free, but mandatory before April 26th: To sign-up go to https://bit.ly/2slQzzp and fill the registration form.

• BCAMCourse_2019_04_30