Alberto Viscardi - EPH curves: construction and evaluation

07 October 2022
- 07 October 2022

*East Campus USI-SUPSI, Lugano*PH curves are parametric polynomial curves for which the norm of

the first derivative is still a polynomial. Introduced by Farouki

and Sakkalis in 1990, they found several applications in

manufacturing, numerical control machines and robotics. Here we

consider their exponential counterparts, based on exponential

polynomials, in order to expand the design options for this class

of curves. The construction of EPH curves revolves on quaternions

with exponential polynomial coefficients, while their evaluation

presents some numerical issues which are addressed by the new

algorithm proposed.

the first derivative is still a polynomial. Introduced by Farouki

and Sakkalis in 1990, they found several applications in

manufacturing, numerical control machines and robotics. Here we

consider their exponential counterparts, based on exponential

polynomials, in order to expand the design options for this class

of curves. The construction of EPH curves revolves on quaternions

with exponential polynomial coefficients, while their evaluation

presents some numerical issues which are addressed by the new

algorithm proposed.

## The speaker

Alberto Viscardi obtained his bachelor and master degrees in

Mathematics at the University of Milano and a PhD degree at

the University of Milano-Bicocca in consortium with the

University of Pavia in 2018. He spent three years as a post-doc

at the University of Bologna and is now a research fellow at

the University of Torino. He mainly works in the intersection

between numerical analysis, approximation theory and the design

of curves and surfaces.