A. Canton | Searcharxiv

arXiv2025

Rational complex Bezier curves

In this paper we develop the formalism of rational complex Bezier curves. This framework is a simple extension of the CAD paradigm, since it describes arc of curves in terms of control polygons and weights, which are extended to complex values. One of the major advantages of this extension is that we may make use of two different groups of projective transformations. Besides the group of projective transformations of the real plane, we have the group of complex projective transformations. This allows us to apply useful transformations like the geometric inversion to curves in design. In addition to this, the use of the complex formulation allows to lower the degree of the curves in some cases. This can be checked using the resultant of two polynomials and provides a simple formula for determining whether a rational cubic curve is a conic or not. Examples of application of the formalism to classical curves are included.

math.NA↗

arXiv2023

Lessons learned after three years of SPIDER operation and the first MITICA integrated tests

ITER envisages the use of two heating neutral beam injectors plus an optional one as part of the auxiliary heating and current drive system. The 16.5 MW expected neutral beam power per injector is several notches higher than worldwide existing facilities. A Neutral Beam Test Facility (NBTF) was established at Consorzio RFX, exploiting the synergy of two test beds, SPIDER and MITICA. SPIDER is dedicated to developing and characterizing large efficient negative ion sources at relevant parameters in ITER-like conditions: source and accelerator located in the same vacuum where the beam propagates, immunity to electromagnetic interferences of multiple radio-frequency (RF) antennas, avoidance of RF-induced discharges on the outside of the source. Three years of experiments on SPIDER have addressed to the necessary design modifications to enable full performances. The source is presently under a long shut-down phase to incorporate learnings from the experimental campaign. Parallelly, developments on MITICA, the full-scale prototype of the ITER NBI featuring a 1 MV accelerator and ion neutralization, are underway including manufacturing of in-vessel components, while power supplies and auxiliary plants are already under final testing and commissioning. Integration, commissioning and tests of the 1MV power supplies are essential for this first-of-kind system, unparalleled both in research and industry field. The integrated test to confirm 1MV output by combining invertor systems, DC generators and transmission lines extracted errors/accidents in some components. To realize a concrete system for ITER, solutions for the repair and the improvement of the system were developed. Hence, NBTF is emerging as a necessary facility, due to the large gap with existing injectors, effectively dedicated to identify issues and find solutions to enable successful ITER NBI operations in a time bound fashion.

physics.plasm-ph↗

arXiv2016

Implicit equations of non-degenerate rational Bezier quadric triangles

In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bezier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is grounded on the pencil of quadrics circumscribed to a tetrahedron formed by vertices of the control net and an additional point which is required for the Steiner surface to be a non-degenerate quadric.

cs.GR↗