arXiv subjects

Alexandru Ionut

Publications and source records attributed to Alexandru Ionut.

3 recordsLinked to original sources

arXiv2026

Explicit Cartesian Coordinates for Three-Dimensional Clothoids

We combine the spherical-clothoid reconstruction theorem of Lucas and Ortega-Yagues with an explicit spinorial parametrization of the spherical clothoid and a Kampe de Feriet evaluation of Kummer-product integrals. This gives explicit Cartesian coordinates, in arclength, for every nonhelical three-dimensional clothoid. Kummer asymptotics then yield explicit asymptotic lines, including their gamma-digamma offsets and the angle between their axes.

math.DG↗

arXiv2022

On the spherical clothoid

We revisit a nonlinear spline primitive for 3-space first studied by Even Mehlum. It is the spherical clothoid, the spherical curve with geodesic curvature a linear function of arc length. We present its Cartesian coordinate functions using confluent hypergeometric functions (the Kummer functions) and its stereographic projection onto the complex plane. New Humbert series results are also presented along with generating function formulas related to the associated Meixner-Pollaczek polynomials.

math.DG↗

arXiv2020

Fresnel Integral Computation Techniques

This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor series, modified trapezoid rule and an asymptotic expansion for small, medium and large arguments respectively. These special functions can be computed accurately and efficiently up to an arbitrary precision. Error estimates are provided and we give a systematic method in choosing the various parameters for a desired precision. We illustrate this method and verify numerically using double precision.

math.NA↗