Year: 2025
Type: article
Abstract: When a moving frame defined along a space curve is required to keep an axis aligned with the tangent direction of motion, the use of rotation-minimizing frames (RMF) avoids unnecessary rotations in the normal plane. The construction of rigid body motions using a specific subset of quintic curves with rational RMFs (RRMFs) is here considered. In particular, a novel geometric characterization of such subset enables the design of a local algorithm to interpolate an assigned stream of positions, together with an initial frame orientation. To achieve this, the translational part of the motion is described by a parametric G 1 G^1 spline curve whose segments are quintic RRMFs, with a globally continuous piecewise RRMF. A selection of numerical experiments illustrates the performances of the proposed method on synthetic and arbitrary data streams.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4100
Institutions: University of Florence, Charles University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410818726