Reif, Ulrich ; Weinmann, Andreas (2021)
Clothoid fitting and geometric Hermite subdivision.
In: Advances in Computational Mathematics, 47 (4)
doi: 10.1007/s10444-021-09876-5
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Reif, Ulrich ; Weinmann, Andreas |
| Art des Eintrags: | Bibliographie |
| Titel: | Clothoid fitting and geometric Hermite subdivision |
| Sprache: | Englisch |
| Publikationsjahr: | 2021 |
| Ort: | Dordrecht |
| Verlag: | Springer Science |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Advances in Computational Mathematics |
| Jahrgang/Volume einer Zeitschrift: | 47 |
| (Heft-)Nummer: | 4 |
| Kollation: | 22 Seiten |
| DOI: | 10.1007/s10444-021-09876-5 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features. |
| Freie Schlagworte: | Geometric Hermite subdivision, Non-linear subdivision, Circle-preserving scheme, Clothoid fitting, 2D curve design |
| ID-Nummer: | Artikel-ID: 50 |
| Zusätzliche Informationen: | Mathematics Subject Classification 2010: 68U07 · 65D17 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Geometrie und Approximation |
| Hinterlegungsdatum: | 02 Aug 2024 13:17 |
| Letzte Änderung: | 02 Aug 2024 13:17 |
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| Suche nach Titel in: | TUfind oder in Google |
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Clothoid fitting and geometric Hermite subdivision. (deposited 30 Apr 2024 12:44)
- Clothoid fitting and geometric Hermite subdivision. (deposited 02 Aug 2024 13:17) [Gegenwärtig angezeigt]
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