Havemann, Sven ; Edelsbrunner, Johannes ; Wagner, Philipp ; Fellner, Dieter W. (2013)
Curvature-Controlled Curve Editing Using Piecewise Clothoid Curves.
In: Computers & Graphics, 37 (6)
doi: 10.1016/j.cag.2013.05.017
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
Two-dimensional curves are conventionally designed using splines or Bézier curves. Although formally they are C² or higher, the variation of the curvature of (piecewise) polynomial curves is difficult to control; in some cases it is practically impossible to obtain the desired curvature. As an alternative we propose piecewise clothoid curves (PCCs). We show that from the design point of view they have many advantages: control points are interpolated, curvature extrema lie in the control points, and adding control points does not change the curve. We present a fast localized clothoid interpolation algorithm that can also be used for curvature smoothing, for curve fitting, for curvature blending, and even for directly editing the curvature. We give a physical interpretation of variational curvature minimization, from which we derive our scheme. Finally, we demonstrate the achievable quality with a range of examples.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2013 |
| Autor(en): | Havemann, Sven ; Edelsbrunner, Johannes ; Wagner, Philipp ; Fellner, Dieter W. |
| Art des Eintrags: | Bibliographie |
| Titel: | Curvature-Controlled Curve Editing Using Piecewise Clothoid Curves |
| Sprache: | Englisch |
| Publikationsjahr: | 2013 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Computers & Graphics |
| Jahrgang/Volume einer Zeitschrift: | 37 |
| (Heft-)Nummer: | 6 |
| DOI: | 10.1016/j.cag.2013.05.017 |
| Kurzbeschreibung (Abstract): | Two-dimensional curves are conventionally designed using splines or Bézier curves. Although formally they are C² or higher, the variation of the curvature of (piecewise) polynomial curves is difficult to control; in some cases it is practically impossible to obtain the desired curvature. As an alternative we propose piecewise clothoid curves (PCCs). We show that from the design point of view they have many advantages: control points are interpolated, curvature extrema lie in the control points, and adding control points does not change the curve. We present a fast localized clothoid interpolation algorithm that can also be used for curvature smoothing, for curve fitting, for curvature blending, and even for directly editing the curvature. We give a physical interpretation of variational curvature minimization, from which we derive our scheme. Finally, we demonstrate the achievable quality with a range of examples. |
| Freie Schlagworte: | Business Field: Virtual engineering, Forschungsgruppe Semantic Models, Immersive Systems (SMIS), Curvature, Curve modeling, Curve optimization |
| Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik 20 Fachbereich Informatik > Graphisch-Interaktive Systeme |
| Hinterlegungsdatum: | 12 Nov 2018 11:16 |
| Letzte Änderung: | 04 Feb 2022 12:40 |
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