Havemann, Sven and Edelsbrunner, Johannes and Wagner, Philipp and Fellner, Dieter W. (2013):
Curvature-Controlled Curve Editing Using Piecewise Clothoid Curves.
In: Computers & Graphics, 37 (6), pp. 764-773. DOI: 10.1016/j.cag.2013.05.017,
[Article]
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2013 |
| Creators: | Havemann, Sven and Edelsbrunner, Johannes and Wagner, Philipp and Fellner, Dieter W. |
| Title: | Curvature-Controlled Curve Editing Using Piecewise Clothoid Curves |
| Language: | English |
| 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. |
| Journal or Publication Title: | Computers & Graphics |
| Journal volume: | 37 |
| Number: | 6 |
| Uncontrolled Keywords: | Business Field: Virtual engineering, Forschungsgruppe Semantic Models, Immersive Systems (SMIS), Curvature, Curve modeling, Curve optimization |
| Divisions: | 20 Department of Computer Science 20 Department of Computer Science > Interactive Graphics Systems |
| Date Deposited: | 12 Nov 2018 11:16 |
| DOI: | 10.1016/j.cag.2013.05.017 |
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