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Curvature-Controlled Curve Editing Using Piecewise Clothoid Curves

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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