The generalised Cornu spiral and its application to span generation
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Sketch-Based Interfaces and Modeling (SBIM): Sketching piecewise clothoid curves
Computers and Graphics
Technical section: A controlled clothoid spline
Computers and Graphics
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Artifact analysis on B-splines, box-splines and other surfaces defined by quadrilateral polyhedra
Computer Aided Geometric Design
Neatening sketched strokes using piecewise French curves
Proceedings of the Eighth Eurographics Symposium on Sketch-Based Interfaces and Modeling
Proceedings of the 24th annual ACM symposium on User interface software and technology
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Two-dimensional curves are conventionally designed using splines or Bezier curves. Although formally they are C^2 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.