ACM Transactions on Mathematical Software (TOMS)
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Euler Spiral for Shape Completion
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Geometric Hermite curves with minimum strain energy
Computer Aided Geometric Design
An arc spline approximation to a clothoid
Journal of Computational and Applied Mathematics
An Improved Euler Spiral Algorithm for Shape Completion
CRV '08 Proceedings of the 2008 Canadian Conference on Computer and Robot Vision
Technical section: A controlled clothoid spline
Computers and Graphics
3D Euler spirals for 3D curve completion
Proceedings of the twenty-sixth annual symposium on Computational geometry
"Mind the gap": tele-registration for structure-driven image completion
ACM Transactions on Graphics (TOG)
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This paper introduces a special arc spline called an Euler arc spline as the basic form for visually pleasing completion curves. It is considered as an extension of an Euler curve in the sense that the points in the Euler curve are replaced by arcs. A simple way for specifying it, which is suitable for shape completion, is presented. It is shown that Euler arc splines have several properties desired by aesthetics of curves, in addition to computational simplicity and NURBS representation. An algorithm is proposed for curve completion using Euler arc splines. The development of the algorithm involves two optimization processes, which are converted into a single minimization problem in two variables solved by the Levenberg-Marquardt algorithm. Compared to previous methods, the proposed algorithm always guarantees the interpolation of two boundary conditions.