The use of Cornu spirals in drawing planar curves of controlled curvature
Journal of Computational and Applied Mathematics
Euler Spiral for Shape Completion
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The family of biarcs that matches planar, two-point G1 Hermite data
Journal of Computational and Applied Mathematics
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
3D Euler spirals for 3D curve completion
Computational Geometry: Theory and Applications
Planar two-point G1 Hermite interpolating log-aesthetic spirals
Journal of Computational and Applied Mathematics
Interpolation of two-dimensional curves with Euler spirals
Journal of Computational and Applied Mathematics
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Cornu spiral segments are used in applications such as the geometric design of highways and railways, robot path planning, and shape completion. For some applications, e.g. shape completion in computer vision, it is important to use a single visually pleasing curve segment to smoothly fill a gap, even though the gap may not be filled in a curvature continuous manner. An improved method for doing so using a Cornu spiral segment is discussed. The method is generally suitable for any application where it is required to smoothly fit a curve between two given points when the corresponding tangent directions, but not the curvatures, are also given or known.