Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Planar spirals that match G2 Hermite data
Computer Aided Geometric Design
The generalised Cornu spiral and its application to span generation
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
Computer-Aided Design
An involute spiral that matches G2 Hermite data in the plane
Computer Aided Geometric Design
Two-point G2 Hermite interpolation with spirals by inversion of hyperbola
Computer Aided Geometric Design
Spiral fat arcs - Bounding regions with cubic convergence
Graphical Models
On the interpolation of concentric curvature elements
Computer-Aided Design
Shape curvatures of planar rational spirals
Proceedings of the 7th international conference on Curves and Surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
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A method of two-point G^2 Hermite interpolation with spirals is proposed. To construct a sought for curve, the inversion is applied to an arc of some other spiral. To illustrate the method, inversions of parabola are considered in detail. The resulting curve is 4th degree rational. The method allows the matching of a wide range of boundary conditions, including those which require an inflection. Although not all G^2 Hermite data can be matched with a spiral generated from a parabolic arc, introducing one intermediate G^2 data solves the problem. Expanding the method by involving other spirals arcs is also discussed.