A rational cubic spline with tension
Computer Aided Geometric Design
Computer Aided Geometric Design
The rational cubic Be´zier representation of conics
Computer Aided Geometric Design
The NURBS book
Soft Computing and Industry: Recent Applications
Soft Computing and Industry: Recent Applications
Automatic outline capture of Arabic fonts
Information Sciences—Informatics and Computer Science: An International Journal - Special issue: Software engineering: Systems and tools
Local convexity preserving rational cubic spline curves
IV '97 Proceedings of the IEEE Conference on Information Visualisation
Piecewise Interpolation for Designing of Parametric Curves
IV '98 Proceedings of the International Conference on Information Visualisation
On PH quintic spirals joining two circles with one circle inside the other
Computer-Aided Design
G2 Pythagorean hodograph quintic transition between two circles with shape control
Computer Aided Geometric Design
Transition between concentric or tangent circles with a single segment of G2 PH quintic curve
Computer Aided Geometric Design
G2 cubic transition between two circles with shape control
Journal of Computational and Applied Mathematics
Admissible regions for rational cubic spirals matching G2 Hermite data
Computer-Aided Design
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A rational cubic spline, with shape control parameters, has been discussed here with the view to its application in computer graphics. It incorporates both conic sections and parametric cubic curves as special cases. An efficient scheme is presented which constructs a curve interpolating a set of given data points and allows subsequent interactive alteration of the shape of the curve by changing the shape control and shape preserving parameters associated with each curve segment. The parameters (weights), in the description of the spline curve can be used to modify the shape of the curve, locally and globally. The rational cubic spline retains parametric C^2 smoothness. The stitching of the conic segments also preserves C^2 continuity at the neighboring given points. An exact derivative as well as a very simple distance-based approximated derivative schemes are presented to calculate control points. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as segments of a rational cubic spline. We discuss complex cases of elliptic arcs in space and introduce intermediate point interpolation scheme which can force the curve to pass through a given point between any segments.