Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
An algorithm for monotone piecewise bicubic interpolation
SIAM Journal on Numerical Analysis
Choosing nodes in parametric curve interpolation
Computer-Aided Design
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
Geometric Hermite interpolation with Tschirnhausen cubics
Journal of Computational and Applied Mathematics
Shape preserving interpolation by space curves
Computer Aided Geometric Design
Hermite interpolation with Tschirnhausen cubic spirals
Computer Aided Geometric Design
Optimal geometric Hermite interpolation of curves
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
A method for determining knots in parametric curve interpolation
Computer Aided Geometric Design
On the local existence of the quadratic geometric Hermite interpolant
Computer Aided Geometric Design
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
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The problem of constructing a parametric cubic rational curve to interpolate a set of distinct data points is discussed. Unlike the existing methods which include the determination of knots, the new method constructs parametric curve without the process of determining knots. For each point, a quadratic rational Bezier curve is constructed by the five convex data points. For the data point, if there is no five convex data points, the quadratic rational Bezier curve is constructed with four or three points under a constraint. Between each pair of the two adjacent points, a parametric cubic rational curve is constructed by the combination of the two quadratic rational Bezier curves. The constructed cubic rational curve reproduces a conic section exactly if the given data points are taken from the conic section. The comparison of the new method with other ones is included.