Interpolation with quintic Powell–Sabin splines

Data Interpolation by C 2 Quintic Splines

Shape-preserving interpolation by G1 and G2 PH quintic splines

The interpolation of a planar sequence of points p0, . . . , pN by shape-preserving G 1 or G2 PH quintic splines with specified end conditions is considered. The shape-preservation property is secured by adjusting ‘tension’ parameters that arise upon relaxing parametric continuity to geometric continuity. In the G2 case, the PH spline construction is based on applying Newton–Raphson iterations ...

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...

C2 interpolation of spatial data subject to arc-length constraints using Pythagorean-hodograph quintic splines

In order to reconstruct spatial curves from discrete electronic sensor data, two alternative C Pythagorean–hodograph (PH) quintic spline formulations are proposed, interpolating given spatial data subject to prescribed contraints on the arc length of each spline segment. The first approach is concerned with the interpolation of a sequence of points, while the second addresses the interpolation ...

Convergence of Quintic Spline Interpolation

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