Geometrically smooth spline bases for data fitting and simulation

Smooth fitting of B-spline curve with constrained length

Abstract. In this paper, the authors present a method to construct a smooth B-spline curve which fairly fits 3D points and at the same time satisfies the length constraints. By using the Lagrange multiplier’s conditional extreme, resorting to Broyden method, and then finding the least square solution of the control points, we can obtain the fair quasi-fitting modeling B-spline curve.

Fitting a Cm - Smooth Function to Data

Suppose we are given a finite subset E ⊂ R and a function f : E → R. How to extend f to a C function F : R → R with C norm of the smallest possible order of magnitude? In this paper and in [20] we tackle this question from the perspective of theoretical computer science. We exhibit algorithms for constructing such an extension function F , and for computing the order of magnitude of its C norm....

A Smooth Rational Spline for Visualizing Monotone Data

A C curve interpolation scheme for monotonic data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The monotone rational cubic spline scheme has a unique representation.

Least-Squares Fitting of Data with B-Spline Curves

Spatially-adaptive Penalties for Spline Fitting

We study spline fitting with a roughness penalty that adapts to spatial heterogeneity in the regression function. Our estimates are pth degree piecewise polynomials with p− 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty on the jumps of the pth derivative at the knots. To be spatially adaptive, the logarithm of the pen...