In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allow multiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user sp...

This paper studies shapes (curves and surfaces) which can be described by (piecewise) polynomial support functions. The class of these shapes is closed under convolutions, offsetting, rotations and translations. We give a geometric discussion of these shapes and present methods for the approximation of general curves and surfaces by them. Based on the rich theory of spherical spline functions, ...

We present a framework for generating a trivariate B-spline parametrization of turbine blades from measurement data generated by optical scanners. This new representation replaces the standard patchbased representation of industrial blade designs. In a first step, the blade surface is represented by a smoothly varying family of B-spline curves. In a second step, the blade is parametrized by a t...

With the objective of generating “shape-preserving” smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based C1-smooth univariate cubic L1 splines. An L1 spline minimizes the L1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating t...

Based on the cubic B-spline curve, new Chinese fonts are generated by wavelet transforms in this paper. The outlines of Chinese fonts are first transformed into B-spline curves. Then, using wavelet transforms, the control points of each curve are decomposed into hierarchies containing the detailed features of the Chinese fonts. Using the synthesis procedure of wavelet transforms, new fonts can ...

Functional principal component analysis (FPCA) is a dimension reduction technique that explains the dependence structure of a functional data set in terms of uncorrelated variables. In many applications the data are a set of smooth functions observed with error. In these cases the principal components are difficult to interpret because the estimated weight functions have a lot of variability an...

In this paper, we propose a new 3D reconstruction method for general 3D planar curves based on curve correspondences on two views. By fitting the measured and transferred points using spline curves and minimizing the 2D Euclidean distance from measured and transferred points to fitted curves, we obtained an optimum homography which relates the curves across two views. Once two or more homograph...

Based on the cubic B-spline curve, new Chinese fonts are generated by wavelet transforms in this paper. The outlines of Chinese fonts are first transformed into B-spline curves. Then, using wavelet transforms, the control points of each curve are decomposed into hierarchies containing the detailed features of the Chinese fonts. Using the synthesis procedure of wavelet transforms, new fonts can ...

We consider the problem of variational interpolation of subsets of Euclidean spaces by curves such that the L norm of the second derivative is minimized. It is well known that the resulting curves are cubic spline curves. We study geometric boundary conditions arising for various types of subsets such as subspaces, polyhedra, and submanifolds, and we indicate how solutions can be computed in th...

Knot insertion is the operation of obtaining a new representation of a B-spline curve by introducing additional knot values to the defining knot vector. The new curve has control points consisting of the original control points and additional new control points corresponding to the number of new knot values. So knot insertions give additional control points which provide extra shape control wit...