Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

In this paper, we obtain equivalent conditions relating oblique projections to biorthogonal Riesz bases and angles between closed linear subspaces of a Hilbert space. We also prove an extension theorem in the biorthogonal setting, which leads to biorthogonal multiwavelets.

Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic, self-adjoint, nonhomogeneous Dirichlet boundary value problems on rectangles. In the rst scheme, the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gaus...

Let G be a countable group of unitary operators on a complex separable Hilbert space H. We give a characterization of biorthogonality among Riesz multiwavelets in terms of certain invariant properties of their associated core spaces. A large family of non-biorthogonal Riesz multiwavelets is exhibited. We also discuss some results on linear perturbation of orthonormal multiwavelets.

This paper proposes a novel color correction scheme for image stitching where the color map transfer is modelled by a monotone Hermite cubic spline and smoothly propagated into the target image. A three-segments monotone cubic spline minimizing color distribution statistics and gradient differences with respect to both the source and target images is used. While the spline model can handle non-...

We propose a pseudo-physics system and a spine model that can be coupled to generate life-like locomotion animations of quadrupeds and reptiles. The pseudo-physics system uses minimalist particle-based physics and values of the gait pattern to generate the sinusoidal-like ballistic movement of the pelvis observed in nature. While the spine model uses simple geometry-based calculations and 3D He...

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.

A cubic spline approximation in C1 to the solution of a general Volterra integral equation of the second kind is constructed. Under certain conditions, convergence of the approximation and its first two derivatives is proved and error bounds are obtained. The question of stability is not examined.

Shape preservation behavior of a spline consists of criterial conditions for preserving convexity, inflection, collinearity, torsion and coplanarity shapes of data polgonal arc. We present our results which acts as an improvement in the definitions of and provide geometrical insight into each of the above shape preservation criteria. We also investigate the effect of various results from the li...