The reconstruction of a continuous function from discrete data is a basic task in many applications such as the visualization of 3D volumetric data sets. We use a local approximation method for quadratic C1 splines on uniform tetrahedral partitions to achieve a globally smooth function. The spline is based on a truncated octahedral partition of the volumetric domain, where each truncated octahe...

Abstract Multivariate basis splines (B‐splines) and Non‐uniform rational B‐splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical (THB‐splines) provide a solution for this. THB‐splines organize the parameter space into structure, which enables efficient approximation representation of functions with different levels detail. The truncation mechanism ensures...

A fast convergent optimization algorithm is proposed in this paper to calculate sequential optimal trajectories for pursuing a moving target or under dynamically changing environments. The changing boundary conditions or perturbations in such problems require an efficient algorithm to update the optimal trajectories with appropriate time steps. Concepts of a uniform B-spline and differentially ...

The first type of pseudo-splines were introduced by [Daubechies, Han, Ron and Shen, 2003] (DHRS) to construct tight framelets with desired approximation orders via the unitary extension principle of [Ron and Shen, 1997]. In the spirit of the first type of pseudo-splines, we introduce here a new type (the second type) of pseudo-splines to construct symmetric or antisymmetric tight framelets with...

A relation between double Dirichlet averages and multivariate complex B-splines is presented. Based on this reationship, a formula for the computation of certain moments of multivariate complex B-splines is derived.

Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials local support, B-splines shows its advantages when intensive numerical computations involved the subsequent applications. To obtain an optimal B-splines, we need to select bandwidth (i.e., distance of two adjacent knots) for uniform B-spline...

Given an unstructured mesh consisting of quadrilaterals and triangles (we allow both planar non-planar meshes arbitrary topology), we present the construction quadratic splines mixed smoothness — C1 smooth away from regions T C0 otherwise. The have several useful B-spline-like properties – partition unity, non-negativity, local support linear independence for straightforward imposition boundary...

In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in ...