Homogeneous simplex splines, also known as cone splines or mul-tivariate truncated power functions, are discussed from a perspective of homogeneous divided diierences and polar forms. This makes it possible to derive the basic properties of these splines in a simple and economic way. In addition, a construction of spaces of homogeneous simplex splines is considered, which in the non-homogeneous...

This letter develops a framework for EEG analysis and similar applications based on polyharmonic splines. This development overcomes a basic problem with the method of splines in the Euclidean setting: that it does not work on low-degree algebraic surfaces such as spherical and ellipsoidal scalp models. The method's capability is illustrated through simulations on the three-sphere model and usi...

This paper presents a novel computational framework based on dynamic spherical volumetric simplex splines for simulation of genuszero real-world objects. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and ...

Description of mapping methods using spherical splines, both to interpolate scalp potentials (SPs), and to approximate scalp current densities (SCDs). Compared to a previously published method using thin plate splines, the advantages are a very simple derivation of the SCD approximation, faster computing times, and greater accuracy in areas with few electrodes.

This paper addresses the problem of spherical parametrization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. We construct an improved algorithm for parametrization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines. This parametrization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the ...

Spiine, periodic spline and spherical harmonic maximum reach estimation procedures are compared and evaluated based on ease of usage, estimation error and bias. The comparison indicates that each method provides comparable estimates based on percent variance accounted for (Rz) and standard error. Spherical harmonics, however, are less biased and provide accurate estimates of the maximum reach s...

In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spheric...

  Effects of quantum size and potential shape on the spectra of an electron and a hydrogenic-donor at the center of a permeable spherical cavity have been calculated, using linear variational method. B-splines have been used as basis functions. By extensive convergence tests and comparing with other results given in the literature, the validity and efficiency of the method were confirmed.