The forward problem of electrocardiography involves computing the potentials and currents within the body from a known electrical potential distribution or activation sequence in the heart. This paper details an efficient computational model of the human torso for use in electrocardiographic problems. The model uses a combined finite element/boundary element method which uses bicubic Hermite ba...

A nonlinear Dirichlet boundary value problem is approximated by an orthogonal spline collocation scheme using piecewise Hermite bicubic functions. Existence, local uniqueness, and error analysis of the collocation solution and convergence of Newton’s method are studied. The mesh independence principle for the collocation problem is proved and used to develop an efficient multilevel solution met...

An interpolation-based method for computing refrigerant properties which can be used in simulations of vaporcompression air-conditioning equipment is presented. This method uses bicubic functions to interpolate between samples of the Helmholtz energy surface as a function of temperature and density. Three beneficial characteristics of this method are discussed: speed, accuracy, and consistency,...

We present a second order smooth filling of an n-valent Catmull-Clark spline ring with n biseptic patches. While an underdetermined biseptic solution to this problem has appeared previously, we make several advances in this paper. Most notably, we cast the problem as a constrained minimization and introduce a novel quadratic energy functional whose absolute minimum of zero is achieved for bicub...

We describe a method to generate blend surfaces which t with continuous curvature to the primary surfaces. This blend surface is obtained as the bicubic tensor spline minimizing a variational problem. Among all the bicubic tensor splines which give a curvature continuous blend surface, the one is chosen which minimizes a bilinear functional. In Section 2 we summarize and extend the results of a...

Abstract. In this paper, first free parameters are constrained in the description of rational cubic function [6] to preserve the shape of data that lies above the straight line. Then, rational cubic function is extended to rational bicubic partially blended function (Coons patches). A local positivity preserving scheme is developed for positive data by making constraints on free parameters in t...