Two forms of spatial interpolation, the interpolation of point and areal data, are distinguished. Traditionally, point interpolation is applied to isarithmic, that is, contour mapping and areal interpolation to isopleth mapping. Recently, areal interpolation techniques have been used to obtain data for a set of administrative or political districts from another set of districts whose boundaries...

An efficient, stability-preserving model reduction technique for non-linear initial boundary value problems (IBVPs) whose solutions exhibit inherently non-linear dynamics such as metastability and periodic regimes (limit cycles) is developed. The approach is based on the “continuous” Galerkin projection approach, in which the continuous governing equations are projected onto the reduced basis m...

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circumcircle preserving piecewise projective interpolation between discretely con...

This article introduces a bivariate shape-preserving interpolation algorithm to approximate the value function of a dynamic program. First, we present a savings allocation problem between a pension account and another non-pension one. With the objective of maximizing the present value of utility over a life cycle, the investor can distribute his or her savings, in each account, between stocks a...

A new method called ‘‘edge-preserving 8-directional two-layered weighting interpolation’’ is proposed for interpolating unfilled pixels in a perspective-view or panoramic image resulting from unwarping an omni-image taken by a non-single-view-point hypercatadioptric camera. This method can solve the problem of edge preserving in interpolating the input image which has many irregularly-distribut...