A modified Clough-Tocher interpolant

TL;DR: The C’ Powell-Sabin interpolants and the Clough-Tocher split are described, respectively, as well as the general case, Split Triangle Interpolants and Split Triangle square interpolants, which are described as follows:.

TL;DR: In this paper, a survey of the field of interpolation by bivariate splines is presented, where the authors summarize results on the dimension and the approximation order of the spline spaces, and describe interpolation methods for these spaces.

TL;DR: Some results using boundary curves based on a recent technique for point normal interpolation are reported on, which shows some visual smoothness in relation to standard global curve fitting techniques.

TL;DR: In this article, the generalized eigenproblem is studied to establish the ellipticity of the discrete biharmonic operator, and consequently the stability of the numerical method, which renders the interpolant amenable to application in a Galerkin scheme for the solution of fourth order elliptic PDEs.

TL;DR: This chapter discusses algorithm and underlying theory of software for C1 surface interpolation, an interpolation algorithm that is interfaced with algorithms for contour plotting or surface perspective plotting for data given on a rectangular grid.

TL;DR: In this paper, two explicit representations of a C1 quintic interpolant over triangles are derived by generalization of Coons' methods and Bernstein-Bezier methods, respectively.

TL;DR: An adaptive method of contouring a bivariate surface defined over arbitrarily spaced data in two dimensions using an adaptive degree reduction algorithm to minimize the number of subdivisions necessary to obtain the desired smoothness of the contour.