Two dimensional spline interpolation algorithms

Wellesley, Massachusetts, А К Peters, Ltd., 1995. - 308 p., ISBN 1-56881-017-2. Library of Congress Cataloging-in-Publication Data.This is the continuation of One Dimensional Spline Interpolation Algorithms to two dimensions as mentioned in the postscript to that book. We again take the point of view that the nodes (only in the plane) and the values to be interpolated are fixed ahead of time and that no information on a possible underlying function is available.Contents: Preface. Spline Interpolation on Rectangular Grids. Polynomial Interpolation. Rectangular Grids and Product Interpolation. The Lagrange Form of the Bivariate Interpolating Polynomial. Polynomial Interpolation on Special Triangular Grids. Bilinear Spline Interpolation. Searching a Rectangular Grid. Bilinear Interpolation on Rectangles. Biquadratic Spline Interpolants. Knots the Same as Nodes. Knots Different from Nodes. Shape Preservation. A Local Quadratic Method of Interpolation. Bicubic Spline Interpolation. Bicubic Spline Interpolation on Rectangular Grids. Parametric Bicubic Spline Interpolation. Bicubic Hermite Spline Interpolation. Semi-Bicubic Hermite Spline Interpolation. Shape Preservation. Biquadratic Histosplines. Birational Spline Interpolants. Birational Spline Interpolants on Rectangular Grids. Birational Histosplines. Spline Interpolation for Arbitrarily Distributed Points. Global Methods without Triangulation. Existence Problems and Goal Setting. Shepard's Method. Hardy's Multiquadrics. Triangulations. Linear Spline Interpolants over Triangulations. The Approximation of First Partial Derivatives. Quadratic Spline Interpolants over Triangulations. Cubic Spline Interpolation over Triangulations. C1 Spline Interpolation of Degree Five on Triangulations. Postscript. A. Appendix. B. List of Subroutines. Bibliography. Index.