e01saf

Purpose

Synopsis

[triang,grads,ifail] = e01saf(x,y,f<,ifail>)

Description

 
 This routine constructs an interpolating surface F(x,y) through a
 set of m scattered data points (x ,y ,f ), for r=1,2,...,m, using
                                  r  r  r                    
 a method due to Renka and Cline. In the (x,y) plane, the data 
 points must be distinct. The constructed surface is continuous 
 and has continuous first derivatives.
 
 The method involves firstly creating a triangulation with all the
 (x,y) data points as nodes, the triangulation being as nearly 
 equiangular as possible. Then gradients in the x- and 
 y-directions are estimated at node r, for r=1,2,...,m, as the 
 partial derivatives of a quadratic function of x and y which 
 interpolates the data value f , and which fits the data values 
                              r                
 at nearby nodes (those within a certain distance chosen by the 
 algorithm) in a weighted least-squares sense. The weights are 
 chosen such that closer nodes have more influence than more 
 distant nodes on derivative estimates at node r. The computed 
 partial derivatives, with the f  values, at the three nodes of 
                                r                     
 each triangle define a piecewise polynomial surface of a certain 
 form which is the interpolant on that triangle. 
 
 The interpolant F(x,y) can subsequently be evaluated at any point
 (x,y) inside or outside the domain of the data by a call to 
 E01SBF. Points outside the domain are evaluated by extrapolation.
 

Parameters

e01saf

Required Input Arguments:

x (:)                                 real
y (:)                                 real
f (:)                                 real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

triang (:)                            real
grads (2,:)                           real
ifail                                 integer