e01ea:: Interpolation (NAG Toolbox)

The triangulation is encoded in triang as follows:

set j0=0; for each node, k=1,2,…,n, (using the ordering inferred from x and y)
- $i_{k} = j_{k - 1} + 1$
- $j_{k} = triang (6 \times n + k)$
- $triang (j)$ , for $j = i_{k}, \dots, j_{k}$ , contains the list of nodes to which node $k$ is connected. If $triang (j_{k}) = 0$ then node $k$ is on the boundary of the mesh.

Example

In this example, nag_interp_2d_triangulate (e01ea) creates a triangulation from a set of data points. nag_interp_2d_triang_bary_eval (e01eb) then evaluates the interpolant at a sample of points using this triangulation. Note that this example is not typical of a realistic problem: the number of data points would normally be larger, so that interpolants can be more accurately evaluated at the fine triangulated grid.

function e01ea_example


fprintf('e01ea example results\n\n');

% Scattered Grid Data
x = [11.16; 12.85; 19.85; 19.72; 15.91;  0.00;
     20.87;  3.45; 14.26; 17.43; 22.80;  7.58;
     25.00;  0.00;  9.66;  5.22; 17.25; 25.00;
     12.13; 22.23; 11.52; 15.2;   7.54; 17.32;
      2.14;  0.51; 22.69;  5.47; 21.67;  3.31];
y = [ 1.24;  3.06; 10.72;  1.39;  7.74; 20.00;
     20.00; 12.78; 17.87;  3.46; 12.39;  1.98;
     11.87;  0.00; 20.00; 14.66; 19.57;  3.87;
     10.79;  6.21;  8.53;  0.00; 10.69; 13.78;
     15.03;  8.37; 19.63; 17.13; 14.36;  0.33];
% Triangulate on grid
[triang] = e01ea(x, y);

% Convert to form that MATLAB trimesh function can use
n = size(x,1);
t = int64([0;0;0]);
max_t = int64(2*n-5);
tri = int64(zeros(max_t,3));
iend = int64(0);
k = int64(0);
for i = 1:n
   % set up loop of nodes connected to node i
   ibeg = iend + 1;
   iend = triang(6*n+i);
   % first connection setup
   t(1) = i;
   t(2) = triang(ibeg);
   % loop over remaining connections
   ibeg = ibeg + 1;
   for j = ibeg:iend
      t(3) = triang(j);
      if t(3)>0
        if t(2)>i || t(3)>i
        % new triangle here 
          k = k + 1;
          tri(k,1:3) = t(1:3);
        end
        % shuffle down for next connected node
        t(2) = t(3);
      end
   end
end

fprintf('Number of triangles in triangulation = %d\n',k);

%display mesh
fig1 = figure;
trimesh(tri(1:k,1:3),x,y)
xlabel('x');
ylabel('y');
title('Triangulation of scattered data using e01ea');
% Interpolate function values on mesh
f = [22.15; 22.11;  7.97; 16.83; 15.30; 34.60;  5.74; 41.24; 10.74; ...
     18.60;  5.47; 29.87;  4.40; 58.20;  4.73; 40.36;  6.43;  8.74; ...
     13.71; 10.25; 15.74; 21.60; 19.31; 12.11; 53.10; 49.43;  3.25; ...
     28.63;  5.52; 44.08];
px = [2.0500 3.7500 5.0000 8.5400 9.1400];
py = [1.7750 3.2500 5.0000 2.0500 4.4500];

[pf, ifail] = e01eb(...
                    x, y, f, triang, px, py);

fprintf('\n      px        py     Interpolated Value\n');
disp([px' py' pf]);

NAG Toolbox: nag_interp_2d_triangulate (e01ea)

▸▿ Contents

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

Optional Input Parameters

Output Parameters

Error Indicators and Warnings

Accuracy

Further Comments

Example