How can I achieve interpolation over the entire Cartesian space, without being limited by the convex hull of the data points, with TriScatterInterp (or griddata)?

I have written these lines of code and it is prefectly working. The problem is that I would like the interpolation to take place over the entire cartesian space, instead of within the data-points delimited polygon only.

I would like to achieve a full-colored interpolated image, instead of a colored shape immersed in the white surrounding. How can I achieve that?

Thank you all for your help!

% Data points
data_points = [1,1,3;1.02,1.9,3.1; 4,2,3.5; 4,4,2; 5,4.5,3];

% Define the grid within which you want to interpolate
[x_grid, y_grid] = meshgrid(linspace(0, 10, 100), linspace(0, 10, 100));

% Extract x, y, and values from data points
x = data_points(:, 1);
y = data_points(:, 2);
values = data_points(:, 3);

% Create a TriScatteredInterp object for interpolation
F = TriScatteredInterp(x, y, values, 'linear');

% Evaluate the interpolation on the grid
interpolated_values = F(x_grid, y_grid);

% Plot the interpolated result
contourf(x_grid, y_grid, interpolated_values, 50);
colorbar;
hold on;
scatter(x, y, 'r', 'filled', 'DisplayName', 'Data Points');
xlim([0, 10]);
ylim([0, 10]);
xlabel('X');
ylabel('Y');
title('Interpolated Data');
legend('Location', 'Best');
hold off;

Answer 1

[Walter Roberson]

You cannot do that with TriScatteredInterp -- it is strictly limited to interpolation.

These days it is recommended that you switch to griddedInterpolant or scatteredInterpolant making sure to tell them to extrapolate.

[LORENZO DOPPIU]

Thank you, I've successfully managed the problem by switching to scatteredInterpolant.