Simple Example

This is a simple example of using regularizeNd.

clc; clear; close all;

This example uses the etopo_loihi sample data packaged with regularizeNd. Data extracted from:

NOAA National Centers for Environmental Information: DEM Global Mosaic (contains ETOPO 2022 and higher-resolution multibeam sources), centred on Kamaʻehuakanaloa Seamount (18.92°N, 155.27°W). DOI: https://doi.org/10.25921/fd45-gt74. Accessed March 29, 2026.

Note this data set is undersampled and course to keep from attaching a large .mat file. The full structure of the top of the volcano is not resolved. This is due to not enough data and not regularizeNd.

SEAMOUNT_COORDINATES = [-155.27 18.92];

data = load('a01_etopo_loihi.mat');

x = double(data.x);

y = double(data.y);

z = double(data.z);

xLimits = [min(x), max(x)];

yLimits = [min(y), max(y)];

xGrid = {linspace(xLimits(1) - eps(xLimits(1)), xLimits(2) + eps(xLimits(2)), 480), ...

linspace(yLimits(1) - eps(yLimits(1)), yLimits(2) + eps(yLimits(2)), 481)};

smoothness = 0.000001;

zGrid = regularizeNd([x,y], z, xGrid, smoothness, 'cubic');

% equivalents ways to call regularizeNd

% zGrid = regularizeNd([x,y], z, xGrid, smoothness, 'cubic', 'normal');

% Upsample grid since we are using cubic interpolation

zFunction = griddedInterpolant(xGrid, zGrid);

xGrid2= {linspace(xLimits(1) - eps(xLimits(1)), xLimits(2) + eps(xLimits(2)), 2000), ...

linspace(yLimits(1) - eps(yLimits(1)), yLimits(2) + eps(yLimits(2)), 2001)};

xGrid2Expanded = cell(2,1);

[xGrid2Expanded{:}] = ndgrid(xGrid2{:});

zGrid2 = zFunction(xGrid2Expanded{1}, xGrid2Expanded{2});

figure;

surfaceHandle = surf(xGrid2{:}, zGrid2',"EdgeColor","none","FaceColor","interp");

hold on;

contour3(xGrid2{:}, zGrid2', 22, 'k', 'LineWidth', 0.45);

GRAY = [0.5 0.5 0.5];

scatter3(x, y, z, 10, GRAY, 'filled');

colormap(turbo(256));

clim([-5400 -900]);

view(329.7, 61);

xlabel('Longitude');

ylabel('Latitude');

zlabel('Depth (m)');

grid on;

axis tight;

title('3D bathymetry view');

ylabel(colorbar, "Depth (m)");

% datatip(surfaceHandle, SEAMOUNT_COORDINATES(1), SEAMOUNT_COORDINATES(2), zFunction(SEAMOUNT_COORDINATES(1), SEAMOUNT_COORDINATES(2)));

% Licensed under the MIT License

% See LICENSE file in project root