Plot of 3D colour scatter graph

Hello,

I have a 3D data set of surface erosion for over 700,000 points, and this is tabulated in the form (x, y, z, D). That is, for each 3D point (x, y, z), there is a corresponding value of surface erosion suffered (D)?

Please could someone assist me to visualise this data such that erosion depth controls the colour.

Thanks.

[Scott MacKenzie]

What is z in your data set? Perhaps post a subset of your data.

[Nicholas Omoding]

Z is the elevation of the points whilst erosion (relative change at each point is denoted by D). Please see the attached sub-set of the data.

Answer 1

[Scott MacKenzie]

I think this is more or less what you're after:

f = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/679873/point_erosion.xlsx';
M = readmatrix(f);
x = M(:,1);
y = M(:,2);
z = M(:,3);
D = M(:,4);

N = 250; % faster with downsampling; looks the same
xv = linspace(min(x), max(x), N);
yv = linspace(min(y), max(y), N);

[Xm,Ym] = ndgrid(xv, yv);
Zm = griddata(x, y, z, Xm, Ym);
Dm = griddata(x, y, D, Xm, Ym);

surf(xv,yv,Zm,Dm, 'edgecolor', 'none');
xlabel('X'); ylabel('Y'); zlabel('Z');
cb = colorbar;
cb.Label.String = 'Erosion';
cb.Label.FontSize = 12;

[Nicholas Omoding]

Indeed, it is. Many thanks!

[Scott MacKenzie]

@Nicholas Omoding You're welcome. Glad to help. BTW, what is depicted in the chart? Tiers of land? Reminds me of images I've seen of mountainous countries where farming requires the land to be tiered. The flat parts are yellow and there is some blue on the slopes. What is the interpretation of erosion here?

[Nicholas Omoding]

The scenario is similar to what you've described. However, in my case, I'm studying a stepped concrete surface at the sea front eroded by beach shingle. I compared the point cloud of the damaged surface to mesh of the original condition to determine erosion at each point.

[Scott MacKenzie]

Ok, very interesting. Thanks for this explanation. Good luck with your research.

[Scott MacKenzie]

@Nicholas Omoding Just one final thought. You probably want to add a colorbar to the graph, to reveal what the color data represent. I just tweaked my answer to include this.

Answer 2

[Image Analyst]

Is this what you want?

% Scatter3 demo where marker color and size varies according to data value.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 15;

% Create sample data.
numPoints = 300;
x = rand(1, numPoints); % Coordinates
y = rand(1, numPoints);
z = rand(1, numPoints);
maxDataValue = 1000; % Whatever you want the most extreme color to represent.
minDataValue = -200; % Whatever you want the most extreme color to represent.
D = minDataValue + (maxDataValue - minDataValue) * rand(1, numPoints); % Data values might not ever reach minDataValue or maxDataValue
% Define a colormap
numColors = 256;
cmap = jet(numColors);

%=====================================================================================================================
% Demo #1 : Vary size and color according to magnitude of data.
% Get the index (color) for each of the D values
DScaled = (D - minDataValue) / (maxDataValue - minDataValue);
colorIndexes = ceil(numColors * DScaled);
colors = cmap(colorIndexes, :);
% Scale marker sizes so that bigger values get bigger markers.
sizes = rescale(D, 50, 150);
subplot(1, 2, 1);
scatter3(x, y, z, sizes, colors, 'filled');
grid on;
axis equal;
colormap(cmap);
colorbar;
caxis([0, maxDataValue])
xlabel('x', 'FontSize', fontSize);
ylabel('y', 'FontSize', fontSize);
zlabel('z', 'FontSize', fontSize);
title('Marker Color and Size Varied According to Data Value', 'FontSize', fontSize);

%=====================================================================================================================
% Demo #2 : Vary size and color according to distance of data from origin.
distances = sqrt(x.^2 + y.^2 + z.^2);
maxDistanceValue = sqrt(3);
% Get the index (color) for each of the D values
DScaled = distances / maxDistanceValue;
colorIndexes = ceil(numColors * DScaled);
colors = cmap(colorIndexes, :);
% Scale marker sizes so that bigger values get bigger markers.
sizes = rescale(D, 50, 150);
subplot(1, 2, 2);
scatter3(x, y, z, sizes, colors, 'filled');
grid on;
axis equal;
colormap(cmap);
colorbar;
caxis([0, maxDistanceValue])
xlabel('x', 'FontSize', fontSize);
ylabel('y', 'FontSize', fontSize);
zlabel('z', 'FontSize', fontSize);
title('Marker Color and Size Varied According to Distance from Origin', 'FontSize', fontSize);
g = gcf;
g.WindowState = 'maximized'

[Nicholas Omoding]

Thanks for the response. Please kindly see the subset of my data attached.

Answer 3

[Max Heiken]

Since the erosion is specified per vertex, I think scatter3 is to be preferred over surf or mesh.

I would start with something straight-forward like

scatter3(x, y, z, [], D, '.')
cb = colorbar;
ylabel(cb, "erosion")
colormap copper  % change for aesthetics

With 700000 points in one plot, performance will be bad, so depending on that you might need to perform some data reduction.

After observing the scatter plot, you can of course decide if another type of plot would be more appropriate.