A good workflow to be followed will be
- Interpolate your 2D scattered data (xi,yi,pi) onto a 2D grid to create a smooth “height field” (surface).
- Plot that surface in 3D using "surf", "mesh".
- Overlay small spheres at the original data points to visualize exact measurement locations/values.
This approach should help you build a nice 3D visualization similar in spirit to your reference figure though of course the exact “shape” depends on your interpolation and how you scale/color the spheres. I have done the process with some random data
% --- 1) Create some sample scattered data (x, y, p) ---
% (Replace this part with your real data)
N = 30; % Number of sample points
theta = 2*pi*rand(N,1); % Random angles
r = 10*rand(N,1); % Random radii
x = r .* cos(theta); % X-coordinates in a circular region
y = r .* sin(theta); % Y-coordinates in a circular region
p = x.^2 + y.^2; % Some function of x,y (example)
% --- 2) Interpolate onto a grid ---
numGrid = 50; % how many points in each dimension of the grid
xMin = min(x); xMax = max(x);
yMin = min(y); yMax = max(y);
% Create a mesh grid covering the data extent
[xq, yq] = meshgrid(linspace(xMin, xMax, numGrid), ...
linspace(yMin, yMax, numGrid));
% Interpolate p onto the grid
% (methods: 'linear', 'cubic', 'natural', etc.)
zq = griddata(x, y, p, xq, yq, 'cubic');
% --- 3) Plot the interpolated surface ---
figure('Color', 'w'); % new figure, white background
surf(xq, yq, zq);
shading interp; % smooth shading
colormap jet; % choose a colormap
colorbar; % show a color scale
hold on;
axis equal; % preserve aspect ratio (so circles remain circular)
xlabel('X'); ylabel('Y'); zlabel('Parameter');
title('3D Surface + Spheres at Original Data Points');
% --- 4) Overlay small spheres at each original point ---
% Generate a unit sphere for re-use
[sphereX, sphereY, sphereZ] = sphere(12); % 12 = resolution of the sphere
% Loop through each data point and place a small sphere
for i = 1:length(x)
% Radius can be constant or scaled by p(i)
% (Here we just pick a small constant radius)
r = 0.5;
% Shift the unit sphere to (x_i, y_i, p_i)
Sx = r*sphereX + x(i);
Sy = r*sphereY + y(i);
Sz = r*sphereZ + p(i);
% Create the sphere surface
hsphere = surf(Sx, Sy, Sz, ...
'EdgeColor', 'none', ... % no mesh lines
'FaceColor', 'interp'); % interpolate face colors
% Color the entire sphere by p(i) (or you can get fancy with gradients)
cdata = p(i)*ones(size(Sx)); % each vertex has color p(i)
set(hsphere, 'CData', cdata);
end
% Optional: adjust view angle
view(45, 30); % rotate camera [az, el]
Karan
