How to plot the surface of an arbitrary given TABLE (not matrix) with X,Y,Z values?

To plot the surface for a table with arbitrary $X,Y,Z$ values, you need to organize the $Z$ values into a grid format that corresponds to $X,Y$ pairs. The function surf requires $Z$ to be a 2D matrix, where each element corresponds to a specific $X,Y$ pair.

Here’s how you can handle this step by step:

Steps to Create the Surface Plot

1. Prepare the Data: Import your table and extract $X,Y,Z$ columns.
2. Convert $X,Y,Z$ into Gridded Format: Use griddata or accumarray to arrange $Z$ values into a grid based on unique $X$ and $Y$ values.
3. Plot the Surface: Use surf to create the plot.

Code Example

Given Data:

% Define your table data
X = [1; 1; 1; 2; 2; 2; 3; 3; 3]; % X-coordinates
Y = [1; 2; 3; 1; 2; 3; 1; 2; 3]; % Y-coordinates
Z = [0.1711; 0.0326; 0.5612; 0.8819; 0.6692; 0.1904; 0.3689; 0.4607; 0.9816]; % Z-values

Solution:

% Create a grid of unique X and Y values
[Xq, Yq] = meshgrid(unique(X), unique(Y));

% Interpolate Z values into the grid using griddata
Zq = griddata(X, Y, Z, Xq, Yq);

% Plot the surface
surf(Xq, Yq, Zq);

% Add labels and title
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Surface Plot from Arbitrary X, Y, Z Data');
colorbar;

Key Notes

1. Data Structure:
   • X, Y, and Z should be column vectors, as in your example.
2. griddata: This function interpolates scattered data into a regular grid, making it suitable for surface plotting.
3. Visualization:
   • surf plots the 3D surface.
   • Add a colorbar for better visualization of $Z$-values.

Error Explanation

The error occurred because surf requires $Z$ to be a matrix matching the dimensions of $X$ and $Y$. By using griddata to interpolate or organize $Z$, you convert it into a compatible format.

With this approach, you can handle any arbitrary $X,Y,Z$ data imported as a table!