Variable breakpoints in 3D-Lookup table?

Hi guys,

I'm using a 3D-Lookup table. My problem is, that the the used range of the x- and y-axis varies very much with the z-axis. To avoid very big matrices, I'm looking for a way, to use variables for defining the breakpoints 1 and 2 depending on the actual value of breakpoint 3. I hope you understand what I mean.

Thanks, Benedikt

Answer 1

[BhaTTa]

Hi Benedikt,

It sounds like you want to create a 3D lookup table in MATLAB where the range of the x- and y-axis breakpoints depends on the value of the z-axis breakpoint. This can be achieved by using a combination of cell arrays or nested structures to store the varying breakpoints and the corresponding data.

Here's a step-by-step approach to implement this:

1. Define the breakpoints for the z-axis.
2. For each z-axis breakpoint, define the corresponding breakpoints for the x- and y-axis.
3. Store the data in a 3D cell array or structure where each cell contains a 2D matrix corresponding to the x- and y-breakpoints for a specific z-breakpoint.

Here's an example to illustrate this:

% Define the breakpoints for the z-axis
z_breakpoints = [1, 2, 3];

% Define the corresponding breakpoints for the x- and y-axis for each z-breakpoint
x_breakpoints = {
    [0, 1, 2],    % x-breakpoints for z = 1
    [0, 0.5, 1],  % x-breakpoints for z = 2
    [0, 1]        % x-breakpoints for z = 3
};

y_breakpoints = {
    [0, 1, 2, 3], % y-breakpoints for z = 1
    [0, 1, 2],    % y-breakpoints for z = 2
    [0, 0.5, 1]   % y-breakpoints for z = 3
};

% Define the data for each combination of breakpoints
data = {
    [1, 2, 3; 4, 5, 6; 7, 8, 9; 10, 11, 12], % Data for z = 1
    [1, 2, 3; 4, 5, 6; 7, 8, 9],             % Data for z = 2
    [1, 2; 3, 4; 5, 6]                       % Data for z = 3
};

% Function to lookup data based on x, y, and z values
function value = lookup_data(x, y, z, z_breakpoints, x_breakpoints, y_breakpoints, data)
    % Find the index of the closest z-breakpoint
    [~, z_idx] = min(abs(z_breakpoints - z));
    
    % Get the corresponding x- and y-breakpoints and data
    x_bp = x_breakpoints{z_idx};
    y_bp = y_breakpoints{z_idx};
    data_matrix = data{z_idx};
    
    % Interpolate the data
    value = interp2(x_bp, y_bp, data_matrix, x, y, 'linear');
end

% Example usage:
x_val = 1.5;
y_val = 2.5;
z_val = 1.5;
result = lookup_data(x_val, y_val, z_val, z_breakpoints, x_breakpoints, y_breakpoints, data);
disp(result);