Looking for a way to partition an alphaShape object between its respective alphaShape sub-regions.

I have an alphaShape object (shp) made of 11 distinct sub-regions (N=11).

I want to partition my alphaShape between it's 11 respective sub-regions.

I want to plot each region in a different color and compute its respective area.

x and y are the coordinates of shp.

For n=1, I compute the x-y coordinates of the sub-region (x1 & y1) , make a new alphaShape (shp1) and compute its area (area1).

I redo these steps for n=2,3,...,N.

The file data.mat attached contains the variables shp, x and y.

Here what it looks like for n=1:

Load('data.mat')

N       = numRegions(shp);      %# of regions in shp

%For n=1
tf1     = inShape(shp,x,y,1);   %true (1) for points in region n=1
index1  = find(tf1==1);         %corresponding index for region n=1
x1      = x(index1);            %corresponding x-coord for region n=1
y1      = y(index1);            %crresponding y-coord for region n=1
shp1    = alphaShape(x1,y1,1);  %create new alphaShape object for region n=1 with alpha radius 1
area1   = area(shp1);           %area for alphaShape object for region n=1

%Redo the steps for n=2,3,...,N

It works but I feel like I am doing a lot of unnecassary steps.

I am looking for a clever way to use the sub-regions of an alphShape object as distinct alphaShape objects on their own.

Thanks

Answer 1

[Milan Bansal]

Hi A LL

To streamline the process of partitioning your alphaShape object into its respective sub-regions, plotting each in a different color, and computing their areas, you can utilize MATLAB's capabilities more efficiently. The approach you've outlined does repeat several steps that can be optimized. Here's a more efficient way to achieve your goal:

1. Use "inShape" more efficiently: "inShape" is used to determine which points belong to which region. However, please avoid calling "find" by directly using logical indexing with "tf1" to extract x and y coordinates.
2. Loop through all regions: Instead of manually repeating the steps for each region, use a loop to iterate over all regions.
3. Plotting: To plot each region in a different color, use MATLAB's built-in color maps or specify a list of colors.

Please refer to the below code snippet for a more efficient code:

load('data.mat');

N = numRegions(shp); % Number of regions in shp
areas = zeros(N, 1); % Pre-allocate array to store areas

figure;
hold on;

% Colors for plotting each region
colors = lines(N); % This generates a colormap with N distinct colors

for n = 1:N
    tf = inShape(shp, x, y, n);  % Logical array for points in region n
 
    % Extracting x and y coordinates for region n using logical indexing
    xn = x(tf);
    yn = y(tf);
    
    shpn = alphaShape(xn, yn, 1); % Create new alphaShape object for region n with alpha radius 1
    areas(n) = area(shpn); % Compute and store area for region n
    
    % Plot region n in a different color
    plot(shpn, 'FaceColor', colors(n,:), 'FaceAlpha', 0.5, 'EdgeColor', 'none');
end

hold off;

% Optionally, print areas
disp('Areas of each sub-region:');

Areas of each sub-region:

disp(areas);

  308.5000
  176.5000
   65.5000
   52.5000
   28.5000
   23.5000
    5.5000
    3.5000
    1.0000
    1.0000
    0.5000

Please refer to the following documentation links to learn more about "inShape", "alphaShape" and "lines" fucntions.

• https://www.mathworks.com/help/matlab/ref/alphashape.inshape.html
• https://www.mathworks.com/help/matlab/ref/alphashape.html
• https://www.mathworks.com/help/matlab/ref/lines.html

Hope this helps!