Remove lines of specified length from triangulation

The following code generates square:

[X,Y]=meshgrid(0:0.5:1);
points=[X(:),Y(:)];
figure('Name','Point set','NumberTitle','off')
scatter(points(:,1),points(:,2),'marker','o','MarkerEdgeColor',[0 0 1],'LineWidth',2)
xlabel('x','FontSize',13);
ylabel('y','FontSize',13);
title('Point set','FontSize',13)
axis square

Then I triangulate these points:

DT=delaunay(points);
figure('Name','Trangulation','NumberTitle','off')
patch('Faces',DT,'Vertices',points,'FaceColor',[1 0.5 0],'EdgeColor',[0 0 1]);
xlabel('x','FontSize',13);
ylabel('y','FontSize',13);
title('Trangulation','FontSize',13)

Triangulation generates diagonal lines that depend on the width and height of the square grid element.

I need to remove these lines and leave the rest. And in general, I would like to understand the principle of how to remove from the triangulation lines that exceed or vice versa are less than some given value.

I was inspired by this code, but whole simplices are removed, and I need to remove only lines:

https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/48509/versions/3/previews/COMP_GEOM_TLBX/html/Concave_mesh_grid_2D.html

[KSSV]

Why you want to remove those lines? What is the criteria to remove? Explain us your final problem instaed of a small example.

[Andrew Sol]

@KSSV I have a set of points (two dimensional figure). I want to build a mesh and then an outer (common for the shape) and an inner boundary (cavity-interiors). Boundaries must be strictly vertical and horizontal. When triangulating, diagonal lines appear. We can remove them according to the criterion of a suitable length.

Since the grid is rectangular, the length of the triangulation line should not exceed the length of the diagonal passing through a single rectangular element of the grid. I was able to do this with https://www.mathworks.com/help/images/ref/bwboundaries.html

I want to compare it with boundaries. obtained through work with a triangulation mesh.

[Andrew Sol]

@KSSV In other words, I want to try building outer and inner boundaries using triangulation.