Draw polygon around grid points

Dear reader,

I want to draw polygon around a set of grid points. For clarity I have added a figure below

I need to draw a polygon around the edges of the smaller red dots in such a way that the larger orange dots are within the polygon. Preferably, all angles of the polygon are 90 degrees. So basically the polygon with the minimum surface area to include all orange points, if that makes sense

My question is whether this is possible, and if so, how to do this?

Many thanks in advance!

[Matt J]

In what form is the input data given?

[Michiel Smit]

Dear Matt,

Data is given in matrix form, where 1st column are the X-coordinates and 2nd column are the Y-coordinates. I have added the specific data below.

The smaller red dots are given by:

small_dots = [2.1250   52.6250
    2.1250   52.8750
    2.1250   53.1250
    2.3750   52.3750
    2.3750   52.6250
    2.3750   52.8750
    2.3750   53.1250
    2.6250   52.3750
    2.6250   52.6250
    2.6250   52.8750
    2.6250   53.1250
    2.6250   53.3750
    2.8750   52.3750
    2.8750   52.6250
    2.8750   52.8750
    2.8750   53.1250
    2.8750   53.3750
    3.1250   52.3750
    3.1250   52.6250
    3.1250   52.8750
    3.1250   53.1250
    3.3750   52.3750
    3.3750   52.6250
    3.3750   52.8750
    3.3750   53.1250
    3.6250   52.3750
    3.6250   52.6250
    3.6250   52.8750
    3.8750   52.3750
    3.8750   52.6250
    3.8750   52.8750
    4.1250   52.3750
    4.1250   52.6250
    4.1250   52.8750];

The larger orange dots are given by:

large_dots = [2.2500   53.0000
    2.2500   52.7500
    2.5000   53.0000
    2.5000   52.7500
    2.5000   52.5000
    2.7500   53.2500
    2.7500   53.0000
    2.7500   52.7500
    3.0000   53.0000
    3.0000   52.7500
    3.0000   52.5000
    3.2500   53.0000
    3.2500   52.7500
    3.2500   52.5000
    3.5000   52.7500
    3.5000   52.5000
    3.7500   52.7500
    3.7500   52.5000
    4.0000   52.7500
    4.0000   52.5000];

I hope this is clear enough.

Many thanks in advance!

Answer 1

[Matt J]

small_dots = [2.1250   52.6250
    2.1250   52.8750
    2.1250   53.1250
    2.3750   52.3750
    2.3750   52.6250
    2.3750   52.8750
    2.3750   53.1250
    2.6250   52.3750
    2.6250   52.6250
    2.6250   52.8750
    2.6250   53.1250
    2.6250   53.3750
    2.8750   52.3750
    2.8750   52.6250
    2.8750   52.8750
    2.8750   53.1250
    2.8750   53.3750
    3.1250   52.3750
    3.1250   52.6250
    3.1250   52.8750
    3.1250   53.1250
    3.3750   52.3750
    3.3750   52.6250
    3.3750   52.8750
    3.3750   53.1250
    3.6250   52.3750
    3.6250   52.6250
    3.6250   52.8750
    3.8750   52.3750
    3.8750   52.6250
    3.8750   52.8750
    4.1250   52.3750
    4.1250   52.6250
    4.1250   52.8750];
large_dots = [2.2500   53.0000
    2.2500   52.7500
    2.5000   53.0000
    2.5000   52.7500
    2.5000   52.5000
    2.7500   53.2500
    2.7500   53.0000
    2.7500   52.7500
    3.0000   53.0000
    3.0000   52.7500
    3.0000   52.5000
    3.2500   53.0000
    3.2500   52.7500
    3.2500   52.5000
    3.5000   52.7500
    3.5000   52.5000
    3.7500   52.7500
    3.7500   52.5000
    4.0000   52.7500
    4.0000   52.5000];


alldots= [small_dots;large_dots];

shp=alphaShape(alldots,0.13);
[~,V]=boundaryFacets(shp);

shp=polyshape(V,'Simplify',false);


plot(alldots(:,1),alldots(:,2),'o'); 
hold on; shp.plot; hold off; axis equal

[Michiel Smit]

Thank you so much. This really does the trick. Never heard of AlphaShape() and boundaryFacets() before, it it works really well.