does two polygons interest or not?

Let's say

these are two non interscting ploygons (shown below). How can i get a logical relationship out of this. Something like, if the polygons intersect or touch

paramter = true;

otherwise

parameter = false;

x1 =[-2.6967   -2.0891   -0.0846    1.5544    2.6872   -2.6967];
x2 = [5.6494    6.6386    6.6898    4.0313    1.3002    1.9802    5.6494];
y1 = [ 0.1340   -1.7104   -2.6987   -2.2076   -0.2624    0.1340];
y2 = [1.8624    3.4274    4.2346    6.6998    3.9686    2.2082    1.8624];
plot(x1,y1,x2,y2);
grid on;
poly1 = polyshape(x1',y1');
poly2 = polyshape(x2',y2');
polyout = intersect(poly1,poly2);

Answer 1

[Steven Lord]

You may be able to use the approach from this blog post that determines if two states (represented as polyshape objects) share a border.

Answer 2

[DGM]

You could test for an overlap using the intersection you calculated:

x1 = [0 1 1 0 0];
y1 = [0 0 1 1 0];
x2 = [1 2 2 1 1]-0.2;
y2 = [1 1 2 2 1]-0.2;

plot(x1,y1,x2,y2);
grid on;

poly1 = polyshape(x1',y1');
poly2 = polyshape(x2',y2');

polyout = intersect(poly1,poly2);
theyintersect = polyout.NumRegions~=0 % returns a logical scalar

theyintersect = logical
   1

Although that won't return true if they are merely tangent.

x1 = [0 1 1 0 0];
y1 = [0 0 1 1 0];
x2 = [1 2 2 1 1];
y2 = [1 1 2 2 1]-0.2;

plot(x1,y1,x2,y2);
grid on;

poly1 = polyshape(x1',y1');
poly2 = polyshape(x2',y2');

polyout = intersect(poly1,poly2);
theyintersect = polyout.NumRegions~=0

theyintersect = logical
   0

[CHANDRABHAN Singh]

@DGM can you please give me some idea what exactly is "polyout.NumRegions"? And thank you for your kind supoort.

[DGM]

From the webdocs:

https://www.mathworks.com/help/matlab/ref/polyshape.html

The NumRegions property is described as:

Number of regions making up the polygon, specified as a scalar integer. A region is an area bounded by an outer boundary, which may contain hole boundaries that lie entirely inside the outer boundary.

So a simple polyshape (e.g. a square) would have one region. If a polyshape intersects itself (e.g. a bowtie), it might have more than one region. If a polyshape encloses zero area, it has zero regions.

As a trivial polyshape has zero vertices, you could alternatively check to see if the vertex list is empty.

theyintersect = numel(poly1.Vertices)~=0

I just chose to use NumRegions instead.