how can i valid if the polygon i have received , X=[x1,x2,x3,x4] Y =[y1,y2,y3,y4] has no internal angle bigger than 180

how can i valid if the polygon i have received , X=[x1,x2,x3,x4] Y =[y1,y2,y3,y4] has no internal angle bigger than 180 ;

i am given X and Y and ineed to check that condition ?

can anybody help me , thx .

i have another question , can i let matlab pick me aroandom coordinates (x,y) such that they are inside or on the polygon ihave recieved .

Answer 1

[Bruno Luong]

That simply means the polygonal is convex. To check it

K = convhull(x,y);
isequal([1:length(x) 1]',K) || isequal([1 length(x):-1:1]',K)

[daniel zayed]

thanks that was the pointx, how about to pick random points in polygon : ?

[Bruno Luong]

If the vertexes are not properly ordered, then

all(ismember([1:length(x)],convhull(x,y)))

Answer 2

[Image Analyst]

I was going to suggest the convex hull like Bruno. I think you might also need to make sure the polygon doesn't cross, like a figure 8.

For the points in a polygon, just get a random point and use inpolygon() to check if it's inside the polygon or not. If it is, keep it, if it's not, keep trying until you have the required number of points inside. Something like (untested)

numRequired = 1000;
rx = rand(1, numRequired*4); % Make sure there are enough to handle rejects.
ry = rand(1, numRequired*4); % Make sure there are enough to handle rejects.
keeperIndexes = false(1, numRequired)*4; % Flag to say if it's inside the x,y polygon.
for k = 1 : length(x)
    if inpolygon(rx, ry, x, y)
        keeperIndexes(k) = true;
        % Break if we've found enough.
        if sum(keeperIndexes) >= numRequired
            break;
        end
    end
end
% Extract the keepers - those inside the polygon.
keeperX = rx(keeperIndexes);
keeperY = ry(keeperIndexes);

Make sure x and y are ordered. I also think the polygon needs to be closed, but I'm not sure.