How do you create delaunay triangulation for random points inside a polygon

I am having a very hard time trying to create a delaunay triangulation constrained by the borders of the provided polygon using the random points generated inside of my polygon. Provided below is my attempt, however I feel I a far from correct. (I also received help on this code below to get to where I am at now) Thank you!

states = shaperead('usastatehi.shp');

st = states(47); %creates a polgon in the shape of Washington State

stBB = st.BoundingBox;

st_minlat = min(stBB(:,2 )); 
st_maxlat = max(stBB(:,2 )); 
st_latspan = st_maxlat - st_minlat;

st_minlong = min(stBB(:,1 )); 
st_maxlong = max(stBB(:,1 )); 
st_longspan = st_maxlong - st_minlong;

stX = st.X ; 
stY = st.Y;

numPointsIn = 42;

for i = 1:numPointsIn 
flagIsIn = 0;

while ~flagIsIn 
x(i) = st_minlong + rand(1) * st_longspan ; 
y(i) = st_minlat + rand(1) * st_latspan ; 
flagIsIn = inpolygon(x(i), y(i), stX, stY ); 
end 
end

mapshow(st, 'edgecolor', 'r', 'facecolor', 'none ') 

hold on 
scatter(x, y , '.') 
dt = delaunayTriangulation(x(i),y(i))
hold on

[KSSV]

.shp file is missing..we cannot run the code unless file is given. Attach your file here.

[Ian Bouchard]

usastatehi.shp? Please forgive my lack of coding knowledge in MATLAB but I am unable to figure out how to get the file. I have MATLAB R2017b and the .shp file is already saved in the database. Is there a way I can download the file?

[KSSV]

Ohh...cool..if it is inbuilt..no problem......will get back to the answer.

Answer 1

[KSSV]

states = shaperead('usastatehi.shp');
st = states(47); %creates a polygon in the shape of Washington State
stBB = st.BoundingBox;
st_minlat = min(stBB(:,2 ));
st_maxlat = max(stBB(:,2 ));
st_latspan = st_maxlat - st_minlat;
st_minlong = min(stBB(:,1 ));
st_maxlong = max(stBB(:,1 ));
st_longspan = st_maxlong - st_minlong;
stX = st.X ;
stY = st.Y;
numPointsIn = 42;
for i = 1:numPointsIn
    flagIsIn = 0;
    while ~flagIsIn
        x(i) = st_minlong + rand(1) * st_longspan ;
        y(i) = st_minlat + rand(1) * st_latspan ;
        flagIsIn = inpolygon(x(i), y(i), stX, stY );
    end
end
mapshow(st, 'edgecolor', 'r', 'facecolor', 'none ')
hold on
scatter(x, y , '.')
dt = delaunayTriangulation(x',y') ;
hold on
triplot(dt) ;

If your idea is to mesh the entire region......then you should have a look here: https://in.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-delaunay-based-unstructured-mesh-generation

[Ian Bouchard]

Thank you!!