Create polyshape with no duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results

I am trying to create convex polygons with n vertices, area = 1 and with no intersections between edges, and even though I try to loop until it's a simple polygon (using issimplified), I still get the warning :

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or

unexpected results. Input data has been modified to create a well-defined polyshape.

> In polyshape/checkAndSimplify (line 480)

In polyshape (line 175)

In PolygonConvexe (line 23)

My goal is to have polygons where edges don't intersect.

What I'm looking for

What I get sometimes

Thank yo very much for your help

function [Xpa,Ypa]=PolygonConvexe(n)
Xa=zeros(1,n);
Ya=zeros(1,n);
convex=false;
simple=false ;
one_region=false;
while convex==false || simple==false  || one_region==false
    for i=1:n
        Xa(i)=rand(1,1);
        Ya(i)=rand(1,1);
    end
    convex=est_convexe(Xa,Ya);
    polygone=polyshape(Xa,Ya);
    simple=issimplified(polygone);
    polyout=simplify(polygone);
    one_region=polyout.NumRegions==1;
end
a=polyarea(Xa,Ya);
Xa=Xa./sqrt(a);
Ya=Ya./sqrt(a);
pgon=polyshape(Xa,Ya);
plot(pgon)
Xpa=Xa;
Ypa=Ya;

Answer 1

[Matt J]

Perhaps as follows.

n=7; %number of vertices

pgon=nsidedpoly(n);


v=rand(2,1);
v=v/norm(v);
v=[v*0.3;0.7];
v=v/norm(v);
R=null(v');
R(:,2)=cross(v,R(:,1));
R(:,3)=v;
R=R';

c=rand(2,1)*3;
P=[2*eye(2),c;0 0 1]*R*[eye(3),[ 0 ;0 ;0]]; %random camera projection
P=P.';

for i=1:2
pgon.Vertices=pmap(P,pgon.Vertices);
end

pgon.Vertices=pgon.Vertices/sqrt(area(pgon));

pgon=simplify(pgon);
area(pgon)

ans = 1

plot(pgon);shg

function V=pmap(A,V)

  m=size(V,1);

  V=[V,ones(m,2)]*A;
  V=V(:,1:2)./V(:,end);

end