How to generate random vertices to form a convex polygon in c++?

Question

I need to generate a set of vertices for a simple convex polygon to do a minimum weight triangluation for that polygon using dynamic programming , I thought about taking a c

Answer 1

btw. +1 for nice approach with that circle ...

1. do not care for number of vertexes

   {
   double x0=50.0,y0=50.0,r=50.0;  // circle params
   double a,da,x,y;
   // [view]                       // my view engine stuff can skip this
   glview2D::_lin l;
   view.pic_clear();
   l.col=0x00FFFFFF;
   // [/view]
   for (a=0.0;a<2.0*M_PI;)         // full circle
       {
       x=x0+(r*cos(a));
       y=y0+(r*sin(a));
       a+=(20.0+(40.0*Random()))*M_PI/180.0;              // random angle step < 20,60 > degrees
   
       // here add your x,y point to polygon
   
       // [view]                   // my view engine stuff can skip this
       l.p0=l.p1;                  // just add line (lust x,y and actual x,y)
       l.p1.p[0]=x;
       l.p1.p[1]=y;
       view.lin.add(l);
       // [/view]
       }
   // [view]                   // my view engine stuff can skip this
   view.lin[0].p0=l.p1;        // just join first and last point in first line (was point0,point0)
   // [view]
   }
   

2. if number of vertexes is known = N

   Set random step to be on average little less then 2PI / N for example:

   da=a0+(a1*Random());
   

   • a0=0.75*(2*M_PI/N) ... minimal da
   • a1=0.40*(2*M_PI/N) ... a0+(0.5*a1) is avg = 0.95 ... is less then 2PI/N

   inside for add break if vertex count reach N. If after for the vertex count is not N then recompute all from beginning because with random numbers you cannot take it that you always hit N vertexes this way !!!

3. sample output from source code above

PS.

You can also use ellipse if the circle shape is not good enough

x=x0+(rx*cos(a));
y=y0+(ry*sin(a));

• rx != ry