How to generate a random polygon without mutual intersections?

Question

Algorithms

In the WxH field, I want to create an N-gon of a random shape. Without "holes", without "islands", without mutual intersections of faces.

1. First thought: just throw random points and connect in the order of generation. There are often overlaps.
   
2. Second thought: divide the field into N equal sectors from the center. Create another point in your sector. You get crooked wheels. But not a single shape, for example, a thick letter "C". And sometimes there are overlaps .
   
3. Intuition tells you that you need to throw in random points, build a Delaunay triangulation , and cut out some of the faces, so as not to lose connectivity and not create islands and lakes.
   

Probably, in game development, this is a typical task when creating level maps. How do they create figures of a difficult random shape with the absence of holes-islands?
I would like to have a chance to appear, for example, this form:

Useful links from @myjcom comments

• генерация внешнего контура массива точек
  
• генерация игровых ландшафтов (но с возможными дырками и островами) на Хабре и оригинал на англ.
  
• список алгоритмов генерации уровней для игр, Random Walk и производные (Drunkard Walk) – интересны, но допускают дырки и острова.
  

Answer 1

My first thought was this:
1. Create a triangle. Add all its edges to the list.
2. Take a random edge from the list, it will be the base of the new triangle.
3. Generate a point so that a new triangle is obtained, none of whose edges intersects the edges from the list. Add two new edges to the list, remove the base.
4. Repeat from step 2 until the desired area of ​​the polygon is reached.

Answer 2

1. create many simple polygons
2. mark connection points
3. constrain adjacent polygons
4. generate multiple polygons with different connections