The possible shapes of the production possibility curve under Cobb-Douglas production function

It is well-known that if returns to scale differ in different output ranges of the same commodity, the production possibility curve may change its shape from concave to convex to the origin. But what is less obvious may be that if they do not differ in different output ranges, the PPC may not be either concave, or convex but may well be both concave and convex. Under Cobb Douglas production functions the PPC changes its curvature at most twice. We draw some examples where the PPC changes its curvature once and twice.