Here's a similar idea, with different coding, and a dynamic clock to animate the morphing:

CirclePoints[{1., Pi/2}, 3*25] //
  {Join @@ MapThread[Most@*Subdivide, {#, RotateLeft@#, #2 {1, 1, 1}}] &[CirclePoints[{1., Pi/2}, 3 ], Length@#/3], #} & //
 Graphics[
   GraphicsComplex[
    {Cos[Clock[Infinity]], Sin[Clock[Infinity]]}^2 .# // Dynamic,
    {EdgeForm[Thick], White, Polygon@Range@Length@First@#}
    ],
   PlotRange -> 1.02] &

Interesting! But it seems that your code simply plots different polynomial functions. I would not call this a proper morphing. In my example, we start with some points forming a tringle and some points forming the circle. Then, all the intermediate lists of points are generated by averaging the corresponding points with a shifting weight. As a matter of fact, if you replace the first table (which defines the three triangle vertexes)

Table[{Cos@x, Sin@x}, {x, -Pi/6, 2 Pi - Pi/6, 2 Pi/3}]

with some random points like

RandomReal[{},{8,2}]

the code generates a morphing from those random points to the circle. In general you can even get rid of the circle and start with two lists of points having the same lenght; my code will morph one into the other.