Algorithm for animating/morphing convex polygon diagrams
If your initial set of polygons is a power-diagram, you can insert a new polygon by inserting a new center and growing its power circle smoothly. You don't have direct control of the polygons but rather of the underlying power circles. Power diagrams as Voronoi diagrams are always made of convex polygons.
https://diglib.eg.org/bitstream/handle/10.2312/evs20201057/109-113.pdf
Another way is to subdivide one of the polygons slicing it with a straight line, similar to a spatial partition tree, to ensure the resulting polygon is still convex. http://proceedings.mlr.press/v84/fan18b/fan18b.pdf