I thought about 4D dual morphing before, but haven't got around to it yet. I guess all you'd be able to see during the morph is the 3D projection, ie not cross-sections or nets, though you could convert a morph to be the new base model to obtain those.
For morph by rectangles (maybe I should rename this morph by expansion?), we have the following:
- each vertex becomes a new small dual cell that grows
- each cell shrinks to nothing, becoming a dual vertex
- each edge becomes a long thin cell that grows wider and shorter till it becomes a dual face
- each face expands into a short prism that grows longer and thinner till it becomes a dual edge
That's probably the easiest one. Morph by tilting quads may not be too hard either if implemented as the dual of a morph by rectangles.
Morph by truncation is trickier to do in a general way (ie not limited to uniform polytopes), as there is no rectified form in general, so I don't rely on that in 3D.
I'll probably look into it sometime.
Thanks,
Rob.
