How to blend between two mesh states non-linearly while respecting shapes?

[probiner]

Lets consider the box to be a mesh with two states, open/close and I would like to pass those (or more) to something that rotates the flaps from one pose to the other while respecting their shape; unlike what happens with linear interpolation with blendspahes/morphs. Is there something I could use in Houdini for that end (not just for boxes) or a search term that deals with something similar?

Thank you.

Edited July 4, 2018 by probiner

[amm]

If both stages are given, just for something like that, should be possible to get the angle by comparing the normals, also a line between two stages. These two, line and angle, should be enough elements to calculate the center of rotation by using some triangle formula (of right triangle). Cross product of normals (at first and last stage) should be a rotation axis. While entire thing will be rotating inward, unless you'll lower the ambition to less than 180 degree between stages. Not in front of Houdini, anyway I'd believe it will work. Multiple stages would be interesting to get by some SLERP , while this a bit too much for me to visualize, right now...

[probiner]

Thanks for the feedback @amm

I was wondering that maybe some dop solver could sort this out already, so checking before I roll up my sleeves and try to come up with something!
Will take your comments into account, but yeah my idea was to get lazy, just feed A and B and magic... Just like I've done to curves. https://streamable.com/8d89a

Thanks! If there's indeed a solver that can do it, lemme know

Edited July 7, 2018 by probiner

[amm]

By the way I've tried what I've suggested, and... really problematic part seems to be building the per-point orientation, somehow it is always arbitrary. So at the end of the day, three stages are minimum to build an curve based interpolation, as an robust method, just like you did  , I guess. If I'm correct, there's something for preserving the curve segment's length in your method, like Maya curve 'lock length'.

About ready for use solvers, while ago I've played with RBD constraints and Bullet, as an replacement for H wire solver, it showed great self-collisions, but entire sim was a bit too wild, more like ropes - 'loose' SDF based collision in Wire solver looked more realistic. H 'connect adjacent pieces' wasn't enough for building the relations (it takes nearby points in 3d space), had to build the replacement of 'connect...' thing.  Other than that, VDB Advect or FEM soft body comes to mind, however there's too long way of forth-back conversions with both (for my taste) to use as rigging tool.

Edited July 7, 2018 by amm