Is it possible to deform vertices or faces in a way that is similar to folded origami paper? I.e. the size of the mesh remains constant when moving points, deforming along the polygon edges but not actually changing size (only orientation and position)?
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If you want to blend between Linear Skinning and Dual Quaternion, change Skinning Method to Weight Blended. For it to work fully, you need to paint its blend weights on top of the skin weights.
I did a 'poke faces' on a plane and had marginal success for the first few folds just using the rotate tool- Ese the tilde ~ key to use the cursors location as the pivot point, and MMB to rotate based on view.
If you wanted full control, you could get crazy with some nested skeleton with constraints and IK solvers. My brain hurts trying to piece that together.
http://frankrause.com/2013/07/origami-mel-script-for-maya/