The Animeshon project tries to solve a seemingly simple problem: how can we animate meshes? In particular we want to solve this problem:
Given a mesh animation, without rigging, how can we copy and paste this animation over another mesh?
Diverse fields, from computer graphics to medical imaging, employ shape theory. Shapes are modeled as points of suitable Riemannian Shape Spaces. The transport of the deformation from one shape to a different one is described through the concept of connection and Parallel Transport of vectors.
Naively, we could deform a mesh by applying the discrete displacement field computed by difference of a mesh and its deformed shape. However, a naïve transport of information between Riemannian manifolds, i.e., applying the same strain tensor field between different meshes, in general, cannot be fully realized.
You can read more in the following papers:
Let's see an example. A simple 2D mesh deformation.
We're given a square, and its final deformed shape, as we can see in the picture. This is just to illustrate the principle, restricting the problem to its core.
We want to copy and paste the deformation on a new mesh, a kite. Naïvely, we deform each triangle, expecting to have a deformed kite as a result.
By attaching to each triangle of the kite the given deformation, we have a non-conforming mesh. Transporting deformations is not trivial even in 2D.
For more information, please contact us.
Franco Milicchio (franco.milicchio@uniroma3.it)
Valerio Varano (valerio.varano@uniroma3.it)
Paolo Piras (paolo.piras@uniroma3.it)
Luciano Teresi (luciano.teresi@uniroma3.it)
Stefano Gabriele (stefano.gabriele@uniroma3.it)