Some pictures of my implementation of the paper “Embedded Deformation for Shape Manipulation” by Robert W. Summer (SIGGRAPH 2007 – ETH Zurich) (link to paper) (link). The algorithm introduces a natural way for deforming shape representations such as triangular meshes. The original movie of the author can be found here. And below you can find a movie of my result.

In most cases a triangular mesh has a high triangle count. Usually we want to deform the mesh at a more global scale and not at single triangle level. Therefore a more sparse graph is constructed, the deformation graph. This deformation graph makes the technique very general. The deformation graph “deforms the space”. And the shape, in our case the mesh, exists in this space.

Each node of the deformation graph is associated with a transformation. The positions of the vertices of the triangular mesh are determined by a weighted average of these transformations. Thus the mesh solely depends on the nodes of the deformation graph. So if we modify these transformations, the space will be deformed and this will result in a deformed mesh.

I used a naive algorithm, starting from the original mesh, in order to create a deformation graph. The deformation graph is shown below.

Then we can interact with this deformation graph. For example we can move nodes around. This will induce a non-linear minimization. The goal of this optimization process is to make the transitions between the transformations of the neighbouring nodes smooth.

Please see the paper for more details.