Material Aware Mesh Deformations

Tiberiu Popa, Dan Julius, Alla Sheffer



International Journal of Shape Modeling – Special Issue on SMI’06 - June 2007

IJSM paper (b/w) ,

SMI paper (color),

Presentation slides (color),

SIGGRAPH poster (ppt) , (pdf) ,

   author = { Tiberiu Popa and Dan Julius and Alla Sheffer},
   title = {
Interactive and Linear Material Aware Deformations},
   journal = {International Journal of Shape modeling},
   year = {2007},


Most real world objects consist of non-uniform materials; as a result, during deformation the bending and shearing are distributed non-uniformly and depend on the local stiffness of the material. In the virtual environment there are three prevalent approaches to model deformation: purely geometric, physically driven, and skeleton based. This paper proposes a new approach to model deformation that incorporates nonuniform materials into the geometric deformation framework. Our approach provides a simple and intuitive method to control the distribution of the bending and shearing throughout the model according to the local material stiffness. It also provides a rich, flexible and intuitive user interface. Thus, we are able to generate realistic looking, material-aware deformations at interactive rates. Our method works on all types of models, including models with continuous stiffness gradation and non-articulated models such as cloth. The material stiffness across the surface can be specified by the user with an intuitive paint-like interface or it can be learned from a sequence of sample deformations.






a) User selects a small set of triangles, called anchor triangles (Figure 3(a)) and apply the desired transformations using a click and drag motion. We support anchor transformations that include any combination of rotations and uniform scales.

b) User defines the stiffness of the material using a simple and intuitive paint-like interface. The method also supports continuous variation of stiffness such as stiffness gradient as the tentacle’s octopus from the above figure.

c, d) The material stiffness can also be computed automatically from a set of sample poses.


e)  From the anchor triangles, we then propagate transformations to the remaining triangles of the mesh consistent to the material properties 

f) We glue the triangles together for a manifold final result




Direct Vertex Manipulation

 In certain cases the user might want to specify positional constraints as well. We developed a method where the user specifies positional constraints on vertices by dragging them on the screen and the system then computes optimal rotations automatically. Figure 5 shows an example where a straight bar (5e) is deformed by dragging one of its vertices. Depending on the energy functional used, our system can simulate various behaviours:

a)      Area

b)      Volume

c)      Shear

d)      Dihedral angles (in the L2 norm)




Material Learning

 In many situations, physically or anatomically correct deformation samples of a given model may already be available. In such cases we would like to derive the material properties from the sample poses to create new deformations which are consistent with the sample set and are therefore also correct.

a)      A set of sample lion poses

b)      Derived material properties

c)      New deformations





Anisotropic Materials


The formulation presented so far assumes that bending flexibility is a non-directional property, which need not be true in practice. For example, a knee joint is only flexible in one direction and rigid in the other two. We extend our formulation to allow different bending stiffness for different axes of rotation.

This figure sows the result of bending and twisting a bar under:

a)      Isotropic uniform material

b)      Isotropic non-uniform material (middle section is isotropically stiffer than the rest of the bar)

c)      Anisotropic non-uniform material (middle section is stiffer under twisting and more flexible under bending than the rest of the bar)