Drivenshape - a datadriven approach for shape deformation

Figure 1: Thedore’s shirt animated with DrivenShape. DrivenShape is a technique developed at Rhythm and Hues Studios, aimed at providing an efficient alternative to expensive deformation computations (e.g. cloth simulations). It allows users to drive defor-mation of one object from the shape of another object. For example, we may wish to drive shape (wrinkles and folding) of a pants based on how the character’s legs are posed. The tool is especially useful when the paired shapes are highly cor-related and the space of all the possible shapes is limited. Such cases are common in animation, such as deformation of tight fitting clothing or muscle flexing, where deformation is almost determined by the pose of the character. (Try raising your arm many times, and observe how your shirts responds to the pose). Overview We start by anaylizing reference animations that contain both pose shape (driver) and its corresponding deformed (driven) shape. For a database of k frames, let us call the pose shape Pi, and the driven shape Di, for 1 ≤ i ≤ k. At runtime, we have a new pose Pnew and wish to reconstruct cor-responding deformation Dnew. We express the new target shape Dnew as weighted sum of Di in the database, Dnew = wi ∗Di, and use Pnew to compute weights such that Pnew = wi ∗Pi. In a mathematical form, we wish to minimize ‖ A ∗ w − b ‖2, where A’s column vectors are filled with vertices of Pi, w is the weights, and b is a column vector with vertices of Pnew. We seek for wi that minimizes the above norm, resulting in the following equations