Linear Subspace Design for Real-Time Shape Deformation

Figure 1: Our linear subspaces are very fast to compute. This enables the users to add (or remove) control handles very quickly, allowing them to realize their creative intent in a single interactive session. We propose a method to design linear deformation subspaces, uni-fying linear blend skinning and generalized barycentric coordi-nates. Deformation subspaces cut down the time complexity of variational shape deformation methods and physics-based anima-tion (reduced-order physics). Our subspaces feature many desirable properties: interpolation, smoothness, shape-awareness, locality, and both constant and linear precision. We achieve these by min-imizing a quadratic deformation energy, built via a discrete Lapla-cian inducing linear precision on the domain boundary. Our main advantage is speed: subspace bases are solutions to a sparse lin-ear system, computed interactively even for generously tessellated domains. Users may seamlessly switch between applying transfor-mations at handles and editing the subspace by adding, removing or relocating control handles. The combination of fast computation and good properties means that designing the right subspace is now just as creative as manipulating handles. This paradigm shift in handle-based deformation opens new opportunities to explore the space of shape deformations