Handle-aware isolines for scalable shape editing

Handle-based mesh deformation is essentially a nonlinear problem. To allow scalability, the original deformation problem can be approximately represented by a compact set of control variables. We show the direct relation between the locations of handles on the mesh and the local rigidity under deformation, and introduce the notion of handle-aware rigidity. Then, we present a reduced model whose control variables are intelligently distributed across the surface, respecting the rigidity information and the geometry. Specifically, for each handle, the control variables are the transformations of the isolines of a harmonic scalar field representing the deformation propagation from that handle. The isolines constitute a virtual skeletal structure similar to the bones in skinning deformation, thus correctly capturing the low-frequency shape deformation. To interpolate the transformations from the isolines to the original mesh, we design a method which is local, linear and geometry-dependent. This novel interpolation scheme and the transformation-based reduced domain allow each iteration of the nonlinear solver to be fully computed over the reduced domain. This makes the per-iteration cost dependent on only the number of isolines and enables compelling deformation of highly detailed shapes at interactive rates. In addition, we show how the handle-driven isolines provide an efficient means for deformation transfer without full shape correspondence.