Handle-Aware Isolines for Scalable Shape Editing

Figure 1: Our method uses handle-aware isolines to build a reduced model. The three images visualize the isolines and rigidity information both associated with the handles (in crimson) at the upper jaw (left), the left fore foot (middle), and the tail (right), respectively. Note that the isolines respect the handles and the shape geometry. We associate a transformation to each isoline and identify the transformations of isolines associated with all the handles as the reduced domain. Handle-based mesh deformation is essentially a nonlinear problem. To allow scalability, the original deformation problem can be ap-proximately 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 sur-face, respecting the rigidity information and the geometry. Specifi-cally, for each handle, the control variables are the transformations of the isolines of a harmonic scalar field representing the deforma-tion 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 inter-polate 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 re-duced 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 com-pelling 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 corre-spondence