ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

As-rigid-as-possible (ARAP) surface modelling is widely used for interactive deformation of triangle meshes. We show that ARAP can be interpreted as minimizing a discretization an elastic energy based on non-conforming elements defined over dual orthogonal cells the mesh. Using intrinsic Voronoi rather than extrinsic mesh guarantees non-negative each cell. represent Delaunay edges extrinsically polylines mesh, encoded in barycentric coordinates relative to vertices. This modification original energy, which we term iARAP, remedies problems stemming from non-Delaunay approach. Unlike spokes-and-rims version approach it less susceptible triangulation surface. provide examples deformations generated with iARAP and contrast them other versions ARAP. also discuss properties Laplace-Beltrami operator implicitly introduced new discretization.