As-Stiff-As-Needed Surface DeformationCombining ARAP Energy with an Anisotropic Material.

The creation of man-made shapes can be seen as the exploration of designers’ ‘Mental Shape Space’, often supported by design reviews. To improve communication among the designers during these reviews, we introduce a new physically-based method to intuitively deform man-made shapes. This method is based on as-rigid-as possible (ARAP) shape deformation methods, known to offer a direct surface manipulation and to generate visually pleasant shapes by minimizing local deviations from rigidity. However, the organic character of ARAP shape deformations leads to undesired effects, such as surface collapsing or bulging because of an inappropriate stiffness model over the object. In this paper, we first link the designers’ needs to ARAP handle-based variational mesh deformation processes. Then, we study and characterize the ARAP energy and its variants from a structural mechanics point of view. Our insight is that controlling the material stiffness could prevent the undesirable organic effects. Yet, we shed light on the fact that none of the ARAP-based methods offers an appropriate stiffness distribution over the object from a mechanical standpoint. We do so by introducing an appropriate anisotropic material, called orthotropic material, to improve the stiffness distribution over the surface and its deformation behavior for man-made shapes. This material is associated with a membrane-like structural behavior to further improve the stiffness distribution. Thanks to these settings, we derive a robust and intuitive deformation process that produces an anisotropic mesh deformation based on new edge weights in the ARAP formulation. The benefits of our new method are finally illustrated by typical design examples from the automotive industry and other man-made shapes.