Bounded biharmonic weights for real-time deformation

Abstract

Object deformation with linear blending dominates practical use as the fastest approach for transforming raster images, vector graphics, geometric models and animated characters. Unfortunately, linear blending schemes for skeletons or cages are not always easy to use because they may require manual weight painting or modeling closed polyhedral envelopes around objects. Our goal is to make the design and control of deformations simpler by allowing the user to work freely with the most convenient combination of handle types. We develop linear blending weights that produce smooth and intuitive deformations for points, bones and cages of arbitrary topology. Our weights, called bounded biharmonic weights, minimize the Laplacian energy subject to bound constraints. Doing so spreads the influences of the controls in a shape-aware and localized manner, even for objects with complex and concave boundaries. The variational weight optimization also makes it possible to customize the weights so that they preserve the shape of specified essential object features. We demonstrate successful use of our blending weights for real-time deformation of 2D and 3D shapes.

Locally controlled as‐rigid‐as‐possible deformation for 2D characters

“…Figures and illustrate the superiority of our LC‐ARAP deformation approach in comparison with the traditional ARAP energy deformation, L p shape deformation (with p =1 and parameters set as in the work of Lin Gao and Lai), linear bend skinning with bounded biharmonic weight (BBW) and topology‐aware MLS deformation . With the manipulation of the handles on some parts of a character, the desired result is that only the related regions change.…”

“…On the basis of controllable conformal maps, a novel deformation system preventing foldovers completely is introduced . Linear blending skinning is another popular space deformation model . Although these space deformation methods can be implemented efficiently, they may lead to some unavoidable artifacts, such as foldover and self‐intersection.…”

Streaming 3D deforming surfaces with dynamic resolution control

“…Interactive space deformation is a powerful approach for editing geometric models and animated characters, which has led to an abundance of methods seeking to improve interactive deformation with intuitive use. Some efficient methods are known to compute high‐quality surface deformations , and each has its own features. Currently, only a space deformation method is adopted in our framework.…”

Example‐based inverse kinematics using cage

“…Our IK method differs from previous nonlinear MeshIK approaches in that it computes interpolation weights on the basis of pose space interpolation . This allows us to extend the method to edit the model locally, by computing interpolation weights only from the handle that is translated and blending deformations based on bounded biharmonic weights (BBWs) (Section 5.2). Unlike the method based on the sophisticated statistical method , we use an RBF because of its efficiency at the training stage to achieve insertions of handles during the editing session.…”

“…For blending weights, we employ BBWs . Unlike harmonic weights that were used in , BBWs are local and smooth, which is suitable for handle‐based deformation.…”