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.
OriginalLBS DQS STBS Figure 1: Left to right: the Beast model is rigged to a skeleton in its rest pose. The neck is stretched and the arms are twisted and stretched using linear blend skinning. LBS relies solely on per-bone scalar weight functions, resulting in the explosion of the head and hands. The candy-wrapper artifact of LBS is also noticeable at the elbows. The dual quaternion skinning (DQS) solution [Kavan et al. 2008] correctly blends rotations, avoiding the candy-wrapper artifact, but reliance on bone weights alone unnaturally concentrates the twisting near the elbows. DQS also does not alleviate the stretching artifacts. Our solution, stretchable, twistable bones skinning (STBS), uses an extra set of weights per bone, allowing stretching without explosions and smooth twisting along the entire length of each arm. AbstractSkeleton-based linear blend skinning (LBS) remains the most popular method for real-time character deformation and animation. The key to its success is its simple implementation and fast execution. However, in addition to the well-studied elbow-collapse and candywrapper artifacts, the space of deformations possible with LBS is inherently limited. In particular, blending with only a scalar weight function per bone prohibits properly handling stretching, where bones change length, and twisting, where the shape rotates along the length of the bone. We present a simple modification of the LBS formulation that enables stretching and twisting without changing the existing skeleton rig or bone weights. Our method needs only an extra scalar weight function per bone, which can be painted manually or computed automatically. The resulting formulation significantly enriches the space of possible deformations while only increasing storage and computation costs by constant factors.
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