Stretchable and Twistable Bones for Skeletal Shape Deformation

Alec Jacobson, Olga Sorkine-Hornung

The Beast's neck is stretched and arms twisted and stretched 
          using previous methods and our new method.

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 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.
Full resolution image


Skeleton-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 candy-wrapper 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.


accompanying video (with narration)

sample results

STBS using different automatic endpoint weight schemes stbs applied to photograph of max schmeling stbs driving a disco dancing ogre


We are grateful to Ofir Weber and Ilya Baran for illuminating discussions. We thank the United States Library of Congress for its collection of public domain photographs including the half-portrait of Max Schmeling. Special thanks to Felix Hornung for beautifying the teaser image. This work was supported by an SNF award 200021_137879.