3D Deformation Using Moving Least Squares

Abstract

We present a 3d deformation method based on Moving Least Squares that extends the work by Schaefer et al. [Schaefer et al. 2006] to the 3d setting. The user controls the deformation by manipulating a set of point handles. Locally, the deformation takes the form of either a rigid transformation or optionally a similarity transformation, and tends to preserve local features. Our derivation of the closed-form solution is based on singular value decomposition, and is applicable to deformation in arbitrary dimensions, as opposed to the planar case in [Schaefer et al. 2006]. Our prototype implementation allows interactive deformation of meshes of over 100k vertices. For the application of 3d mesh deformation, we further introduce a weighting scheme that determines the influence of point handles on vertices based on approximate mesh geodesics. In practice, the new scheme gives much better deformation results for limbed character models, compared with simple Euclidean distance based weighting. The new weighting scheme can be of use to the traditional skinny based deformation technique as well.