Volume 37 (2018), number 1 pp. 32–44
ARAPLBS: Robust and Efﬁcient Elasticity-Based Optimization
of Weights and Skeleton Joints for Linear Blend Skinning
with Parametrized Bones
and E. Eisemann
Deﬂt University of Technology, The Netherlands
LTCI, Telecom-ParisTech, Universit
e Paris-Saclay, Paris, France
We present a fast, robust and high-quality technique to skin a mesh with reference to a skeleton. We consider the space of
possible skeleton deformations (based on skeletal constraints, or skeletal animations), and compute skinning weights based on
an optimization scheme to obtain as-rigid-as-possible (ARAP) corresponding mesh deformations. We support stretchable-and-
twistable bones (STBs) and spines by generalizing the ARAP deformations to stretchable deformers. In addition, our approach
can optimize joint placements. If wanted, a user can guide and interact with the results, which is facilitated by an interactive
feedback, reached via an efﬁcient sparsiﬁcation scheme. We demonstrate our technique on challenging inputs (STBs and spines,
triangle and tetrahedral meshes featuring missing elements, boundaries, self-intersections or wire edges).
Keywords: deformations, animation systems, geometric modelling
ACM CCS: I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling—Curve, surface, solid and object
Linear Blend Skinning (LBS) is a standard technique for skeleton-
based animation and is used extensively in video games, movies,
simulations and virtual-reality systems . It is popular because artists
use skeletons to animate characters and because of its efﬁciency:
it only requires blending bone transformations using pre-computed
Looking at typical meshes and skeletons produced by artists
(Figure 1, left), it is clear that automatic weight computation is
challenging: (i) Models can consist of disconnected parts, which
might not be manifold, or orientable. (ii) The skeletal topology
might differ from the mesh topology (skeletons are conceived to
facilitate animating, not to follow geometric constraints). (iii) The
skeleton can be complex.
Typically, skinning weights should fulﬁl some properties (e.g.
sumto1).Approachesbasedon(k-)harmonic or general partial
differential equations (PDEs) ensure these on the mesh or on an
embedding, while enforcing smoothness. Although smooth weights
are necessary, they do not ensure high-quality deformations.
Our approach produces weights to optimize deformation qual-
ity. Building upon as-rigid-as-possible (ARAP) transformations to
beneﬁt from their properties (angle, edge length preservation), we
construct a set of representative skeleton deformations, exemplars,
sampled from the space of admissible transformations, and opti-
mize the skinning weights jointly to achieve corresponding ARAP
transformations. We can further specialize our weights for skeleton
animations by adding them to our exemplars.
Our approach is general and robust. Although compatible with
volumetric meshes, it does not rely on volumetric structures (which
are sometimes impossible to generate with existing tools) for the
weight computation on surface meshes. Our method handles chal-
lenging inputs, e.g. containing self-intersections, open boundaries,
disconnected parts or wire-edges. It is even compatible with com-
plex bones, e.g.stretchable-and-twistable bones (STBs) [JS11] and
spines. Our solution can also optimize the skeleton joints with re-
spect to the mesh for an optimal deformation quality, which can be
a tedious task when performed manually.
Our method was conceived with efﬁciency and user-friendliness
in mind, and we introduce a weight sparsiﬁcation scheme, which
2017 The Authors
Computer Graphics Forum
2017 The Eurographics Association and
John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd.