# Robert W. Sumner

Inverse Kinematics for Reduced Deformable Models

Articulated shapes are aptly described by reduced deformable models
that express required shape deformations using a compact set of
control parameters. Although sufficient to describe most shape deformations,
these control parameters can be ill-suited for animation
tasks, particularly when reduced deformable models are inferred
automatically from example shapes.

Mesh-Based Inverse Kinematics

The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid mesh configurations, and a selection mechanism for choosing among them. Drawing an analogy to the traditional use of skeleton-based inverse kinematics for posing skeletons, we define mesh-based inverse kinematics as the problem of finding meaningful mesh deformations that meet specified vertex constraints.
Our solution relies on example meshes to indicate the class of meaningful deformations.

Deformation Transfer for Triangle Meshes

Deformation transfer applies the deformation exhibited by a source triangle mesh onto a different target triangle mesh. Our approach is general and does not require the source and target to share the same number of vertices or triangles, or to have identical connectivity. The user builds a correspondence map between the triangles of the source and those of the target by specifying a small set of vertex markers. Deformation transfer computes the set of transformations induced by the deformation of the source mesh, maps the transformations through the correspondence from the source to the target, and solves an optimization problem to consistently apply the transformations to the target shape.