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Mesh-Based Inverse Kinematics

Robert W. Sumner, Matthias Zwicker, Craig Gotsman, Jovan Popovic

SIGGRAPHAcademic326 cites1 descendantRiggingSkinning

Deformation-gradient feature vectors and nonlinear example span enable direct mesh posing through vertex constraints without an explicit skeleton.

Abstract

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. Each example is represented with a feature vector of deformation gradients that capture the affine transformations which individual triangles undergo relative to a reference pose. To pose a mesh, our algorithm efficiently searches among all meshes with specified vertex positions to find the one that is closest to some pose in a nonlinear span of the example feature vectors. Since the search is not restricted to the span of example shapes, this produces compelling deformations even when the constraints require poses that are different from those observed in the examples.

How to read this

Category
Method: example-based mesh deformation (mesh inverse kinematics)
Contributions
  • Defines mesh-based inverse kinematics: finding meaningful deformations that satisfy specified vertex constraints without an explicit skeleton
  • Represents each example mesh by a feature vector of per-triangle deformation gradients relative to a reference pose
  • Poses a mesh by searching for the constrained mesh closest to a nonlinear span of the example feature vectors, allowing compelling results even outside the example shapes
Context
Draws an explicit analogy to skeleton-based inverse kinematics and the deformation-gradient representation used in mesh editing, applying it to example-driven posing.Builds on: Laplacian Surface Editing
Correctness
Quality hinges on the example meshes spanning the desired class of deformations; because the search is not restricted to the example span it can extrapolate, but constraints far from the examples or sparse example sets may yield less meaningful results.
Clarity
The IK analogy makes the goal accessible; a first pass conveys the idea, a second pass is needed for the deformation-gradient feature vector and the nonlinear span optimization.
How to read it
First pass for the concept (skeleton-free, example-driven posing); a second pass on the feature-vector construction and the closest-pose search is worth it if you build deformation or editing tools.

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