Mesh-based Inverse Kinematics

Robert W. Sumner1 Matthias Zwicker1 Craig Gotsman2 Jovan Popovic1
1Massachusetts Institute of Technology 2Technion - Israel Institute of Technology

In ACM Transactions on Graphics (Proceedings of SIGGRAPH), 24(3), July 2005

Top row: Ten lion example poses. Bottom row: A sequence of posing operations. (A) Two handle vertices are chosen. (B) The front leg is pulled forward and the lion continuously deforms as the constraint is moved. (C) The red region is selected and frozen so that the front leg can be edited in isolation. (D) A similar operation is performed to adjust the tail. The final pose is different from any individual example.


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. Furthermore, because the span is formed by a nonlinear blend of the example feature vectors, the blending component of our system may also be used independently to pose meshes by specifying blending weights or to compute multi-way morph sequences.

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