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Bounded Biharmonic Weights for Real-Time Deformation
Bounded biharmonic weight computation for cage and skeleton deformation providing smooth, localized, non-negative influence functions.
Abstract
Object deformation with linear blending dominates practical use as the fastest approach for transforming raster images, vector graphics, geometric models and animated characters. Unfortunately, linear blending schemes for skeletons or cages are not always easy to use because they may require manual weight painting or modeling closed polyhedral envelopes around objects. Our goal is to make the design and control of deformations simpler by allowing the user to work freely with the most convenient combination of handle types. We develop linear blending weights that produce smooth and intuitive deformations for points, bones and cages of arbitrary topology. Our weights, called bounded biharmonic weights, minimize the Laplacian energy subject to bound constraints. Doing so spreads the influences of the controls in a shape-aware and localized manner, even for objects with complex and concave boundaries. The variational weight optimization also makes it possible to customize the weights so that they preserve the shape of specified essential object features. We demonstrate successful use of our blending weights for real-time deformation of 2D and 3D shapes.
How to read this
- Category
- Method: a skinning-weight computation (bounded biharmonic weights)
- Contributions
- Bounded biharmonic weights that minimize Laplacian energy subject to bound constraints for smooth, intuitive linear-blend deformation
- Unified support for mixed handle types (points, bones, cages of arbitrary topology) with shape-aware, localized, non-negative influence
- Variational weight customization to preserve specified essential features, enabling real-time deformation of 2D and 3D shapes
- Context
- Advances generalized-coordinate/weight schemes for linear blend skinning, building on the Harmonic Coordinates for character articulation line of work while adding bound constraints and mixed handle support.Builds on: Harmonic Coordinates for Character Articulation
- Correctness
- The core guarantees (smoothness, locality, non-negativity, partition-of-unity behavior) follow from the constrained Laplacian-energy minimization; the weights are precomputed via a variational optimization, so a reader should keep the precompute cost and reliance on a meaningful interior discretization in mind, with deformation itself remaining real-time.
- Clarity
- Clearly written but mathematically grounded; a first pass conveys what the weights deliver, and a second pass is needed for the variational optimization and bound constraints.
- How to read it
- Focus first on the four desirable weight properties and the mixed-handle motivation; a second pass on the constrained Laplacian optimization pays off if you implement or extend it.
Builds on
Related work
- Robust Skin Weights Transfer via Weight Inpainting 2023 / SIGGRAPH Asia
- Real-Time Deformation with Coupled Cages and Skeletons 2020 / SCA
- Stretchable and Twistable Bones for Skeletal Shape Deformation 2011 / SIGGRAPH Asia
- Fast Automatic Skinning Transformations 2012 / SIGGRAPH
Keywords
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