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Sharp Kelvinlets: Elastic Deformations with Cusps and Localized Falloffs
Extends Kelvinlet sculpting with a multi-scale convolution scheme enabling cusp-like elastic edits with sharp, localised falloff profiles.
Abstract
In this work, we present an extension of the regularized Kelvinlet technique suited to non-smooth, cusp-like edits. Our approach is based on a novel multi-scale convolution scheme that layers Kelvinlet deformations into a finite but spiky solution, thus offering physically based volume sculpting with sharp falloff profiles. We also show that the Laplacian operator provides a simple and effective way to achieve elastic displacements with fast far-field decay, thereby avoiding the need for multi-scale extrapolation. Finally, we combine the multi-scale convolution and Laplacian machinery to produce Sharp Kelvinlets, a new family of analytic fundamental solutions of linear elasticity with control over both the locality and the spikiness of the brush profile. Closed-form expressions and reference implementation are also provided.
How to read this
- Category
- Method: an analytic elastic-deformation brush for volume sculpting
- Contributions
- A multi-scale convolution scheme that layers Kelvinlet deformations into a spiky solution for cusp-like, non-smooth edits
- Use of the Laplacian operator to obtain fast far-field decay without multi-scale extrapolation
- Sharp Kelvinlets, a family of closed-form elasticity solutions with control over both locality and spikiness, plus a reference implementation
- Context
- A direct extension of Regularized Kelvinlets (de Goes and James 2017), which built sculpting brushes on fundamental solutions of linear elasticity; this work adds non-smooth, sharply-localized falloff profiles.Builds on: Regularized Kelvinlets: Sculpting Brushes Based on Fundamental Solutions of Elasticity
- Correctness
- Grounded in closed-form fundamental solutions of linear elasticity, so the deformations are physically based within that linear regime; the brushes are a controllable sculpting tool rather than a full physical simulation, so behavior under large or coupled deformations is outside the stated scope.
- Clarity
- Clear and self-contained with closed-form expressions and reference code; a first pass conveys the brush idea, a second pass is needed to follow the convolution and Laplacian derivations.
- How to read it
- Read 2017 Regularized Kelvinlets first; on the first pass focus on what cusp/spikiness control buys you, then do a formula-level second pass on the multi-scale convolution and Laplacian construction if you intend to implement it.
Builds on
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Related work
- Interactive Skeleton-Driven Dynamic Deformations 2002 / SIGGRAPH
- Physically Based Rigging for Deformable Characters 2005 / SCA
- Harmonic Coordinates for Character Articulation 2007 / SIGGRAPH
- Regularized Kelvinlets: Sculpting Brushes Based on Fundamental Solutions of Elasticity 2017 / SIGGRAPH
Keywords
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