Regularized Kelvinlets: Sculpting Brushes Based on Fundamental Solutions of Elasticity

How to read this

Category

Method: closed-form elastic deformation primitives (sculpting brushes)

Contributions

• Brush-like grab, scale, twist, and pinch displacements derived as regularized fundamental solutions of linear elasticity in 2D and 3D
• Compound brushes with arbitrarily fast spatial decay for fine local control
• Pointwise constraints on the displacement field and its derivatives via a single linear solve

Context

Grounds interactive sculpting in classical linear elasticity (Kelvin's fundamental solutions), offering an analytical alternative to mesh-based or FEM volume deformation for pose-space sculpting workflows.

Correctness

Built on linear elasticity in infinite media, so results are physically plausible rather than exact for finite or nonlinear materials; the closed-form, regularized formulation buys real-time interactivity but the demonstrations are sculpting and image-editing examples rather than a quantitative validation.

Clarity

Conceptually accessible (brush metaphor); a first pass conveys the idea, a second pass is needed for the elasticity formulation and regularization.

How to read it

First pass for the brush vocabulary and the regularization idea; do a careful second pass on the fundamental-solution math and the constraint solve if you intend to implement or extend the brushes.