Energy Minimizers for Curvature-Based Surface Functionals

Energy Minimizers for Curvature-Based Surface Functionals

We compare curvature-based surface functionals by comparing the aesthetic properties of their minimizers. We introduce an enhancement to the original inline curvature variation functional. This new functional also considers the mixed cross terms of the normal curvature derivative and is a more complete formulation of a curvature variation functional. To give designers an intuitive feel for the ...

Minimizers of Curvature-Based Surface Energy

Curvature based surface optimization is an important constituent of various geometric modeling and scientific computing tasks. Smooth surfaces are often modelled in a variational setting, where the objective function is used to express the beauty of the shape. Optimization is also used for fitting a smooth, virtual surface to samples of a real, scanned object. Energy minimizing surfaces are als...

Characterization of Minimizers of Convex Regularization Functionals

We study variational methods of bounded variation type for the data analysis. Y. Meyer characterized minimizers of the Rudin-Osher-Fatemi functional in dependence of the G-norm of the data. These results and the follow up work on this topic are generalized to functionals defined on spaces of functions with derivatives of finite bounded variation. In order to derive a characterization of minimiz...

Kinetic - energy functionals studied by surface calculations

Existence of Minimizers for NonLevel Convex Supremal Functionals

The paper is devoted to determine necessary and sufficient conditions for existence of solutions to the problem inf { ess sup x∈Ω f(∇u(x)) : u ∈ u0 +W 1,∞ 0 (Ω) } , when the supremand f is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Severa...