Energy Minimizers for Curvature-Based Surface Functionals

Abstract

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 preferred shapes attained by these different functionals, we present a catalog of the minimum energy shapes for various symmetrical, unconstrained input surfaces of different genera.

Keywords:

• surface optimization
• bending energy
• curvature variation
• aesthetic design