Modeling 3D Curves of Minimal Energy

Abstract

Modeling a curve through minimizing its energy yields an overall smooth curve. A common way to model shape features is to perform the minimization subject to a number of interpolation constraints. This way of modeling is attractive because the designer is not bothered with the precise representation of the curve (e.g. control points). However, local shape specification by means of interpolation constraints is very limited. On the other hand, local deformation by repositioning control points is powerful but very laborious, and destroys the minimal energy property. In this paper, deform operators are introduced for 3D curve modeling that have built-in energy terms that have an intuitive effect. These operators allow local shape modification and do justice to the energy minimization way of modeling.