Variational Geometry with Algebraic Level Set Model

Variational Geometry technique, also known as Constraints Satisfaction Problem technique (CSP), is one of the core components in modern CAD systems. One of the known problems of the existing technique is its inability of solving topological changes. In this paper, we propose a new Varaitional Geometry technique with Algebraic Level Set (ALS) geometric model. Based on half-space model theory and classic Level Set formulation, Algebraic Level Set concept is first described, its merits are also addressed within this context. Using this geometry representation, the topological changing problem caused by constraint variations could be solved in a natural way. This proposed method is capable of performing shape deformation capability that can be provided by conventional Variational Geometry technique, meanwhile, keeps the implicit topological definition of Algebraic Level Set functions which accounts for the topological changes in our proposed framework. Several numerical results demonstrate the preliminary capacity of our proposed approach.