Localized Blending for Exact Control of Shapes With Applications to Shape Modeling and 2d Animation

Abstract

Blending of two shapes generates a smooth transition between them by adding or removing material. In this work, new analytical formulations of localized blending for functionally defined set-theoretic operations are proposed. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. An additional bounding solid defines the shape and location of the blend. The proposed bounded blending can be applied to a single selected feature of a shape (comer, edge, and others). We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. It is shown to have versatile applications in interactive design. We also describe the application of the bounded blending to the 2D shape transformation problem we encounter in animation.