Area, perimeter and derivatives of a skin curve

AbstractThe body defined by a finite collection of disks is a subset of the plane bounded by a tangent continuous curve, which we call the skin. We give analytic formulas for the area, the perimeter, the area derivative, and the perimeter derivative of the body. Given the filtrations of the Delaunay triangulation and the Voronoi diagram of the disks, all formulas can be evaluated in time proportional to the number of disks

Design and Analysis of Planar Shape Deformation

Shape deformation refers to the continuous change of one geometric object to another. We develop a software tool for planning, analyzing, and visualizing deformations between two shapes in R 2 . The deformation is generated automatically without any user intervention or specification of feature correspondences. A unique property of the tool is the explicit availability of the two-dimensional shape space, which can be used for designing the deformation either automatically by following constraints and objectives or manually by drawing deformation paths. 1 Introduction This paper describes a method for the deformation of one geometric shape in the plane to another and a software tool that implements it. In computer graphics this operation is commonly referred to as morphing. In that area the focus is on the creation of image sequences that display the morph [8, 9, 10]. In contrast, this paper constructs the deformation as a 1-dimensional family of genuine geometric objects. Rationale..

Design and analysis of planar shape deformation

Shape deformation refers to the continuous change of one geometric object to another. We develop a software tool for planning, analyzing and visualizing deformations between two shapes in R-2. The deformation is generated automatically without any user intervention or specification of feature correspondences. A unique property of the tool is the explicit availability of a two-dimensional shape space, which can be used for designing the deformation either automatically by following constraints and objectives or manually by drawing deformation paths. (C) 2001 Elsevier Science B.V All rights reserved