Web-based Constructive Shape Modeling Using Real Distance Functions

Abstract

Abstract:We present an approach and a web-based system implementation for modeling shapes using real distance functions. The system consists of an applet supporting the HyperFun modeling language. The applet is extended with primitives defined by Euclidean distance from a point to the surface of the shape. Set-theoretic operations (union, intersection, difference) that provide an approximation of the Euclidean distance to a shape built in a constructive way are introduced. Such operations have a controllable bounded error of the exact Euclidean distance to the shape and preserve C 1 continuity of the overall function, which is an important condition for further operations and applications. The proposed system should help model various shapes, store them in a concise form, and exchange them easily between different entities on a network. The applet offers also the possibility to export the models defined in the HyperFun language to other formats for raytracing or rapid prototyping. Department of Digital Media Faculty of Computer and Information SciencesHosei University 3-7-2 Kajino-cho, Koganei-shi Tokyo 184-8584 Japan SummaryWe present an approach and a web-based system implementation for modeling shapes using real distance functions. The system consists of an applet supporting the HyperFun modeling language. The applet is extended with primitives defined by Euclidean distance from a point to the surface of the shape. Set-theoretic operations (union, intersection, difference) that provide an approximation of the Euclidean distance to a shape built in a constructive way are introduced. Such operations have a controllable bounded error of the exact Euclidean distance to the shape and preserve C 1 continuity of the overall function, which is an important condition for further operations and applications. The proposed system should help model various shapes, store them in a concise form, and exchange them easily between different entities on a network. The applet offers also the possibility to export the models defined in the HyperFun language to other formats for raytracing or rapid prototyping.

Local metamorphosis of functionally defined shapes

“…First, we would like to include the SARDF operations [Fayolle et al 2005] and distance based primitives to check if the distance field provides better control of the metamorphosis, and also to help the user define the partitions. Indeed, in the FRep model, to find a proper thr the user before it can be set.…”

An object-oriented approach for mechanical components design and visualization

“…Cartwright et al [6] describe experiments for designing and developing a geometrical modeler combining ideas from empirical modeling and from implicit surface modeling. Another approach for shape modeling was proposed in [16], where a system implementation for modeling shapes using real distance functions have been used.…”