Bounded blending operations

Abstract

New analytical formulations of bounded 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. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional bounding solid. The proposed blending using a bounding solid can be applied to a single selected edge or a vertex. 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.

Tweening grammars: Deformation rules for representing change between discrete geographic entities

“…Their approach and concerns are for more realistic tweens, but they have not focused on tweens directly related to geospatial processes. Pasko et al 1999;Gotsman and Surazhsky 2001;Surazhsky et al 2001;Winnemöller and Bangay 2001;Pasko et al 2002;Van den Bergh et al 2002;Glassner 2003;Che et al 2004) Deformation methods (Skeleton, TIN) (Kirkpatrick and Radke 1985) Images (General) (Lee et al 1996;Surazhsky et al 2001) Medical Imaging (Shih et al 1998;Pasko et al 1999;Treece et al 1999;Surazhsky et al 2001) Topography The second table (Table 2) shows the interdisciplinary scope of this problem and that many researchers are interested in tweening. The table categorizes the research papers into the fields of the lead authors.…”

“…Discipline of lead author of the publication. Computer Graphics, Science, Animation (Martyn;Blum 1967;Blum and Nagel 1978;Catmull 1978;Reeves 1981;Kirkpatrick and Radke 1985;DeCarlo and Metaxas 1995;Shapira and Rappoport 1995;Lee et al 1996;DeCarlo and Metaxas 1998;Gao and Sederberg 1998;Lee et al 1998;Pasko et al 1999;Johan et al 2000;Bradley and Stuart 2001;Gotsman and Surazhsky 2001;Winnemöller and Bangay 2001;Pasko et al 2002;Van den Bergh et al 2002;Glassner 2003;Torsello and Hancock 2004;Yang et al 2004) Architecture & Engineering (Stiny and Gips 1972;Bertalmio et al 1998;Shih et al 1998;Treece et al 1999;Treece et al 2001) Mathematics Che et al 2004) 3. Methods…”

Generalized sweep templates for implicit modeling

“…The use of gw here is not significant, any smooth interpolating function can be used. This method is similar to the boundedblending techniques used to control implicit volume composition operators [Pasko et al 2002] [Galbraith et al 2004]. An example is shown in Figure 5.…”

BlobTree trees

“…The BlobTree is an extensible data structure, currently supporting the following modeling techniques: CSG, space warping, PCM, 2D texture mapping [29], controlled blending [14], local refinement [19] and R-functions [24]. As Pasko [25] points out, there are problems with using the max/min functions for CSG in certain circumstances. However, these are not problems in the case of the tree examples presented in this paper.…”