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Splitting a Complex of Convex Polytopes In Any Dimension
, 1996
"... Introduction We present a localitybased algorithm to solve the problem of splitting a complex of convex polytopes with a hyperplane or a convex subset of it. The solution to this problem has several applications. One goal is to perform boolean set operations. The solution can also be used to decom ..."
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Introduction We present a localitybased algorithm to solve the problem of splitting a complex of convex polytopes with a hyperplane or a convex subset of it. The solution to this problem has several applications. One goal is to perform boolean set operations. The solution can also be used to decompose a polyhedron into convex polytopes [3] and to generate good meshes [4]. In higher dimensional spaces it can be used to efficiently compute isocontours of linear approximations of scalar fields (a basic technique of Scientific Visualization) [17, 19]. The approach taken here can also be included in a set of robust algorithms [11, 13, 15, 20, 27, 28] based on finite precision arithmetic. It is also defined in a dimension independent framework [5, 16, 24, 25]. The main contributions of this approach are: (i) it can be applied to polyhedral complexes of any dimension d; (ii) the algorithm is robust (it always produces valid output) and consistent (the topological structure of the resu
WebBased Approach for Very Complex Animations Through Geometric Programming
"... this paper is specified here. In order to focus the main aspects of the animation problem several definitions are given. Most of them are quite standard in the animation field, but it seems useful to provide a precise meaning to concepts used in the remainder of this work. Animation An animation is ..."
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this paper is specified here. In order to focus the main aspects of the animation problem several definitions are given. Most of them are quite standard in the animation field, but it seems useful to provide a precise meaning to concepts used in the remainder of this work. Animation An animation is a pair !scene, behaviour?. A graphics scene is here defined as a function of some real parameters, with values in some suitable data type. Each feasible set of parameters defines a configuration of the scene. A pair !time,
Web Based Collaborative CAAD
"... this paper we introduce a new framework that implements a collaborative CAAD software architecture to regulate multiple graphical web clients interacting with multiple distributed computation servers. The key components of the system are: (a) geometric modeling services for CAAD, (b) a shared langua ..."
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this paper we introduce a new framework that implements a collaborative CAAD software architecture to regulate multiple graphical web clients interacting with multiple distributed computation servers. The key components of the system are: (a) geometric modeling services for CAAD, (b) a shared language interface, (c) a distribution layer for hierarchical object communication and standard JDBC interfaces to database system, (d) collaboration layer for multiuser coordination and control, and (e) a shared Java
Transfinite Blending Made Easy
, 1999
"... In this paper transfinite interpolation/approximation is discussed. This is a powerful approach to generation of curves, surfaces and solids (and even higher dimensional manifolds) by blending lower dimensional geometric objects. Transfinite blending, e.g. used in GordonCoons patches, is well known ..."
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In this paper transfinite interpolation/approximation is discussed. This is a powerful approach to generation of curves, surfaces and solids (and even higher dimensional manifolds) by blending lower dimensional geometric objects. Transfinite blending, e.g. used in GordonCoons patches, is well known to mathematicians and CAD people. It is presented here in a very simple conceptual and computational framework, which leads such a powerful modeling to be easily handled by the non mathematically sophisticated user of graphics techniques. Transfinite blending is discussed in this paper by making use of a very powerful and simple functional language for geometric design.
Bijective DimensionIndependent Boundary to Interior Mapping with BSP Trees
, 1996
"... In this paper we discuss two algorithms for performing both ways the conversion between the boundary and the interior of ddimensional polyhedra. Both a dpolyhedron and its (d \Gamma 1)faces are represented as BSP trees. An algorithm for boundary to BSP conversion starting from a standard Brep wa ..."
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In this paper we discuss two algorithms for performing both ways the conversion between the boundary and the interior of ddimensional polyhedra. Both a dpolyhedron and its (d \Gamma 1)faces are represented as BSP trees. An algorithm for boundary to BSP conversion starting from a standard Brep was given by Thibault and Naylor in [15]. In this paper we assume no structure, no ordering and even no orientation on the set of boundary BSPtrees. The resulting algorithm can be executed on a parallel computing architecture. Also, if the incidence relations between faces of various dimension are known, then the algorithm can be executed iteratively, so allowing for reconstructing a dpolyhedron from its (d \Gamma k)faces, 1 k d. The converse algorithm allows to compute the BSP of the intersection of a generic hyperplane in E d with the BSP representation of a dpolyhedron. If such section hyperplane is the support of a (d \Gamma 1)face, then a BSP tree of the face is generated. This s...
Prototype Shape Modeling with a Design Language
"... A programming approach to the rapid prototyping of architectural design is discussed in this paper. This is done with particular reference to the early steps of design development, where a number of preliminary design alternatives should be generated and evaluated. At this purpose we show that the g ..."
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A programming approach to the rapid prototyping of architectural design is discussed in this paper. This is done with particular reference to the early steps of design development, where a number of preliminary design alternatives should be generated and evaluated. At this purpose we show that the generation of the 3D shape of each design alternative can be automated starting from the 2D layout of plans, sections and elevations. Each such geometric object can be symbolically defined with few lines of code using design variables and constraint operators. The 3D models generated by evaluation of program scripts may then be used as input to standard engineering evaluation methods concerning costs, heat exchanges and structural behaviour. 1. Introduction The aim of this paper is to show the capability of the geometric language PLaSM (Programming Language for Symbolic Modeling) to aid the designer in the early phases of the design process, focusing on the peculiarities of architectural sh...
Securing the Cultural Heritage via Geometric Programming and Modeling
"... Figure 1: Geometric modeling of the Leaning Tower of Pisa, a flagship element of the Italian cultural heritage, using a streaming progressive ..."
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Figure 1: Geometric modeling of the Leaning Tower of Pisa, a flagship element of the Italian cultural heritage, using a streaming progressive
In this work a highlevel animation methodology oriented towards building, simulating
, 1998
"... Webbased approach for very complex animations through geometric programming ..."
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Webbased approach for very complex animations through geometric programming