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39
A Procedural Approach to Authoring Solid Models
, 2002
"... We present a procedural approach to authoring layered, solid models. Using a simple scripting language, we define the internal structure of a volume from one or more input meshes. Sculpting and simulation operators are applied within the context of the language to shape and modify the model. Our fra ..."
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Cited by 39 (2 self)
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We present a procedural approach to authoring layered, solid models. Using a simple scripting language, we define the internal structure of a volume from one or more input meshes. Sculpting and simulation operators are applied within the context of the language to shape and modify the model. Our framework treats simulation as a modeling operator rather than simply as a tool for animation, thereby suggesting a new paradigm for modeling as well as a new level of abstraction for interacting with simulation environments.
Dual/Primal Mesh Optimization for Polygonized Implicit Surfaces
, 2002
"... A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a be ..."
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Cited by 34 (4 self)
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A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard marching cubes mesh [11] (in our experiments we use VTK marching cubes [16]). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that "double dual" mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvatureweighted vertex resampling. The proposed method outperforms approaches based on the mesh evoPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.
Dynamic Meshes for Accurate Polygonization of Implicit Surfaces With Sharp Features
 PROCS. OF SHAPE MODELING AND APPLICATIONS ’01
, 2001
"... The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals. ..."
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Cited by 26 (2 self)
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The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals.
Constructive Hypervolume Modelling
, 2001
"... This paper deals with modelling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real object or process under consideration. An attribute is a mathematical model of a real object or process property of an arbitrary nature (material, pho ..."
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Cited by 21 (11 self)
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This paper deals with modelling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real object or process under consideration. An attribute is a mathematical model of a real object or process property of an arbitrary nature (material, photometric, physical, statistical, etc.) defined for any point of the point set. We provide a survey of different modelling techniques related to point sets with attributes. This survey spans such different areas as solid modelling, heterogeneous objects modelling, scalar fields or "implicit surface" modelling, and volume graphics. Then, on the basis of this survey we formulate requirements to a general model of hypervolumes (multidimensional point sets with multiple attributes). A general hypervolume model and its components such as objects, operations, and relations are introduced and discussed. A function representation (FRep) is used as the basic model for the point set geometry and attributes represented independently using realvalued scalar functions of several variables. Each function defining the geometry or an attribute is evaluated at the given point by a procedure traversing a constructive tree structure with primitives in the leaves and operations in the nodes of the tree. This reflects the constructive nature of the symmetric approach to modelling geometry and associated attributes in multidimensional space. To demonstrate a particular application of the proposed general model, we consider in detail the problem of texturing, introduce a model of constructive hypervolume texture, and discuss its implementation. The wellknown concept of solid texturing is extended in two directions: constructive modelling of space partitions for texturing and modelling of mul...
Cellularfunctional Modeling of Heterogeneous Objects
 Proceedings of the seventh ACM Symposium on Solid Modeling and Applications
, 2002
"... The paper presents an approach to modeling heterogeneous objects as multidimensional point sets with multiple attributes (hypervolumes). A theoretical framework is based on a hybrid model of hypervolumes combining a cellular representation and a constructive representation using realvalued function ..."
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Cited by 10 (3 self)
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The paper presents an approach to modeling heterogeneous objects as multidimensional point sets with multiple attributes (hypervolumes). A theoretical framework is based on a hybrid model of hypervolumes combining a cellular representation and a constructive representation using realvalued functions. This model allows for independent but unifying representation of geometry and attributes, and makes it possible to represent dimensionally nonhomogeneous entities and their cellular decompositions. Hypervolume model components such as objects, operations and relations are introduced and outlined. The framework's inherent multidimensionality allowing, in particular, to deal naturally with time dependence promises to model complex dynamic objects composed of different materials with constructive building of their geometry and attributes. Attributes given at each point can represent properties of arbitrary nature (material, photometric, physical, statistical, etc.). To demonstrate a particular application of the proposed framework, we present an example of multimaterial modeling  a multilayer geological structure with cavities and wells. Another example illustrating the treatment of attributes other than material distributions is concerned with timedependent adaptive mesh generation where function representation is used to describe object geometry and density of elements in the cellular model of the mesh. The examples have been implemented by using a specialized modeling language and software tools being developed by the authors.
Dynamic Mesh Optimization for Polygonized Implicit Surfaces with Sharp Features
 The Visual Computer
, 2002
"... The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals. Given an initial polygonization of an implicit s ..."
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Cited by 10 (0 self)
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The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals. Given an initial polygonization of an implicit surface, a mesh evolution process initialized by the polygonization is used. The evolving mesh converges to a limit mesh which delivers a high quality approximation of the implicit surface. For analyzing how close the evolving mesh approaches the implicit surface we use two error metrics. The metrics measure deviations of the mesh vertices from the implicit surface and deviations of mesh normals from the normals of the implicit surface. 1
SpaceTime and Higher Dimensional Modeling for Animation
, 2000
"... There are limitations to the current BRep based "model then animate" paradigm when animating timedependent (dynamic) objects. This paper describes an approach to modeling dynamic objects directly in spacetime or even higher dimensional space. The use of the function representation (FRep) ..."
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Cited by 8 (3 self)
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There are limitations to the current BRep based "model then animate" paradigm when animating timedependent (dynamic) objects. This paper describes an approach to modeling dynamic objects directly in spacetime or even higher dimensional space. The use of the function representation (FRep) is proposed due to the ease with which it handles higher dimensions. After creating a multidimensional FRep object, it then needs to be mapped to "multimedia" space. In the case of animation this means at least one geometric coordinate must be mapped to a dynamic coordinate (time). A case study is presented to explain the technique and demonstrate its use in the animated metamorphosis between several shapes of differing topology.
Blobtree trees
 In CGI ’04: Proceedings of the Computer Graphics International
, 2004
"... In recent years several methods for modelling botanical trees have been proposed. The geometry and topology of tree skeletons can be well described by Lsystems, however there are several approaches to modelling smooth surfaces to represent branches, and not all of the observed phenomena can be repr ..."
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Cited by 7 (1 self)
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In recent years several methods for modelling botanical trees have been proposed. The geometry and topology of tree skeletons can be well described by Lsystems, however there are several approaches to modelling smooth surfaces to represent branches, and not all of the observed phenomena can be represented by current methods. Many tree types exhibit nonsmooth features such as branch bark ridges and collars. In this paper we present a botanical tree modelling approach that uses a hierarchical implicit modelling system. The BlobTree provides several techniques to control the combination of primitives, and allows both smooth and nonsmooth effects to be combined in a single blend volume in an easily controlled fashion. We use the BlobTree to produce models of botanical tree branching structures that capture smooth branching, branch collars and branch bark ridges in a single model. The BlobTree is used as a procedural surface modelling system, taking input from Lsystem botanical tree descriptions. We show that smooth, C1 continuous blends can be obtained without noticable bulging, using summation blending. We implement irregular effects using Precise Contact Modelling, Constructive Solid Geometry and space warping. Key words: implicit surfaces, BlobTree.
Implicit visualization and inverse modeling of growing trees
 Computer Graphics Forum (Proceedings of Eurographics 2004
, 2004
"... A method is proposed for photorealistic modeling and visualization of a growing tree. Recent visualization methods have focused on producing smoothly blending branching structures, however, these methods fail to account for the inclusion of nonsmooth features such as branch bark ridges and bud sca ..."
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Cited by 7 (0 self)
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A method is proposed for photorealistic modeling and visualization of a growing tree. Recent visualization methods have focused on producing smoothly blending branching structures, however, these methods fail to account for the inclusion of nonsmooth features such as branch bark ridges and bud scale scars. These features constitute an important visual aspect of a living tree, and are also observed to vary over time. The proposed method incorporates these features by using an hierarchical implicit modeling system, which provides a variety of tools for combining surface components in both smooth and non smooth configurations. A procedural interface to this system supports the use of inverse modeling, which is a globaltolocal methodology, where the local properties of plant organs are described in terms of their global position within the tree architecture. Inverse modeling is used to define both the tree structure at any time, and a continuous developmental sequence for the tree from a seedling. These techniques provide an intuitive paradigm for the definition of complex tree growth sequences and their subsequent visualization, based solely on observed phenomena. Thus, a key advantage is that they do not require any knowledge of, or simulation of, the underlying biological processes.
Functionbased shape modeling: mathematical framework and specialized language
 Automated Deduction in Geometry, Lecture Notes in Artificial Intelligence 2930
, 2004
"... In this survey, we describe the following different aspects of modeling multidimensional point sets (shapes) using realvalued functions of several variables: algebraic system as a formal framework; representation of shapes, operations, and relations using realvalued functions, internal representa ..."
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Cited by 6 (1 self)
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In this survey, we describe the following different aspects of modeling multidimensional point sets (shapes) using realvalued functions of several variables: algebraic system as a formal framework; representation of shapes, operations, and relations using realvalued functions, internal representation of the modeling system; specialized language for functionbased modeling, and model extension to point sets with attributes (hypervolumes).