Constructive Hypervolume Modeling

Pasko, Alexander; Adzhiev, Valery; Sliwa, Benjamin; Schlick, Christophe

doi:10.1006/gmod.2001.0560

Cited by 77 publications

(55 citation statements)

References 48 publications

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“…Existing heterogeneous material representation methods mainly include voxel based model, B-rep based model, explicit functional representation based model, compound model, etc [1][2][3]. The voxel based model method is adapted to model the interface functional graded material.…”

Section: Hierarchical Modeling Methods For the Cladding Partmentioning

confidence: 99%

A Hierarchical Modeling Method for the Cladding Part

Yang¹,

Xiao-qian²,

Zhang³

et al. 2012

Proceedings of the 2nd International Conference on Electronic and Mechanical Engineering and Information Technology (2012)

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Section: Hierarchical Modeling Methods For the Cladding Partmentioning

confidence: 99%

A Hierarchical Modeling Method for the Cladding Part

Yang¹,

Xiao-qian²,

Zhang³

et al. 2012

Proceedings of the 2nd International Conference on Electronic and Mechanical Engineering and Information Technology (2012)

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“…Modeling of multidimensional point sets with multiple attributes (hypervolumes) is discussed in [24,25]. The proposed constructive hypervolume model is based on function representation (FRep) [26] and supports uniform constructive modeling of point set geometry and attributes using real-valued functions of several variables.…”

Section: Other Workmentioning

confidence: 99%

“…On the basis of the survey presented in [24], we can formulate the requirements for a general model of hypervolumes that are multidimensional point sets with multiple attributes: · Independent representation of geometry and attributes; in particular, this means that geometry and attributes can be defined in different domains of an entire point set. Accordingly, we treat an attribute not just as a property of a geometric object but rather a property of a space the attribute is associated with, and a geometric object can or cannot possess (that is to say be susceptible to) a certain attribute; · Coverage of time-dependent and other multidimensional models; · Constructive modeling of both point set geometry and attributes using primitives, operations, and relations; · The ability to model geometry and attributes using realvalued functions (scalar fields).…”

Section: Cellular-functional Hypervolume Modelmentioning

confidence: 99%

“…Multidimensional point sets with a fixed dimensionality and with multiple attributes can be quite effectively modeled by the constructive hypervolume model based on real-valued vectorfunctions as it was recently proposed in [24,25]. The requirement of dimensional heterogeneity naturally brings the idea of adding a kind of cellular representation to the model.…”

Section: Introductionmentioning

confidence: 99%

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Cellular-functional modeling of heterogeneous objects

Adzhiev

Kartasheva

Kunii

et al. 2002

Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications

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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 real-valued functions. This model allows for independent but unifying representation of geometry and attributes, and makes it possible to represent dimensionally non-homogeneous 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 time-dependent 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.

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“…A survey of modeling techniques for point sets with attributes and details of the hypervolume model with the outline of the formal framework can be found in [17]. Here, we use a specific implementation of the presented hypervolume model:…”

Section: Constructive Hypervolume Modelmentioning

confidence: 99%