# Constructive hypervolume modeling

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG3-46X2K28-3&_user=1682380&_coverDate=11/30/2001&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000011378&_version=1&_urlVersion=0&_userid=1682380&md5=caa3c0056e65d0e3424fd11223a29935

Journal: Graphical Models

Volume: 63

Issue: 6

Pages: 413-442

Publisher: Elsevier

ISSN: 1530-9827

DOI: 10.1006/gmod.2001.0560

This paper deals with modeling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real/abstract object or process under consideration. An attribute is a mathematical model of an object property of arbitrary nature (material, photometric, physical, statistical, etc.) defined at any point of the point set. We provide a brief survey of different modeling techniques related to point sets with attributes. It spans such different areas as solid modeling, heterogeneous objects modeling, scalar fields or “implicit surface” modeling 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 real-valued 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 modeling 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 then discuss its implementation, as well as the special modeling language we used for modeling hypervolume objects.

This data was imported from DBLP:

Journal: Graphical Models

Volume: 63

Pages: 413-442

This data was imported from Scopus:

Journal: Graphical Models

Volume: 63

Issue: 6

Pages: 413-442

ISSN: 1524-0703

DOI: 10.1006/gmod.2001.0560

This paper deals with modeling point sets with attributes. A point set in a geometric space of an arbitrary dimension is a geometric model of a real/abstract object or process under consideration. An attribute is a mathematical model of an object property of arbitrary nature (material, photometric, physical, statistical, etc.) defined at any point of the point set. We provide a brief survey of different modeling techniques related to point sets with attributes. It spans such different areas as solid modeling, heterogeneous objects modeling, scalar fields or "implicit surface" modeling 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 real-valued 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 modeling 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 then discuss its implementation, as well as the special modeling language we used for modeling hypervolume objects. © 2001 Elsevier Science (USA).

This data was imported from Web of Science (Lite):

Journal: GRAPHICAL MODELS

Volume: 63

Issue: 6

Pages: 413-442

ISSN: 1524-0703

DOI: 10.1006/gmod.2001.0560

The data on this page was last updated at 05:14 on July 22, 2019.