Modelling function-based mixed-dimensional objects with attributes

Benjamin Schmitt, Alexander Pasko, Valery Adzhiev, Galina Pasko, Christophe Schlick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The implicit complex model allows for the representation of heterogeneous objects as multidimensional point sets with multiple attributes, where elements of different dimensions and with attributes of different nature are combined together in a topological structure. In this chapter, we present in detail the underlying function-based model for a certain class of cells to be used among several others in the implicit complex model. Each cell is dimensionally homogeneous and defined by a real vector-function. We provide a brief survey of different modelling techniques related to point sets with attributes. It spans such different areas as solid modelling, scalar fields, volume models, and material modelling. Then, on the basis of this survey we formulate requirements to a more general model. In the presented generalizing constructive hypervolume model, point set geometry and attributes are represented independently using real-valued scalar functions with their underlying tree data structures. While 3D and higher dimensional entities have been widely studied, we present function-based definitions of lower dimensional entities, such as surface patches and curve segments, with a corresponding trimming technique. A high level language supporting modelling function-based cells and attributes is described and illustrative examples are provided.

Original languageEnglish
Title of host publicationHeterogeneous Objects Modelling and Applications - Collection of Papers on Foundations and Practice
EditorsAlexander Pasko, Peter Comninos, Valery Adzhiev
Number of pages28
Publication statusPublished - 2008
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4889 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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