ISSN 2079-3537      

Scientific Visualization
Issue Year: 2016
Quarter: 1
Volume: 8
Number: 1
Pages: 58 - 94
Authors: D. Manakov (Russian Federation), V. Averbukh (Russian Federation)
Address: D. Manakov
Institute for Mathematics and Mechanics named by N.N. Krasovskii, Urals Branch of Russian Academy of Science, Ekaterinburg, Russian Federation

V. Averbukh
Institute for Mathematics and Mechanics named by N.N. Krasovskii, Urals Branch of Russian Academy of Science, Ekaterinburg, Russian Federation
Urals Federal University, Ekaterinburg, Russian Federation
Abstract: The paper is devoted the problems of verification of computer visualization based on formal or formalized approaches. Verification of visualization means existence of formal model. This model differs from similar models for poorly formalizable phenomena (for example, formal verification of the software) generally speaking only in application environment. Possible approaches to models of visualization are reported in the article. The analysis of existing solution is made. Also some conceptions were added. In particular the semiotical definition of visualization metaphor was widened. In this paper a visualization metaphor is considered as continuous mapping from source into target domains. In this case the continuity property is added to the standard (Lakoffs) definition of the metaphor. (Denotational semantics is the similar and most well-known approach in the field of Computer Science.) The topological definition of continuity based on the construct of closure with such defining properties as monotonicity and the existence of supremum is constructive. The uses multiple (binary) views are detailed for such domains of Computer Visualization as Scientific Visualization, Information Visualization and Software Visualization. Some computable models for evaluating the effectiveness in the field of Software Visualization for parallel computing are proposed. The first model involves the concept of temporal fuzzy number. The second model is a development of the idea of parallel coordinates is in the direction of the Theory of Possibility. Finally, we propose a model based on the consideration of the convergence rate of the two solutions. In fact this is the optimization problem.
The formalization of visualization and data parallel filtration are considered in details. This formalization bases on linguistic or semiotic approaches.
Some unsolved problems are concerned, for example:
* Construction of a hierarchy of models.
It is challenging that the models, their terminology and the corresponding concepts of programming languages are to a high degree of synonymousness. The formation of the mental space of visualization is one of the key tasks of this work.
* Scalability of views.
Supercomputing involves the processing of Big Data, and therefore the models for limiting cases are required.
* The challenge of integration, when verification is not enough for one view or one model or one group of researchers.
Possible solutions to this problem are connected with such approaches as topological products, construction of grill grids, rough sets.
Language: Russian

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