SCIENTIFIC VISUALIZATION AS THE TOOL OF THE ANALYSIS OF MATHEMATICAL MODELING

V.M. Kryukov , D.V. Mogilenskikh, V.V. Fyodorov
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 56.

      Visualization promotes the labor productivity increase and enables the effective and fast analysis of obtained results, as well as duly detection of features during solution of complex two- and three-dimensional problems.
      The existing 3-D-visualization systems are as a rule oriented to specific applications much different from scientific visualization.
      Presentation of the created three- and two-dimensional scientific visualization systems is offered.
      There are practically no scientific visualization systems which are well oriented and adapted for specific mathematical modeling applications. At present, the transition to calculations by three-dimensional techniques is taking place resulting in huge quantity of data and conventional methods are not very effective and involve much time for analysis. Therefore, problems of development and creation of scientific visualization systems become important.
      Not only geometrical properties of models are of interest, but also three-dimensional interpretation of various physical magnitudes through isosurfaces, isolines, applying of color, shades and isolines to geometrical forms.
      Scientific visualization is the combination of systematized tools, methods, operations on geometrical and, first of all, on physical data, as well as on functions of the image, that permits to reflect the behavior and development of physical or any other processes on a monitor screen using computer graphics.
      The following issues were stated in the report:
      1. Main mathematical objects for 3-D-visualization, the data classified according to their structure and physical sense:
      — the data described by structured and unstructured three-dimensional grids;
      — the functions of two variables, set on regular, irregular, structured, unstructured grids, as well as set by lines of constant functions value or by random discrete point set;
      — three-parameter data, that is data set in each volume point;
      — data, domain of definition of which do not tear-apart to a plane;
      — three-dimensional tracks of some processes presented in the form of three-dimensional bent tube;
      — results of two-dimensional calculations, which can be presented as three-dimensional objects with the help of creation of figures of rotation about axes of symmertry or time can serve as the third dimension;
      — analytical functions.
      2. Methods and tools of scientific 3-D-visualization.
      3. Methods of three-dimensional and two-dimensional presentation of physical system evolution dynamics.
      4. Formalization of some concepts of 3-D-visualization.
      5. Principles of reception of three-dimensional objects images in the form of a framework and its application to scientific visualization.
      6. Main functions, interface of developed scientific 3-D and 2-D visualization systems.
      7. Potentials for development of similar scientific visualization systems.
      Illustrations are available.