Computer Graphics
& Geometry
COMPUTER VISUALIZATION OF SCIENTIFIC DATA AND ITS APPLICATIONS IN NANOSTRUCTURES RESEARCH
V. Pilyugin*, E. Malikova*, N. Matveeva*, V. Adzhiev**, А.Pasko**
pilyugin@cgg-journal.com, malikova@cgg-journal.com, matveeva@cgg-journal.com, vadzhiev@bournemouth.ac.uk, apasko@bournemouth.ac.uk
* Moscow
Engineering Physics Institute (
** National Centre for Computer Animation,
Contents
Key words: Computer visualization of scientific data, scientific visualization, HyperFun, function of several variables, nano-objects visualization
Computer visualization of scientific data that is well known as scientific visualization is a modern efficient method of data analysis. This method is widely used in different theoretical and experimental researches [1]. Its main idea is to set up a correspondence between the given data being analyzed and its static or dynamic graphic interpretation, that is analyzed visually, and results of such analysis are interpreted in respect to the given data. Data analyzed using scientific visualization can be of different nature. The aims of analysis can be different as well. Accordingly, the corresponding graphic interpretations can be different.
It can be said that the main aim of scientific visualization is to give an opportunity to make invisible visible. Under invisible we mean real and abstract objects and events of different scale that human eye cannot see. They are real macro structures, for example, galaxies, physical fields, as well as microstructures and nanostructures of the real world [2].
It is a long way that scientific visualization has passed from simple visualization of functional dependencies in the form of plots and contour lines to complex methods of volume visualization of physical fields and computer animation of global changes in the universe. The fields of its application span different branches of physics, medical research, geology, meteorology and other fields.
Physical properties of objects of micrometer and nanometer scale are dramatically different from properties of larger objects and their transformations happen in the femtoseconds time scale. Researches and modeling in nanoscale require visualization of atom positions and orbitals in arbitrary nanostructures. Atoms and their links are typically represented with three-dimensional primitives such as spheres and cylinders. Visualization is also used for the three-dimensional representation of density distribution of different substances (chemical visualization). Nanotechnology gives an opportunity to create different materials with new physical properties, for example, optical dispersion. Research in dynamics of electromagnetic fields requires their visualization in the form of semi-transparent color fields (volume rendering), isosurfaces or vector fields.
Visualization is
one of the basic elements of experimental tools in nanoscale sciences such as remote controlling systems for experimental facilities. For
example, any typical scanning tunneling microscope (
The Function Representation (FRep) defines a geometric object as a whole by a real function of multiple variables F(X). The FRep technique is a step to a more general modeling approach unifying the models based on voxels, implicitly defined skeleton representations, and set-theoretical methods of solid modeling [4]. Such a model was used in [5] for modeling heterogeneous objects with non-uniform distributions of materials.
Modeling on the basis of FRep can be conducted using a high-level language HyperFun [7] and supporting its software products. The language HyperFun supports all the basic concepts of FRep for constructing a single defining function for an object of complex geometry and its properties. The procedure for calculating the value of the function at a given point in space can be described using known constructions of the structured programming such as the conditional operator or the cycle operator, as well as special symbols for set-theoretic operations. The simulation of heterogeneous object properties in HyperFun is supported by a special vector of attributes. HyperFun has the following universal features appropriate for modeling and visualization:
1. the broad and easily extensible set of geometric primitives and operations;
2. the procedural generation of geometric structures of high complexity;
3. the representation of physical properties using the point attributes;
4. the visualization of isosurfaces using their piecewise linear approximation (polygonization) and raytracing.
Back in 1986, an algorithm of isosurface polygonization was proposed and implemented [8]. It is free from topological ambiguities, which are essential to the well-known algorithm of marching cubes. The trilinear interpolation inside a cubic cell and the bilinear interpolation on a cell face are used for the hyperbolic arcs detection at the cell faces and for the construction of the edges connectivity graph to resolve topological ambiguities.
Because of its advanced level of geometric modeling HyperFun can be an effective tool for scientific visualization of micro- and nanostructures. The works on the development of the software product HyperFun were linked to earlier works at the Moscow Engineering Physics Institute (MEPHI) on the software complex SAGRAPH and its application software [9]. These products are widely used in MEPHI and other organizations for scientific visualization in experimental nuclear physics, physics of superconductivity, physics of protection of nuclear and physical objects, and others.
Currently in MEPHI works are underway toward the
establishment and the implementation of a complex of software system for scientific
visualization (on the base of HyperFun, 3dsMax, Jmol and others) , which is the successor of the complex SAGRAPH. These works are
jointly undertaken by a number of departments of MEPHI and the British National
Centre for Computer Animation in the
Let us present some examples below obtained with the mentioned programs for scientific data visualization and nano-object description is a part of them. Figure 1 shows results of visualization of a function of three variables f(х1,х2,х3), defined by formula for given domain. Isosurfaces of this function are visualized. A four dimensional arithmetic space was used for solving this problem.
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f(x1,x2,x3)= 1/12x1^2+1/12x2^2+1/12x3^2 =0.5, -4<=xi<=4, 1<=i<=3 |
f(x1,x2,x3)= 1/12x1^2+1/12x2^2+1/12x3^2 =1, -4<=xi<=4, 1<=i<=3 |
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f(x1,x2,x3)= 1/12x1^2+1/12x2^2+1/12x3^2 =3, -4<=xi<=4, 1<=i<=3 |
f(x1,x2,x3)= 1/12x1^2+1/12x2^2+1/12x3^2 =3.5, -4<=xi<=4, 1<=i<=3 |
Figure.1
Visualization results of function of six variables f(х1,х2,х3,x4,x5,x6) are shown in Figures 2 and 3. For visualization there were used matrices of isusurfaces of functions of three variables (Figure 2) and animation for one of variables xi (Figure.3).
Figure.2
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Figure.3
Visualization of physical fields is illustrated in Figure 4. Here, isosurfaces of electrostatic fields of four pointed sources are shown. This isosurfaces are known in literature as «blobby objects».
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Figure.4
Visualization of a moving special object is shown in Figure 5. It is represented as sweeping or some sort of a trace made by a moving object (a solid ball moving along a straight line in this case). For solving this problem of visualization there was used four dimensional arithmetic space as well.
Figure.5
Visualization of geological data is shown on Figure 6. As an example of such data there was used multi-layered structure of different materials with cavities.
Figure.6
In Figure 7, a result of visualization of biological data of the porous structure of a human bone can be seen.
Figure. 7
Figure 8 shows a result of visualization of a fragment of a metal structure made of rectangular cells. Dimensions of cells are defined by density of this structure.
Figure. 8
Figures 9 –15 present examples of visualization of results of computer modeling of explored nanostructures. These are concerned with investigations made by physicists at MEPHI at present.
In Figure 9, a result of animation visualization of ensemble of clusters of “boat” type N192 is shown.
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Figure. 9
Visualization of the process of destruction of this cluster is shown in Figure 10.
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Figure.10
Figure 11 demonstrates visualization of another nanostructure - fullerene С20. Some physical characteristics are shown as well: distance between atoms, angle between bonds and so on.
(you need to download Java for preview) |
Figure.11
Visualization of processes of successful and unsuccessful union of two fullerenes in one dimmer is shown on Figures.12 and13 accordingly.
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Figure.12
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Figure 13
Figure 14 presents visualization of the process of destruction of fragment of the nitrogen gosh structure N511.
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Figure 14
Animated visualization of nanostructures N46 and isusurface of its electrostatic density is shown in Figure 15.
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Figure.15
We have briefly described and illustrated in this paper the early stage of our project on scientific visualization for nanostructures research. It is planned that our future works will cover broadening of existing programs for scientific visualization. This works include functional extension of existing complex of instrumental software tools components and creation of new ones, as well as creation of new application programs for scientific visualization.
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