UDC 002.53; 004.89; 621.3.068 Article submission date: 14.03.2014

COGNITIVE TECHNOLOGIES FOR VISUALIZING MULTIDIMENSIONAL DATA FOR INTELLIGENT DECISION SUPPORT

V.V. Tsaplin, Ph.D., Associate Professor, Chief Researcher(Research Institute "Tsentrprogramsistem", ave. 50 let Oktyabrya, 3a, Tver, 170024, Russia, [email protected]); V.L. Gorokhov, Doctor of Technical Sciences, Professor (St. Petersburg State University of Architecture and Civil Engineering, 2nd Krasnoarmeiskaya str., 4, St. Petersburg, 190005, Russia, [email protected]); V.V. Vitkovsky, Candidate of Physical and Mathematical Sciences, Professor (Special Astrophysical Observatory of the Russian Academy of Sciences, Nizhny Arkhyz, 1, Karachay-Cherkessia, 369167, Russia, [email protected])

The article outlines the principles of cognitive computer graphics and provides examples of its practical application for the development of decision support systems (DSS). The phenomenon of cognitive computer graphics consists in generating images on the display screen that create spectacular images in the mind of the human operator. These images have aesthetic appeal and stimulate a person's intuition. The image on the display creates in his mind a moving three-dimensional image, which is formed by the entire set of multidimensional data and visually displays the properties of the studied subject area. When perceiving these images, a person

operator is able to identify individual geometric properties the observed image and connect them with the subject content of the processed multidimensional data. It is very important to be able to combine the proposed cognitive technology with modern possibilities intelligent programming interfaces and multidimensional programs statistical analysis data. Fundamentally new algorithmic approaches to cognitive visualization based on hyperbolic geometry and algebraic varieties are proposed. AT in a certain sense we can talk about the emergence of a new type of DSS - cognitive decision support systems.

Keywords: cognitive image in multidimensional space, cognitive visualization of multidimensional statistical data, algorithms for cognitive visualization of the situation, decision support systems, emergency situations.

Received 03/14/2014

MULTIDIMENSIONAL DATA VISUALIZING COGNITIVE TECHNOLOGIES FOR DECISION-MAKING INTELLIGENT SUPPORT Tsaplin V. V., Ph.D. (Military Sciences), Associate Professor, Chief Researcher (Research Institute "Centerprogramsistem", 50 let Oktyabrya Ave. 3a, Tver, 170024, Russian Federation, [email protected]);

Gorokhov V.L., Dr.Sc. (Engineering), Professor (St. Petersburg State University of Architecture and Civil Engineering, 2nd Krasnoarmeyskaya St. 4, St. Petersburg, 190005, Russian Federation, [email protected]);

Vitkovskiy V.V., Ph.D. (Physics and Mathematics) (Special Astrophysics Observatory of the Russian Academy of Sciences, Nizhny Arkhyz 1, Karachaevo-Cherkesiya, 369167, Russian Federation, [email protected])

abstract. The article describes principles and examples of cognitive machine graphics for developing Decision Support Systems (DSS). The cognitive machine graphics phenomenon is displaying graphic representations which create spectacular images in the human operator brain. These images stimulate its descriptive impressions, closely related to the intuitive mechanisms of thinking. The cognitive effect is in the fact that man perceives the moving projection as a three-dimensional picture characterized by multidimensional data properties in the multidimensional space. After the multidimensional data visual aspects study there appears the possibility for a user to paint interesting separate objects or groups of objects by standard machine drawing. Next user can return to the image rotation procedure to check the intuitive user's ideas about the clusters and the relationship in multidimensional data. It is possible to develop the cognitive machine drawing methods in combination with other information technologies. They are the packets of digital in special sense it is possible to say that new kind of DSS - Cognitive Decision Support Systems (CDSS) appear .

Keywords: cognitive image in multidimensional space, cognitive visualization of the multidimensional statistical data, algorithms of environment cognitive visualization, decision support systems, emergency situations.

At present, the problem of operational analysis of a large volume of dynamically changing parameters of the entire complex of objects under study is becoming relevant. Such a problem arises, for example, in the military sphere in the tactical analysis of military operations, man-made disasters, strategic planning and modeling of the use of weapons systems, in the creation of a new generation of dispatching systems that reflect the situation in controlled airspace or other operational space. These problems are intensively solved within the framework of both strategic and tactical martial arts (using the entire arsenal of modern mathematics: the theory of operations research, the theory of optimal control and optimization), and the creation of automated systems of modern weapons.

When solving these and other similar problems, one has to face a number of significant difficulties associated with the huge role of the operator's intuition, which is based on the inherent ability of a person to directly perceive a combat situation or an emergency (ES). Modern conditions of hostilities and man-made disasters leave the operator alone with the terminals, where at the same time

thousands of parameters are fixed, which he is not able to quickly perceive and creatively process in his mind. The main difficulty is that a person is just an element of a complex automated control and management system that is not adapted to his creative capabilities. The methods of integrating the operator into such a system, developed earlier within the framework of ergonomics, partly made it possible to adapt it to the so-called ergotechnical systems, but the huge potential of creative and professional intuition was not fully used.

However, thanks to progress in the field of cognitive sciences, cognitive psychology, epistemology and information technology, fundamentally new opportunities have appeared for a radical solution of the above problems. This progress was especially manifested in the creation of new technologies and methods of cognitive computer graphics.

Work principles. The approach proposed by the authors makes it possible to project multidimensional data presented in the form of Grassmann manifolds onto a plane arbitrarily specified by the operator-researcher in a multidimensional configuration (phase) space.

Rice. 1. Stratification of victims Pic. 2. Stratification of sources in case of provision of regions with emergency situations by timing and regions

technical means of rescue

Fig. 2. Danger sources 1. Regions stratification stratification on date

on technical assurance means and region

Rice. 3. Stratification of state and availability technical means rescue by region

Fig. 3. Regions stratification on salvation facilities and technical condition

stve. At the same time, the selection best position the projection plane is carried out by the user himself, relying on his intuition and cognitive image before his eyes. Having the ability to actively influence the orientation of the projection plane in multidimensional space, the researcher is free from preliminary considerations about the statistical (geometric) structure of the data that objects represent. A person directly sees on the screen projections of clusters or multidimensional surfaces into which his data is formed. This spectacular image stimulates his intuitive understanding of the objects under study.

Below is a brief example of the use of the means of cognitive visualization of the situation developed by the authors, capable of solving the problem of active and controlled stimulation of the intuition and empirical experience of the operator to make adequate decisions in today's complex and rapidly changing environment. In addition, fundamentally new algorithmic approaches based on hyperbolic geometry and algebraic varieties are proposed and developed.

An example of cognitive visualization is a cognitive analysis of technospheric hazards, performed

ned within the framework of cooperation with the Ministry of Emergency Situations of Russia. The study was conducted with the participation and expertise of employees of the All-Russian Research Institute for Civil Defense and emergencies EMERCOM of Russia" (Federal Center for Science and high technology)). Information on emergencies recorded in the 1st quarter of 2012 (703 emergencies) was used as the initial data for the analysis. Emergencies that occurred at hundreds of facilities were analyzed according to the following selected parameters: month, state, scale, region, number of victims, number of deaths, personnel, equipment, source of emergencies.

Possible options cognitive images in a static position for the analysis of these emergency situations (the projection of a multidimensional cloud onto a plane specified by a pair of parameter axes) are shown in Figures 1-3.

It can be concluded that the use of visualization of multidimensional statistical data using the generation of a cognitive image as an additional tool in the analysis and forecast of emergencies made it possible to draw attention to their special classes, which could not be detected without the use of intuitive perception of cognitive images.

Rice. 4. Cognitive images in the hyperbolic visualizer 4. Cognitive images in hyperbolic visualizer

New algorithms for cognitive visualization. Offered further development cognitive visualization algorithms based on the interpretation of the k-dimensional projective space Pk into a ^-dimensional hyperbolic space in ^, followed by the transformation of the latter into a cognitive three-dimensional image. This formation of the hyperbolic geometry of multidimensional data occurs using Plücker coordinates. Such algorithms are capable of cognitively visualizing even terabyte collections of objects. A cognitive image of this type is shown in Figure 4.

The hyperbolic visualization algorithm supports an efficient mode of interaction with hierarchies much bigger size than conventional hierarchy renderers. While a normal 2D renderer in a 600x600 pixel window can display 100 nodes, a hyperbolic browser can display 1,000 nodes, of which about 50 are in focus and easy to read.

This is especially important when analyzing statistical relationships, factor analysis, target detection and recognition. The dynamic visualization procedure does not rely on incomplete and possibly false a priori information about the nature of objects, and therefore, without introducing the distorting influence of a particular model into the projections, it makes it possible to use visualized images in conditions of deep a priori uncertainty of the subject area of ​​combat operations and weapons. The authors have developed multiplatform Java versions software systems SpaceWalker and , capable of implementing technologies for cognitive visualization of the operational environment for general dispatching services.

There is one more possibility of cognitive control of the slightest changes in the state of objects. Studies have shown that even small changes in the parameters of objects significantly change their cognitive images, which allows the operator to instantly notice a change in the characteristics of objects. It should be emphasized that the use of hyperbolic geometry when creating a cognitive image makes it possible to visually represent the content of terabyte multidimensional arrays. In addition, the use of these applications of cognitive graphics will be even more effective when it is implemented in network technologies. An impressive effect can be obtained by introducing the method of operational analysis in online space monitoring systems.

operational analysis of large volumes of multidimensional data - from operations planning to monitoring and modeling of technical systems.

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DEVELOPMENT OF COGNITIVE COMPUTER GRAPHICS WITHIN THE FRAMEWORK OF APPLIED SCIENCE OF COMPUTER SCIENCE

Art. teacher of the department of ISvEC

Branch of SPbGIEU

Numerous studies by psychologists devoted to the analysis of the process of solving problems by people have shown that the first two stages are the most time-consuming in this process. A person spends maximum effort on the process of transition from a vague feeling of a certain situation to a clearly formulated task. As a rule, this stage is perceived by most researchers as creative. On what the idea of ​​the problem is formed and its formulation is sought. Further, in many cases, the matter concerns only the application of a professional.

The stages of the formulation of the problem under the conditions of using the algebraic approach remain out of the field of vision of science. This problem is clearly not algorithmic. Each task has individual character, and the existence of any general procedures, except for purely methodological ones (such as invention search algorithms, is hardly possible here). However, as eminent mathematicians who seriously thought about the procedures of mathematical creativity have repeatedly noted, at the stage of searching for the formulation of a problem, an important role was often played by geometric representations and models. And it is interesting that often they were not directly related to the nature of the problem being solved, but simply associatively evoked this formulation. The same phenomenon is noted by psychologists. Let's try to list the features that are characteristic of a new direction in computer science, called cognitive graphics. A more detailed discussion of this direction is contained in the world's first monograph dedicated specifically to cognitive graphics.

Computer graphics is a field of computer science that covers all aspects of the formation of images using a computer.

Appearing in the 1950s, at first it made it possible to display only a few dozen segments on the screen.

The basis of computer graphics steel fundamental sciences: mathematics, chemistry, physics, etc.

Computer graphics are used in almost all scientific and engineering disciplines for visual perception and transmission of information. It is also common practice to use computer simulations in the training of pilots and other professions (simulators). Knowledge of the basics of computer graphics is now necessary for both an engineer and a scientist.

The end result of the application of computer graphics is an image that can be used for various purposes.

Cognitive computer graphics- computer graphics for scientific abstractions, contributing to the birth of new scientific knowledge. The technical basis for it is powerful computers and high-performance visualization tools.

An example of the use of cognitive computer graphics in applied informatics can be cognitive visualization of algorithm flowcharts, three-dimensional representation of research objects, visual representation of data models, etc.

A similar technique was used for periodic functions. As you know, the graphs of periodic functions have repeating sections, therefore, if you shift the graph of a periodic function to notes, then the music will have repeating fragments.

Solving the problem of monitoring the implementation of national projects requires taking into account many factors. The scale and dynamism of the situation in the implementation of national projects necessitates the rapid processing of a significant amount of initial data, the development and adoption of adequate and timely decisions.

This raises the problem of perception and interpretation of heterogeneous information by the decision maker, which determines the relevance of solving the problem of finding forms of its presentation that exclude or reduce the ambiguity of understanding the current situation.

Human thinking is built in such a way that a person thinks not in words and numbers, but in images. The situation is exactly the same with the perception of information about the surrounding world: the images formed by various bodies feelings are perceived as a whole.

Studies show that the visual component of the perceived image is of the greatest importance. This implies the need for a priority solution of the problem of visualization of numerical and non-numerical (verbal, graphical) initial data and the results of their analytical processing.

Within the framework of computer science, cognitive computer graphics is developing in the following areas:

– study of the general construction of cognitive graphic images of methods, methods of cognitive computer graphics;

- study individual features perception, in particular its apperception;

– development of a decision makers information perception model;

– formation of an alphabet of a conceptual and figurative language for data representation, including stereotypical symbols that display objects and phenomena of the surrounding world with varying degrees of similarity, associatively understandable graphic primitives from which GO of any complexity are synthesized, and auxiliary symbols necessary to connect graphic primitives and attract attention to the most relevant civil defense;

- study of the properties of GO that affect the decision maker when they are perceived at the level of sensations - energy, geometric, dynamic;

- the formation of the "grammar" of the conceptual-figurative language, that is, the basic rules for the formation of GO and cognitive scenes;

– development of a prototype subsystem for visualizing the results of information and analytical support for monitoring the implementation of priority national projects based on a conceptual and figurative data presentation language;

- experimental verification of the effectiveness of the developed prototype in terms of efficiency, completeness, accuracy of information perception by the decision maker.

The main directions of applied cognitive science. Artificial intelligence: opportunities and limitations. Expert systems and decision support systems. Modeling decision-making in the economy and the problem of human rationality. The problem of natural language processing and machine translation systems. The main directions of robotics: the problems of modeling the construction of movement, orientation in space and training of mobile robots. Human-computer interaction: basic approaches and research methods. Cognitive ergonomics. Design and computer graphics. Virtual Realities.

The widespread use of hypertext technologies and the multimedia paradigm closely related to these technologies also stimulates the development of cognitive graphics. As you know, the multimedia paradigm equalizes the rights of texts and images. In a non-linear representation (in the form of a network), which is typical for hypertext technologies, the multimedia paradigm allows you to navigate the network, both at the text level and at the image level, making a transition from text to images at any time, and vice versa.

Thus, systems of the type "Text-Drawing" and "Drawing-Text" are closely related to the multimedia paradigm and cognitive graphics, and are themselves one of the results of the interaction between cognitive graphics and hypertext technology.

In research automation systems, cognitive graphics can be used as a means of visualizing ideas that have not yet received any precise expression. Another example of using these tools is a special cognitive graphics for selecting basic operations in fuzzy logics, in which the global color distribution of blue and red areas characterizes the "rigidity" of defining operations such as conjunction and disjunction.

In this area, cognitive graphics are used at the stage of formalizing problems and in the procedure for putting forward plausible hypotheses.

In the field of artificial intelligence systems, cognitive computer graphics will achieve greater results than other systems due to the algebraic and geometric approach to modeling situations and various options their decisions.

So, in scientific research, including fundamental, characteristic for initial stage the emphasis on the illustrative function of the ICG is increasingly shifting towards the use of those ICG capabilities that make it possible to activate human the ability to think in complex spatial patterns. In this regard, two functions of the ICG are beginning to be clearly distinguished: illustrative and cognitive.

The illustrative function of the ICG makes it possible to embody in a more or less adequate visual design only what is already known, i.e. already exists either in the world around us, or as an idea in the head of the researcher. The cognitive function of the ICG is to use some kind of ICG image to obtain a new, i.e., knowledge that does not yet exist even in the head of a specialist, or, according to at least, contribute to the intellectual process of obtaining this knowledge.

This basic idea of ​​differences between the illustrative and cognitive functions of the ICG fits well into the classification of knowledge and computer systems educational purpose. The illustrative functions of ICG are implemented in educational systems of a declarative type when transferring to students an articulated part of knowledge, presented in the form of pre-prepared information with graphic, animation, audio and video illustrations. The cognitive function of the ICG manifests itself in procedural-type systems, when students "obtain" knowledge through research on mathematical models objects and processes being studied, and, since this process of knowledge formation is based on the right hemispheric mechanism of thinking, this knowledge itself is largely personal in nature. Each person forms the techniques of the subconscious mental activity in my own way. Modern psychological science does not have strictly substantiated methods for the formation of a person's creative potential, even if it is a professional one. One of the well-known heuristic approaches to the development of intuitive professionally oriented thinking is the solution of research problems. The use of educational computer systems of a procedural type makes it possible to significantly intensify this process, eliminating routine operations from it, and making it possible to conduct various experiments on mathematical models.

The role of the ICG in these academic research hard to overestimate. It is the ICG images of the course and results of experiments on mathematical models that allow each student to form his own image of the object or phenomenon being studied in all its integrity and variety of connections. There is also no doubt that ICG images perform, first of all, a cognitive, and not an illustrative function, since in the process of educational work with computer systems of a procedural type, students form purely personal, i.e., components that do not exist in this form for anyone. knowledge.

Of course, the differences between the illustrative and cognitive functions of computer graphics are rather arbitrary. Quite often, an ordinary graphic illustration can prompt some students to a new idea, allow them to see some elements of knowledge that were not "invested" by the teacher-developer of the declarative educational computer system. Thus, the illustrative function of the ICG image turns into a cognitive function. On the other hand, the cognitive function of the ICG image during the first experiments with educational systems of the procedural type in further experiments turns into an illustrative function for the already "discovered" and, therefore, no longer a new property of the object under study.

Nevertheless, fundamental differences in the logical and intuitive mechanisms of human thinking, arising from these differences in the form of knowledge representation and methods of their development, make it useful methodologically to distinguish between the illustrative and cognitive functions of computer graphics and allow more clearly formulating the didactic tasks of ICG images in the development computer systems for educational purposes.

List of sources used

1. Zenkin A. A. Cognitive computer graphics. - M.: Nauka, 1991. - 192 p.

Scene Analysis

Image processing and analysis

Pictorial computer graphics

Directions of computer graphics

In the current, well-established state, it is customary to divide computer graphics into the following areas:

• visual computer graphics,
• image processing and analysis,
• scene analysis (perceptual computer graphics),
• computer graphics for scientific abstractions (cognitive computer graphics - graphics that contribute to cognition).

Objects: synthesized images.

• building an object model and generating an image,
• model and image transformation,
• identification of the object and obtaining the required information.

Objects: Discrete, numerical representation of photographs.

• improving image quality,
• image evaluation - determination of the shape, location, size and other parameters of the required objects,
• image recognition - selection and classification of object properties (processing of aerospace images, input of drawings, navigation, detection and guidance systems).

So, image processing and analysis are based on image representation, processing and analysis methods, plus, of course, visual computer graphics, at least to present the results.

Subject: research of abstract models of graphic objects and relationships between them. Objects can be either synthesized or highlighted in photographs.

The first step in scene analysis is to isolate the features that form the graphical object(s).

Examples: machine vision (robots), analysis of X-ray images with isolation and tracking of an object of interest, such as a heart.

So, scene analysis (perceptual computer graphics) is based on visual graphics + image analysis + specialized tools.

Only a emerging new direction, not yet clearly defined.

This is computer graphics for scientific abstractions, contributing to the birth of new scientific knowledge. Base - powerful computers and high-performance visualization tools.

The general sequence of cognition consists in, possibly cyclic, progress from a hypothesis to a model (object, phenomenon) and a decision, the result of which is knowledge. The model of the general sequence of knowledge is presented in Figure 2.1.

Figure 2.1 - The sequence of the process of cognition

Human cognition uses two main mechanisms of thought, each of which is assigned to half of the brain:

• conscious, logical-verbal, manipulates abstract sequences of symbols (objects) + semantics of symbols + pragmatic representations associated with symbols. The age of this mechanism associated with the presence of speech is up to 100 thousand years:
• unconscious, intuitive, figurative, works with sensual images and ideas about them. The age of this mechanism is the time of existence of the animal world on Earth.

Initially, computers had a low performance of processors and computer graphics tools, i.e. in fact, they had the opportunity to work only with symbols (some simplified analogue of logical thinking).

With the advent of super-computers with a capacity of a billion or more operations per second and graphic super-stations with a capacity of up to hundreds of millions of operations per second, it became possible to manipulate images (pictures) quite effectively.

It is important to note that the brain not only knows how to work with two ways of presenting information, and it works with images differently and more efficiently than a computer, but also knows how to correlate these two ways and make (in some way) transitions from one representation to another.

In this context, the main problem and task of cognitive computer graphics is the creation of such knowledge representation models in which one could uniformly represent both objects characteristic of logical (symbolic, algebraic) thinking and objects characteristic of figurative thinking.

Other critical tasks:

• visualization of those knowledge for which there are no (yet?) symbolic descriptions,
• search for ways to move from the image to the formulation of a hypothesis about the mechanisms and processes represented by these (dynamic) images on the display screen.

The emergence of cognitive computer graphics is a signal of the transition from the era of extensive development of natural intelligence to the era of intensive development, characterized by deeply penetrating computerization, giving rise to human-machine technology of cognition, an important point of which is a direct, purposeful, activating effect on the subconscious intuitive mechanisms of figurative thinking.

One of the brightest and earliest examples of the application of cognitive computer graphics is the work of C. Strauss "Unexpected use of computers in pure mathematics" (TIEER, vol. 62, N 4, 1974, pp. 96 - 99). It shows how an "n-dimensional" board based on a graphic terminal is used to analyze complex algebraic curves. Using input devices, a mathematician can easily obtain geometric images of the results of a directed change in the parameters of the dependence under study. He can also easily manage the current values ​​of the parameters, "thereby deepening his understanding of the role of variations in these parameters." As a result, "several new theorems were obtained and directions for further research were identified."

Already today we can state with all certainty that a fundamentally new human-machine reality is being born before our eyes, creating the preconditions for an intensive technology of cognition. We are talking about new directions in the field of human-machine interaction and artificial intelligence - systems of cognitive graphics and virtual reality.

Psychologists have proven that it is unlawful to associate a person's mental abilities only with the highest verbal-logical level of mental reflection of reality. This reflection also includes the sensory-perceptual and figurative levels and the abilities corresponding to them, which are manifested in the processes of sensation, perception, figurative memory and imagination, so there is a need to create means for the development of such abilities. To date, the level of development of computing facilities is so high that it has made it possible to start developing tools for building systems that work not only at the symbolic-logical, but also at the sensory-perceptual and figurative levels. And the leading role here belongs to the indicated two new directions in the development of modern computational science.

The term cognitive graphics was first considered by the Russian scientist A.A. Zenkin in his work on the study of the properties different concepts from number theory. Using visual images of abstract numerical concepts, he obtained results that were previously impossible to obtain. The direction of work on cognitive graphics is rapidly developing, and now there are many similar systems in various subject areas: in medicine, to support decision-making on the management of complex technological systems, in systems based on natural language.

Two functions of cognitive graphics systems should be noted: illustrative and cognitive. If the first function provides purely illustrative possibilities, such as the construction of diagrams, histograms, graphs, plans and diagrams, various pictures reflecting functional dependencies, then the second allows a person to actively use his inherent ability to think in complex spatial images.

The term "virtual reality" was coined by former computer hacker Jaron Lenier, who founded the HP Research Corp. in 1984. in Foster, California. This is the first company to create VR systems. Since the beginning of the 90s, conferences have been held on virtual reality simulation tools and the construction of systems that allow a person to act in an environment that may be qualitatively different from the conditions of the reality in which he lives.

There are two properties that make it possible to distinguish a program that creates a "virtual world" (VR system) from traditional computer graphics systems.

1. In addition to the simple transmission of visual information, these programs simultaneously affect several other senses, including hearing and even touch.

2. VR systems interact with a person, and in the most advanced of them, the user, for example, can touch an object that exists only in the computer’s memory by putting on a glove stuffed with sensors. In a number of systems, you can use a joystick or mouse - then you can do something with the object shown on the screen (say, turn it over, move it, or look at it from the back).

The development of systems based on the virtual reality model forces us to solve a number of problems that are typical for multimedia technologies and cognitive graphics technologies. This paper considers the problems associated with the development of graphical tools for generating figurative representations of dynamic scenes representing various realities, including imaginary ones.

Consider the problem of building a virtual reality system for learning based on the "imaginary world" paradigm physical laws statics, kinematics and dynamics. We will consider the following dynamic world: a three-dimensional closed space, a set of objects in it, an actor in this space (he is also a learner, let's call him an Actor). The task of the actor is to understand the laws inherent in the world in which he is and acts, performing some physical actions with objects in time and space.

Let's highlight the main types of concepts that the Actor will encounter. These are objects, relationships, movements and physical actions. Let us set the task of constructing an imaginary world that reflects these categories; at the same time, the states of such an imaginary reality will be described in the form of texts in ordinary natural language. An important module of such a VR system is a subsystem that builds a dynamically changing graphic image from the text. To solve this problem, the TEKRIS system developed by the authors is used. Below we consider a general description of the TEKRIS system and graphical tools for building such systems.

Structural diagram of the TEKRIS system

The TEKRIS system is a set of software tools that allow building a dynamically changing graphic image of the described situation using natural language text. As restrictions imposed on the initial description, the following should be noted: 1) the description of the initial static scene must be present in the text; 2) all subsequent changes in the scene are the result of actions performed by some subject (human, robot). A typical example Such a description could be as follows:

There is a table in the room. There is a lamp on the table. There is a chair next to the table. Behind the table, not far to the left, is a bookcase. To the right of the chair is a sofa. Ivan is standing next to the closet. Ivan went to the table. I took the lamp. I put it on the closet.

The block diagram of the system is shown in Figure 1. In this diagram, the software components are presented in the form of rectangles, and the source and intermediate files are in the form of ovals.

The description of the dynamic situation in natural language is fed to the input of the linguistic processor. Using the dictionary of the subject world, it converts the text into an internal frame representation, which is then fed to the solver and scheduler.

The solver, using a block of qualitative physical reasoning and a logical block, builds a description of the trajectory of the development of the situation in the form of a temporal sequence of scenes that reflects the dynamics of the development of the situation given by the text.

The scheduler builds a graphic image of each scene from a given sequence, calculating for this purpose the dimensions and coordinates of all the objects that make up the scene, and also forms the trajectories of movement of objects necessary for displaying and passes all this to the input of the visualizer.

The visualizer sequentially with some delay reproduces the generated images on the display screen. For example, for the above text description, the initial scene shown in Figure 2 will be generated.

Just as the linguistic processor is linked to the subject area through a dictionary of terms, so the visualizer is linked to the same area through the base of graphic objects.

The database of graphic objects is a set of three-dimensional descriptions of objects and subjects that can be found in the analyzed scenes. To create a base for a particular application, an additional program called the graphic object librarian is used.

Rice. 2. Initial scene Graphic object base

The database of graphical objects consists of a set of descriptions of objects and subjects associated with the subject area under consideration. Each database object consists of a name (or type) unique for this database (for example, "chair", "table", "sofa", etc.), and a description of the composition and relative position of the components that make it up.

The basic element from which all graphic objects are built is a rectangular parallelepiped (see Fig. 3). To construct complex objects, other previously defined objects can also be used as components. For example, to build such a complex object as "Ivan", you can first define the following simpler objects: "head", "hand", "leg", and then build "Ivan" from the already existing "bricks".

Figure 3 shows the "table" object, which consists of five basic elements. For each object, a rectangular parallelepiped is defined in which it can be inscribed (indicated by a dotted line in the figure), and the base angle in which the origin of the object is located.

In addition, for each object, a set of colors is defined, with which its component parts are painted when displayed on a computer screen:

number of colors

To specify one color, three triples of numbers are indicated, where the fill type determines the order in which the primary colors are mixed:
fill type i

fill type2

fill type

When rendering, four types of shading are used with a solid primary or combined color, as shown in Figure 4.

Three sets of numbers allow you to set three different shades of color for coloring various

component l

Each component of an object is determined by its position (coordinates relative to the base angle), dimensions and color of the faces.

A component that is a basic element is described as follows:

2) base angle coordinates in the system

object coordinates;

3) angles of rotation around the axes of the system

coordinates of the object until it coincides with the coordinate axes of the element;

4) element dimensions (dx, dy, dz);

5) color number.

A component, which in turn is an object, is defined as follows: 1) type(=1);

2) object name;

3) base angle coordinates;

4) angles of rotation;

5) dimensions;

6) color number.

When an object is rendered, all its components are ordered depending on the distance to the projection area (display screen). The farthest components are drawn first, then the closest ones, which allows you to close the invisible parts of the farthest components from the observer.

The faces of the cuboid are also arranged in order of approach to the projection area. For each face vertex, 3D coordinates are translated from the scene coordinate system into 2D coordinates of the display screen using the formulas shown below (see Fig. 5). Then the direction of the normal vector is determined and the appropriate type of face shading is selected, after which a quadrilateral corresponding to the face is drawn on the display screen. Since the elements closest to the observer are displayed last, they will cover the invisible edges.

Rice. 5. Projection of the object onto the visualization plane

The coordinates of a point belonging to an element in the object coordinate system (x, y, z) are calculated using the following formulas:

where (x\ y", z1) are the coordinates of the point in the element system;

(xq, уо", zq) - coordinates of the base angle, tij - direction cosines, i.e. cos of the angle between the axes / and j of the object system.

The following formula is used to calculate direction cosines:

sina-sinp-cozy+cosa-sinp-cosa-sinp-cosy+sina-sinp

Sina-sinp-siny+cosa-cosy cosa-sinp-siny+sina-cosy

Sina cosp cosa cosp

The matrix M specifies a sequential rotation around the x-axis on oc, y on p, z on y. The coordinates of the projection of a point onto the screen area are calculated in a similar way.

Graphics Librarian

The graphic object librarian is a program designed to create a set of objects and subjects that can be found in the analyzed texts. This program allows you to create a new database of objects, load an existing database, save the database to a file, add a new object to the database, modify and delete an object.

Rice. 6. Working screen of the librarian of graphic objects

parts, as well as the values ​​of the parameters of the current (edited) component.

The rest of the space on the screen is occupied by three orthogonal projections of the object and its isometric projection, and it is possible to change the point of view on the object by setting the angles of rotation around the coordinate axes.

The main menu of the program contains the following items:

Base - creating a new database of objects, saving and loading the old database.

Kind - change isometric view(object rotation).

Objects - displaying a list of all objects in the database, with the ability to navigate to the selected object.

Component - setting the parameter values ​​for the object component (position, dimensions, color).

Colors - setting a set of colors for the object.

Room - building and viewing a room from existing objects (not implemented in the version under consideration).

Exit - Exit the program.

The buttons below the main menu perform the following functions:

The working screen of the program is shown in fig. 6. At the top of the screen is the main menu, at the bottom - a set of primary colors (16 colors) and four types of shading. In the upper left (after the menu) corner of the screen there are five buttons for creating and editing an object. Directly below them is the name of the object, a list of its composition

Add a new base or compound component to an object

Change the size (dimensions) of a component

Change component location

Rotate Component

Delete component

When a new object is created, a cuboid is created with default dimensions. The dimensions of the object's components are set as integers in the range from 1 to 400, so when creating the object base, you need to determine the scale in such a way that the displayed (not real) dimensions of the object fall into this interval.

To resize a component, click the "Size" button. After that, the program will switch to the mode of changing the dimensions, which is done by moving the lower right corner of the rectangle corresponding to the component in one of the three orthogonal projections. Moving is done with the help of the "mouse" manipulator with the left button pressed.

The component is moved in the same way when the "Move" button is pressed. To rotate the component, click the "Turn" button. Adding a new component is carried out by pressing the "New" button. When performing any operation with a component, the dimensions of the object and the coordinates of all its components are automatically recalculated.

If necessary, using the "Del" button, the component of the object can be deleted, which also leads to the recalculation of coordinates and dimensions. In addition to position and size, each component of an object defines three shades of color for its faces. The choice of one or another shade depends on the position of the plane of the face (its normal) in space. If the component, in turn, is an object, then the colors of the sub-object are inherited with the possibility of replacing them with the colors of the edited object.

To set colors for an object or define a color for a component, select "Colors" from the main menu. A window will appear on the display screen (Fig. 7).

In the left part of this window there is a list of colors for the object, in the right part there is a shading pattern for three possible cases, in the bottom part there are four buttons.

To set the shading, you must select a face (A, B or C) and from the bottom of the screen the type of shading, the main (left mouse button) and additional (right button) colors. When you click the "Save" button, the selected color is assigned to the component. The "Add" and "Remove" buttons allow you to add and remove elements of the color list.

If there is no "mouse" manipulator, you can use the "Component" main menu item to set component parameter values. In this case, the window shown in Figure 8 will appear on the screen. In the upper part of this window, the name of the component is specified (in the figure "left handle" of the chair), which can be changed if necessary.

In the left half of the window, the values ​​of the component parameters are set, in the right - a set of buttons for sorting through the components, adding and deleting, setting the color and saving or refusing to save changes.

With this window, using only the keys, you can fully describe the object. To set the parameter value, go to the required line using the cursor keys ("Up", "Down") and print a new value. Note that in Figure 8 the dimensions are shown in gray, i.e. are inaccessible to change, since the arm of the chair, in turn, is an object and inherits its dimensions.

When you finish editing one object, you can move on to creating or editing another. Before exiting the program, the database of objects should be saved to a file for further use in the program for visualizing three-dimensional scenes.

Visualization of 3D scenes

The visualizer program can work in two modes. The main mode is when the scheduler builds the current 3D scene and passes it to the renderer for rendering. In another mode of operation, the scheduler generates a sequence of scenes for the analyzed text and writes it to a file, which is later used by the visualizer. In this case, the renderer acts as a demonstrator of the generated sequences.

Two files are fed to the program input - the base of graphic objects and the sequence of scenes - in the following form:

One scene is separated from another with a special PAUSE command (pause between scenes).

Each scene is described as a sequence of commands:

Team 1

Team t

Commands are divided into object description commands and control commands. The description command contains the following fields:

The unique name of the object used

in later scenes;

Object type (name in the database);

Coordinates of the left rear lower

angle in the room coordinate system;

Rotation angles around the coordinate axes

Size modifier (L - large, M -

medium, S - small);

Color (from 0 to 8). If color=0, then object

displayed in the color used in the database. Otherwise: 1 - black, 2 - blue 8 - white.

Among the set of objects describing the initial scene, there must be an object of the "scene" (room) type. This object is built-in (not present in the base of graphical objects). It sets the dimensions of the room, as well as the position of the observer. By setting new angles of rotation each time, you can change the position of the observer to view previously unseen objects. For example, Figure 9 shows the second scene of the text discussed at the beginning of the article from a different angle.

Rice. 9. Second scene from a different angle

The following control commands are used to create a sequence of scenes:

PAUSE - pause between scenes;

MOVE - move an object to a new one

position;" TRACE - show the trajectory of the object's movement;

DEL - remove object from scene

(used to visualize the concept of "take").

In conclusion, it can be noted that the developed graphical tools are focused on use in intelligent CAD systems, robots, training systems, building computer games, "in virtual reality systems. The system software tools allow you to represent data expressed in textual and graphical forms and manipulate them.

The next step in the development of these tools is the development of a system that allows you to manipulate within not one single scene, but in some of their combination, which will allow you to create more complex worlds.

When considering the problems of constructing methods and tools for creating systems of new generations in the field of human-machine interaction (in the broad sense of the word), I would like to emphasize once again the exceptional role of figurative, non-verbal representations in various creative and intellectual processes, including learning, discovery of new knowledge, management complex objects, etc., so new tools are needed to help use the full range of human abilities. And here, of course, important role belongs to computer systems with new technologies to support these abilities, in particular, based on cognitive graphics and virtual reality systems.

Bibliography

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7. Rakcheeva T.A. Cognitive representation of the rhythmic structure of the ECG // Software products and systems. - 1992. -L6 2.- S. 38-47.

4. Eremeev A.P., Korotkoe O.V., Popov A.V. Visual controller for decision support systems // Proceedings / Sh Conf. on artificial intelligence. Tver.-1992. T. 1.- S. 142-145.

2. Bakharev I.A., Leder V.E., Matekin M.P. Smart Day Graphics Tools display

complex dynamics technological process// Software products and systems. -1992. - No. 2.- S. 34-37.

8. V.Bajdoun, LXitvintseva. SJvfalitov et al. Tekris: The intelligent system for text animation // Proc. of East-West Conf. on Art. Intel. EWAIC93. September 7-9, Moscow, Russia. 1993.

3. Hamilton J., SmithA., McWilliams G. et al. A virtual reality// Business week. - 1993. - No. 1.

6. Litvintseva L.V. Conceptual model of a visualization system for three-dimensional dynamic scenes // Software products and systems. No. 2.1992.

1. Baidun V.V., Bunin A.I., Bunina O.Yu. Analysis of textual descriptions of dynamic spatial scenes in the TEKRIS system // Software products and systems. -1992. -No. 3. - S. 42-48.

4. COGNITIVE COMPUTER GRAPHICS IN ENGINEERING TRAINING

The emergence and development of interactive computer graphics (ICG) tools opens up fundamentally new graphic possibilities for the education sector, thanks to which students can dynamically control their content, shape, size and color in the process of image analysis, achieving the greatest visibility. These and a number of other possibilities of the ICG are still poorly understood by teachers, including the developers of information technologies of education, which does not allow to fully use training potential IKG. The fact is that the use of graphics in educational computer systems not only increases the speed of information transfer to students and increases the level of its understanding, but also contributes to the development of such important qualities for a specialist in any industry as intuition, professional "flair", imaginative thinking.
The impact of ICG on the intuitive, creative thinking led to the emergence of a new direction in the problems of artificial intelligence, called in the work of cognitive (i.e., facilitating cognition) computer graphics. AT this section the role and place of cognitive computer graphics in engineering training are considered, a number of well-known ones are discussed and new more cognitive ways of graphic display of fields are proposed. physical parameters, algorithms for constructing the corresponding images are described, and the results of comparing the considered visualization methods from the standpoint of their cognitive efficiency are presented.

4.1. The dualism of human thinking
The human mind uses two mechanisms of thought. One of them allows you to work with abstract strings of characters, with texts, and so on. This mechanism of thinking is usually called symbolic, algebraic or logical. The second mechanism of thinking provides work with sensory images and ideas about these images. It is called figurative, geometric, intuitive, etc. Physiologically, logical thinking is associated with the left hemisphere human brain, and figurative thinking - with the right hemisphere.
The main differences in the work of the hemispheres of the human brain were discovered by the American scientist R. Sperry, who once risked cutting interhemispheric connections in patients with epilepsy for therapeutic purposes. A person whose right hemisphere was "disabled" and the left hemisphere "worked" retained the ability to communicate verbally, responded correctly to words, numbers, and other conventional signs, but often turned out to be helpless when it was necessary to do something with objects of the material world or their images. When only one "right" hemisphere worked, the patient easily coped with such tasks, was well versed with works of art, melodies and intonations of speech, oriented himself in space, but lost the ability to understand complex speech constructions and could not speak in any coherent way at all.
Each of the hemispheres of the human brain is an independent system for perceiving the external world, processing information about it and planning behavior in this world. The left hemisphere is, as it were, a large and powerful computer that deals with signs and procedures for their processing. Natural language speech, thinking in words, rational-logical procedures for processing information, etc. - all this is realized in the left hemisphere. In the right hemisphere, thinking is realized at the level of sensory images: aesthetic perception of the world, music, painting, associative recognition, the birth of fundamentally new ideas and discoveries, etc. All that complex mechanism of imaginative thinking, which is often defined by the single term "intuition", is the right hemispheric area of ​​brain activity.
Often, right-brain thinking is associated with activities in art. Sometimes this thinking is even called artistic. However, even more formalized activities to a large extent use the intuitive mechanism of thinking. The statements of prominent scientists about the role of intuition in scientific activity are curious. "The true value," said A. Einstein, "is, in essence, only intuition. For me, there is no doubt that our thinking proceeds, basically, bypassing symbols (words) and, moreover, unconsciously." And elsewhere: "No scientist thinks in formulas."
Even such an abstract formalized field of science as mathematics makes significant use of right-brain thinking. "You have to guess mathematical theorem before you prove it; you have to guess the idea of ​​the proof before you go through it in detail." A. Poincaré speaks even more clearly: "... in order to create arithmetic, as well as in order to create geometry or any kind of science , you need something other than pure logic. We have no other word for this other than "intuition."
The difference between the two mechanisms of thinking can be illustrated by the principles of compiling a coherent text from individual elements of information: left-brain thinking creates an unambiguous context from these elements, i.e. of all the countless connections between objects and phenomena, it actively selects only a few that are most essential for a given specific task. Right hemispheric thinking creates a multi-valued context, thanks to the simultaneous grasping of almost all signs and connections of one or many phenomena. In other words, logical-sign thinking introduces some artificiality into the picture of the world, while figurative thinking provides a natural immediacy of perception of the world as it is.
Human thinking and human behavior are conditioned joint work both hemispheres of the human brain. In some situations, the logical component of thinking predominates, in others, the intuitive one. According to psychologists, all people are divided into three groups: with predominant "left hemisphere" thinking, with "right hemisphere", with mixed thinking. This division is genetically predetermined, and there are special tests to determine the tendency to one or another type of thinking.
The fundamental differences between the left and right hemisphere information processing strategies described above are directly related to the formation of various abilities. So, for scientific creativity, i.e. to overcome traditional ideas, it is necessary to perceive the world in its entirety, which involves the development of abilities to organize a multi-valued context (figurative thinking). Indeed, there are numerous observations that for people who retain the ability to think creatively, creative activity is less tiring than routine, monotonous work. But people who have not developed the ability for imaginative thinking often prefer to do mechanical work, and it does not seem boring to them, since they are, as it were, "enslaved" by their own formal-logical thinking. From this it is clear how important it is from an early age to build education and training correctly so that both necessary to a person types of thinking developed harmoniously, so that figurative thinking would not be constrained by rationality, so that the creative potential of a person would not run out.
In the development of intelligent systems, as D.A. Pospelov, there is a "left hemispheric roll". To an even greater extent, apparently, such a "left hemispheric tilt" is characteristic of modern education, including the computer methods and means used in it. The phenomenon is not so harmless. The negative impact of the computerization of engineering training, which was discussed above (see paragraph 3.1), is largely due to the weak impact of the computer systems used on the intuitive, imaginative mechanism of thinking.
In this regard, a clear allocation of implicit, subconscious components of knowledge also allows us to clearly set the task of their development, to formulate appropriate requirements for methods and teaching aids, including computer graphics methods.

4.2. Illustrative and cognitive functions of computer graphics

At present, interactive computer graphics is one of the most rapidly developing areas of new information technologies. Thus, in scientific research, including fundamental research, the emphasis on the illustrative function of the ICG, which is characteristic of the initial stage, is increasingly shifting towards the use of those ICG capabilities that allow activating "... the human ability to think in complex spatial images" . In this regard, they begin to clearly distinguish between two functions of the ICG: illustrative and cognitive.

The illustrative function of the ICG makes it possible to embody in a more or less adequate visual design only what is already known, i.e. already exists either in the world around us, or as an idea in the head of the researcher. The cognitive function of the ICG is to use some ICG image to get a new one, i.e. knowledge that does not yet exist even in the head of a specialist, or at least contribute to the intellectual process of obtaining this knowledge.

The main idea of ​​the differences between the illustrative and cognitive functions of the ICG, highlighted in the paper when describing the use of the ICG in scientific research, fits well into the classification of knowledge and computer systems for educational purposes (see Section 1.1). The illustrative functions of the ICG are implemented in educational systems of a declarative type when transferring to students an articulated part of knowledge, presented in the form of pre-prepared information with graphic, animation, audio and video illustrations (Fig. 4.1). The cognitive function of the ICG manifests itself in systems of a procedural type, when students "obtain" knowledge through research on mathematical models of the objects and processes being studied, and since this process of knowledge formation is based on an intuitive right-hemispheric mechanism of thinking, this knowledge itself is largely personal in nature. . Each person forms the techniques of subconscious mental activity in his own way. Modern psychological science does not have strictly substantiated methods for the formation of a person's creative potential, even if it is a professional one. One of the well-known heuristic approaches to the development of intuitive professionally oriented thinking is the solution of research problems. The use of educational computer systems of a procedural type makes it possible to significantly intensify this process, eliminating routine operations from it, and making it possible to conduct various experiments on mathematical models.

Rice. 4.1. Conceptual difference between cognitive and illustrative functions of computer graphics

The role of the ICG in these educational studies cannot be overestimated. It is the ICG images of the course and results of experiments on mathematical models that allow each student to form his own image of the object or phenomenon being studied in all its integrity and variety of connections. There is also no doubt that ICG images perform, first of all, a cognitive, and not an illustrative function, since in the process of educational work with computer systems of a procedural type, students form purely personal, i.e. not existing in this form for anyone, components of knowledge.

Of course, the differences between the illustrative and cognitive functions of computer graphics are rather arbitrary. Often, an ordinary graphic illustration can prompt some students to a new idea, allow them to see some elements of knowledge that were not "invested" by the teacher-developer of an educational computer system of a declarative type. Thus, the illustrative function of the ICG image turns into a cognitive function. On the other hand, the cognitive function of the ICG image during the first experiments with educational systems of the procedural type in further experiments turns into an illustrative function for the already "discovered" and, therefore, no longer a new property of the object under study.

However, the fundamental differences in the logical and intuitive mechanisms of human thinking, arising from these differences in the form of knowledge representation and methods of their development, make it useful methodologically to distinguish between the illustrative and cognitive functions of computer graphics and make it possible to more clearly formulate the didactic tasks of ICG images in the development computer systems for educational purposes.

4.3. Tasks of cognitive computer graphics

In the preface to the work, a well-known expert in the field of artificial intelligence D. A. Pospelov formulated three main tasks of cognitive computer graphics. The first task is to create such models of knowledge representation in which it would be possible to represent both objects characteristic of logical thinking and images-pictures with which figurative thinking operates with uniform means. The second task is the visualization of those human knowledge for which it is not yet possible to find textual descriptions. The third is the search for ways to move from the observed images-pictures to the formulation of some hypothesis about the mechanisms and processes that are hidden behind the dynamics of the observed pictures.

Developers of systems for engineering analysis, computer-aided design, and educational computer systems of a procedural type are dealing with the second of the tasks of cognitive graphics described here, when knowledge about a technical object obtained in the course of research on multidimensional mathematical models and presented in the usual symbolic-digital form becomes inaccessible to human analysis due to the large amount of information. Let us further consider a number of methods for displaying the fields of physical characteristics of technical objects and algorithms for constructing corresponding images with a high cognitive potential.

4.4. Assumptions of visualization algorithms

We will assume that a set of standard graphical functions that programmers use when developing educational application programs allows you to highlight a point on the display screen, indicating its coordinates and color, draw a straight line segment, indicating its color and coordinates of the ends, perform geometric coordinate transformations and projection transformations .

We will also assume that the depicted field of physical characteristics is presented as discrete values ​​in the nodes of a flat network of elements (PSE) of a triangular or quadrangular shape. This network can display either the entire field or its fragment, for example, a section of a three-dimensional field by a plane. Note that this form of representation of parameters is natural for a number of numerical grid methods, for example, the finite element method widely used in CAD involves grid approximation.

So, at the input of applied graphic programs that implement the algorithms considered below, there should be a topological and geometric description of the PSE with the values ​​of the displayed characteristics in the network nodes. It is convenient to store the network topology in the form of a matrix, in each row of which the number of the PSE element and the numbers of the nodes surrounding it are indicated. The geometric description of the PSE is a matrix, in the lines of which the coordinates of the network nodes are indicated.

Depending on the visualization method, we will use two types of approximation of the displayed parameters within the PSE element: constant and bilinear. For a constant approximation within quadrangular element PSE is the value of the displayed parameter , where are the values ​​of the parameters in the network nodes surrounding the PSE element.

For a bilinear approximation, we introduce dimensionless coordinates and and an auxiliary square (Fig. 4.2). The corresponding transformation of the coordinates and the displayed parameter is carried out according to a formula similar to the so-called shape functions in the finite element method:

(4.1)

Rice. 4.2. Transformation of an arbitrary quadrilateral into an auxiliary square.

To regularize the algorithms, we will consider an element of a triangular shape to be a special case of a quadrilateral with two adjacent corners combined.

Let's consider sequentially 7 ways of displaying physical characteristics: 4 ways - for visualization of scalar fields and 3 ways - for displaying vector characteristics, such as the strength or magnetic induction of an electromagnetic field, streamlines in aerohydrodynamics, distribution of forces or a reinforcing set in load-bearing structures. We will illustrate the methods under consideration with fragments of a graphical dialogue conducted in simulators and training PPPs of the CADIS system.

4.5. Solid Color Images

The essence of this visualization method is that inner region PSE is painted over in various colors, corresponding to certain intervals of the value of the displayed parameter. A color scale is usually used, in which, as the value of the parameter decreases, the colors change from warm (red and yellow) to cold (blue and purple). The image is built on the elements of the PSE. Algorithms for coloring an element are based either on the idea of ​​line-by-line scanning along an auxiliary square with a step corresponding to the size of the display raster grid element, and coloring these elements, called pixels or pels, in accordance with expression (4.1), or on the idea of ​​raster scanning along the axis and building color segments along the axis. In the second algorithm, the color of the segment is determined by the interval , and the coordinates of the ends of the segment are found from (4.1) for fixed values ​​and boundaries preset intervals. The transition of the color palette through the boundaries of the PSE elements occurs smoothly, since the approximating function (4.1) is linear along the sides of the PSE quadrangles, which ensures the continuity of the surface of the displayed parameter.

For monochrome displays, tone images can be built using such algorithms (Fig. 4.3).

Figure 4.3. A tone image of the optimal distribution of material in a plate under load.

4.6. equal level lines

The construction of lines of equal level (LRU) is carried out according to the elements of the PSE. The next two algorithms are based, like the shading algorithms, on scanning along an auxiliary square grid, the step of which corresponds to the display raster. In one of these algorithms, on the scanning grid lines parallel to the axis , points are found with given values ​​of the levels of the displayed parameter. points with equal values parameters on adjacent scanning lines are connected by segments of straight lines, if there is no "trough" or "elevation" of the bilinear surface (4.1) between these points. The constructed segments, lengthening during the scanning process, form a family of LRUs on each element of the FSE. In another algorithm, not the values ​​of the levels are specified, but the intervals of values ​​that form a series of "bands" of a given level. The construction of LRU is carried out by shading the stripes. The thickness of the LRU on the display screen depends on the specified interval width and on the nature of the change in the displayed surface. In both algorithms, the joining of the LRS at the boundaries of the PSE elements occurs in a natural way, since the approximating function (4.1) is linear along the sides of the PSE quadrangles (see Fig. 3.22).

4.7. Bitmaps

The field of each PSE element on the display screen is filled with luminous dots. The density of dots corresponds to the value of the displayed parameter. The filling of PSE sections with a constant density (this can be the field of the entire quadrangle or part of it) is carried out using a sensor random numbers(DSCH). Such filling smooths out the discontinuities of the displayed surface even with a constant approximation of the parameter within one PSE element (Fig. 4.4). Before building a bitmap, the maximum value is found, to which the dot filling density equal to 80-90% of the solid shading density is assigned. According to this limit, the filling density of points on each quadrilateral of the PSE is further normalized. When constructing an image on a PSE element, the auxiliary square is preliminarily divided by axes and into quarters, since standard DFS operate with numbers in the interval . Within each quarter, the point density is assumed to be constant. The coordinates of the points and are determined using the DFS, converted by formula (4.1) into coordinates, and then converted to the screen coordinate system. The color of the dots is determined by the given color intervals using the expression (4.1).

Rice. 4.4. Bitmap of optimal material distribution in the plate under load.

4.8. Polygon networks

The image is displayed as a central projection of the displayed parameter surface. The surface is approximated by a network of triangles and quadrilaterals with straight sides. Such a network is called polygonal. The simplest polygonal network can be obtained by displaying the PSE on a parametric surface (Fig. 4.5). The clarity of the image largely depends on the choice of the position of the observer's point of view in the central projection and on the presence or absence of invisible surface areas. The construction of polygonal networks according to the given PSE is not difficult and does not require large computational costs. The corresponding algorithm is reduced to the usual geometric transformations of coordinates and projection transformations of the nodal points of the base PSE and the parametric surface, which are then connected by straight line segments. However, line visibility analysis significantly increases computational costs, sometimes by two or three orders of magnitude.

4.9. Images as oriented segments of variable length

This method is used to display vector characteristics, for example, force flows. For it, a constant law of parameter approximation is used within the PSE element. Oriented segments are displayed in the centers of the elements, their lengths in the selected scale correspond to the values ​​of the parameters (Fig. 4.6). Before constructing the image, for reasons of clarity, the maximum length of the segment is calculated, relative to which the segments on all elements are further normalized. The image is built on the elements of the PSE. A local rectangular coordinate system is placed in the center of the quadrangle, one of the axes of which is oriented in the direction of the displayed parameter. Further, in the coordinates of the local system, the end points of the segment are determined so that its middle coincides with the center of the element, the obtained coordinates are transformed into a common system, and a straight line is drawn connecting the end points of the segment.

Fig 4.6. The distribution of forces in the plate, presented as oriented segments of variable length.

4.10. Images as short oriented segments of constant length

This rendering method is also designed to display vector characteristics. After each element, the PSE is filled with short oriented segments of constant length using a DFS. The density of the segments corresponds to the value of the displayed parameter (Fig. 4.7). Before building the image, the maximum density of segments is calculated for reasons of clarity, relative to which the density of segments on all elements of the PSE is normalized. A rectangular local coordinate system is placed in the center of the PSE quadrangular element, one of the axes of which is oriented in the direction of the displayed parameter. The coordinates of the midpoints of the segments are determined using the DFS, as is done when constructing point images. In the future, the construction of each segment is carried out in the same way as in the previous algorithm.

Fig 4.7. The distribution of forces in the plate, presented as short oriented segments of constant length.

4.11. Oriented lattice images

For this visualization method, as well as for the two previous methods, a constant approximation over the elements of the FSE is used. The field of the element is filled with a lattice in the form of one or two families of unidirectional lines, the density and orientation of which correspond to the magnitudes and orientations of the displayed characteristics (Fig. 4.8). Color is used to identify the family. The image is constructed on the basis of the same algorithmic ideas as in the previous two methods: the ultimate lattice density is determined; a rectangular local coordinate system is built on each element; inside the elements, segments of straight lines are drawn, the ends of which are located on the sides of the elements.

Rice. 4.8. The distribution of forces in the plate, presented as oriented lattices.

4.12. Image management

In the process of analyzing the results of calculations, the user of the application program should be able to choose the image method and adjust it to achieve the greatest visibility. When setting up an image, you can choose: color gamut (number, type and sequence of colors used); the number of levels for building LRU; the position of the observer's point of view and the type of central projection for polygonal networks; length of short oriented segments; contrast ratio.

Image contrasting can be used to more clearly identify patterns in the distribution of displayed parameters, while the difference between large and small values ​​is artificially overestimated. Contrasting is carried out using the following relationship: , where, where - the number of particular criteria; - evaluation by a particular criterion, ; is a weighting factor that takes into account the significance of the corresponding criterion, .
As particular criteria, 8 indicators were used that characterize the following aspects of the methods under consideration: adequacy to the goals and content of the design of load-bearing structures; adequacy to the teaching methods implemented in educational applied programs; naturalness and accessibility for human perception; convenience for the analysis of qualitative patterns of distribution of parameters; aesthetic appeal; ease of image construction control; speed of image formation; algorithmic simplicity.
The study was conducted with the help of expert assessments of the Delphi method. University teachers and engineers, developers and users of educational and industrial CAD of load-bearing structures were involved as experts. The research results show that in the interactive design of load-bearing structures, it is advisable to use point images to display scalar characteristics, and oriented grids to display vector fields (Fig. 4.9). The results and methodology of the study are described in more detail in the work.

Fig 4.9. Results of studies on the effectiveness of various imaging methods:
a - scalar images; b - vector images.