Ministry of Education and Science of the Russian Federation

BUZULUK HUMANITARIAN AND TECHNOLOGICAL INSTITUTE (BRANCH) OF THE FEDERAL STATE BUDGETARY EDUCATIONAL INSTITUTION

HIGHER PROFESSIONAL EDUCATION

"ORENBURG STATE UNIVERSITY"

Faculty of Distance Learning

Department of Physics, Informatics, Mathematics

COURSE WORK

in the discipline "Computer graphics and modeling"

The history of the emergence of computer graphics

Buzuluk 2012

annotation

Course work on the topic "History of the development of computer graphics methods" contains 32 pages, including 15 figures, 20 sources of literature.

The first section describes the history of the emergence of computer graphics.

The second section describes the types of graphics and the use of graphics in various fields of human activity.

Introduction

The history of the development of information technology is characterized by a rapid change in conceptual concepts, technical means, methods and areas of their application. In modern realities, the ability to use industrial information technologies has become very relevant for most people. The penetration of computers into all spheres of social life convinces that the culture of communication with a computer is becoming a common culture of a person.

The purpose of this work is to study the history of the emergence of computer graphics.

The object of study is computer graphics.

Subject of study: the history of the emergence of computer graphics.

Coursework objectives:

) study and analyze the literature on this topic;

) give the concept of the main types of computer graphics;

) consider the possibilities of computer graphics.

1. The history of the development of computer graphics

1.1 The emergence of computer (machine) graphics

Computer graphics have not more than a decade in their development, and even less for commercial applications. Andriesvan Dam is considered one of the fathers of computer graphics, and his books are fundamental textbooks on the entire spectrum of technologies underlying computer graphics. Also known in this area is Ivan Sutherland, whose doctoral dissertation was the theoretical basis for computer graphics.

Until recently, experimenting with the power of interactive computer graphics was the privilege of only a small number of professionals, mainly scientists and engineers involved in design automation, data analysis, and mathematical modeling. Now the study of real and imaginary worlds through the "prism" of computers has become available to a much wider circle of people.

There are several reasons for this change in the situation. First of all, as a result of a dramatic improvement in the cost / performance ratio for some components of computer hardware. In addition, standard high-level graphics software has become widely available, making it easier to write new application programs that are portable from one type of computer to another.

The next reason is due to the influence that displays have on the quality of the interface - the means of communication between man and machine - to provide the best user experience. New, user-friendly systems are built largely on the WYSIWYG approach (an abbreviation of the English expression "Whatyouseeiswhatyouget" - "What you see is what you have"), according to which the image on the screen should be as similar as possible to the one that as a result printed.

Most traditional computer graphics applications are two-dimensional. Recently, there has been an increasing commercial interest in 3D applications. It is driven by significant progress in solving two interrelated problems: modeling three-dimensional scenes and rendering as realistic as possible. For example, flight simulators emphasize response times to commands from the pilot and instructor. To create the illusion of smooth movement, the simulator must generate an extremely realistic picture of a dynamically changing "world" at a rate of at least 30 frames per second. In contrast, images used in advertising and the entertainment industry are computed autonomously, often over hours, in order to achieve maximum realism or to make a strong impression.

The development of computer graphics, especially at its initial stages, is primarily associated with the development of technical means, and especially displays:

arbitrary beam scanning;

raster beam scanning;

storage tubes;

plasma panel;

liquid crystal indicators;

electroluminescent indicators;

field emission displays.

Arbitrary beam scanning. Display graphics emerged as an attempt to use randomly scanned cathode ray tubes (CRTs) to output an image from a computer. According to Newman, apparently, the first machine where CRTs were used as an output device was the Whirlwind-I (Hurricane-I) computer, manufactured in 1950. at the Massachusetts Institute of Technology. This experiment began the development stage of vector displays (displays with arbitrary beam scanning, calligraphic displays). In professional jargon, a vector is a straight line segment. This is where the name "vector display" comes from.

When the beam moves across the screen at the point on which the beam hits, the glow of the phosphor of the screen is excited. This glow stops rather quickly when the beam is moved to another position (the usual persistence time is less than 0.1 s). Therefore, in order for the image to be constantly visible, it has to be re-issued (regenerated) 50 or 25 times per second. The need to re-issue an image requires storing its description in a specially allocated memory called refresh memory. The image description itself is called a display file. It is understood that such a display requires a sufficiently fast processor to process the display file and control the movement of the beam across the screen.

Usually serial vector displays managed to build only about 3000-4000 segments 50 times per second. With a larger number of segments, the image begins to flicker, since the segments built at the beginning of the next cycle completely disappear by the time the last ones are drawn.

Another disadvantage of vector displays is the small number of gradations in brightness (usually 2-4). Two-three-color CRTs were developed, but did not find widespread use, which also provided several gradations of brightness.

In vector displays, it is easy to erase any element of the image - it is enough to delete the erased element from the display file during the next construction cycle.

Text dialogue is supported using an alphanumeric keyboard. Indirect graphical dialogue, as in all other displays, is carried out by moving the crosshair (cursor) across the screen using various crosshair controls - coordinate wheels, control lever (joystick), trackball (ball handle), tablet, etc. A distinctive feature of vector displays is the possibility of a direct graphical dialogue, which consists in a simple indication of objects on the screen (lines, symbols, etc.) with the help of a light pen. To do this, it is enough to determine the moment of drawing with the help of a photodiode and, therefore, the beginning of the glow of the phosphor of any part of the required element.

The first serial vector displays appeared abroad in the late 60s.

Ray raster scanning.

Advances in microelectronic technology have led to the overwhelming use of raster beam scanning displays since the mid-1970s.

Memory tubes.

At the end of the 60s, a storage CRT appeared, which is capable of storing the constructed image directly on the screen for a fairly long time (up to an hour). Therefore, no refresh memory is necessary, and no fast processor is needed to perform image refresh. Erasing on such a display is possible only for the entire picture as a whole. The complexity of the image is practically unlimited. The resolution achieved on the storage tube displays is the same as on vector displays or higher - up to 4096 dots.

Text dialogue is supported using an alphanumeric keyboard, an indirect graphical dialogue is carried out by moving the crosshair across the screen, usually using the coordinate wheels.

The appearance of such displays, on the one hand, contributed to the widespread use of computer graphics, on the other hand, it represented a certain regression, since relatively low-quality and low-speed, not very interactive graphics were spreading.

Plasma panel.

In 1966. a plasma panel was invented, which can simply be represented as a matrix of small multi-colored neon lamps, each of which is switched on independently and can glow with adjustable brightness. It is clear that the deflection system is not necessary, and the regeneration memory is not necessary either, since by the voltage on the light bulb it is always possible to determine whether it is on or off, i.e. whether or not there is an image at this point. In a sense, these displays combine many of the useful properties of vector and raster devices. The disadvantages include high cost, insufficient resolution and high supply voltage. In general, these displays are not widely used.

Liquid crystal indicators. Displays on liquid crystal indicators work similarly to indicators in electronic watches, but, of course, the image does not consist of several segments, but of a large number of separately controllable dots. These displays have the smallest dimensions and power consumption, therefore they are widely used in laptop computers, despite the lower resolution, lower contrast and a noticeably higher price than for raster CRT displays.

Electroluminescent indicators. Displays on electroluminescent indicators have the highest brightness, contrast, operating temperature range and durability. Advances in technology have made them available for use not only in expensive high-end systems, but also in general industrial systems. The operation of such displays is based on the glow of a phosphor under the influence of a relatively high alternating voltage applied to mutually perpendicular sets of electrodes, between which the phosphor is located.

Displays with field emission. Displays on cathode-ray tubes, despite their relative cheapness and widespread use, are mechanically fragile, require a high supply voltage, consume a lot of power, have large dimensions and have a limited service life associated with the loss of emission from cathodes. One of the methods for eliminating these disadvantages is the creation of flat displays with field emission from cold cathodes in the form of highly sharpened microneedles.

Thus, starting in 1950, computer graphics have now gone from exotic experiments to one of the most important, all-pervading tools of modern civilization, ranging from scientific research, design and manufacturing automation, business, medicine, ecology, media, leisure and ending with household equipment.

2. Computer graphics

The scope of computer graphics is not limited to artistic effects alone. In all branches of science, technology, medicine, in commercial and management activities, computer-generated schemes, graphs, diagrams are used, designed to visually display a variety of information. Designers, when developing new car and aircraft models, use 3D graphics to represent the final appearance of the product. Architects create a three-dimensional image of the building on the monitor screen, and this allows them to see how it will fit into the landscape.

You can consider the following areas of application of computer graphics.

Scientific graphics.

The first computers were used only for solving scientific and industrial problems. To better understand the results obtained, they were processed graphically, built graphs, diagrams, drawings of the calculated structures. The first graphics on the machine were obtained in the mode of symbolic printing. Then special devices appeared - plotters (plotters) for drawing drawings and graphs with an ink pen on paper. Modern scientific computer graphics makes it possible to carry out computational experiments with a visual presentation of their results.

Business graphics.

Business graphics is an area of ​​computer graphics designed to visualize various indicators of the work of institutions. Planned indicators, reporting documents, statistical summaries - these are the objects for which illustrative materials are created using business graphics. Business graphics software is included in spreadsheets.

Design graphics.

Design graphics are used in the work of design engineers, architects, inventors of new technology. This type of computer graphics is an indispensable element of CAD (design automation systems). By means of design graphics, it is possible to obtain both flat images (projections, sections) and spatial three-dimensional images.

Illustrative graphics.

Illustrative graphics are freehand drawing and plotting on a computer screen. Illustrative graphics packages are general purpose application software. The simplest illustrative graphics software is called graphics editors.

Artistic and advertising graphics - which have become popular largely thanks to television. With the help of a computer, commercials, cartoons, computer games, video tutorials, video presentations are created. Graphic packages for these purposes require large computer resources in terms of speed and memory. A distinctive feature of these graphics packages is the ability to create realistic images and "moving pictures". Obtaining drawings of three-dimensional objects, their rotations, approximation, removal, deformation is associated with a large amount of computation. The transfer of the illumination of an object depending on the position of the light source, on the location of shadows, on the surface texture, requires calculations that take into account the laws of optics.

One of the earliest known films was Star Wars. It was created with the help of the Sgau supercomputer. The stages of further development of computer cinema can be traced in such films as "Terminator 2", "Babylon 5", etc. Until recently, computer graphics technologies were used for special effects, creating images of exotic monsters, simulating natural disasters and other elements that were just a background for the play of live actors. In 2001, the full-length film "Final Fantasy" was released, in which everything, including images of people, was synthesized by a computer - live actors only voiced the roles behind the scenes.

Computer animation.

Computer animation is the acquisition of moving images on a display screen. The artist creates on the screen a drawing of the initial and final position of moving objects, all intermediate states are calculated and displayed by the computer, performing calculations based on the mathematical description of this type of movement. The resulting drawings, displayed sequentially on the screen with a certain frequency, create the illusion of movement.

Graphics for the web.

Types of computer graphics.

There are three types of computer graphics. These are raster graphics, vector graphics and fractal graphics. They differ in the principles of image formation when displayed on a monitor screen or when printed on paper.

Raster method - the image is represented as a set of colored dots. Raster graphics are used in the development of electronic (multimedia) and printing publications. Bitmap illustrations are rarely created by hand using computer programs. Most often, scanned illustrations prepared by artists or photographs are used for this purpose. Recently, digital cameras and video cameras have been widely used to enter raster images into a computer.

Pixel is the main element of bitmaps. These are the elements that make up the bitmap.

A digital image is a collection of pixels. Each pixel of a raster image is characterized by x and y coordinates and brightness V (x, y) (for black and white images). Since pixels are discrete, their coordinates are discrete quantities, usually integers or rational numbers. In the case of a color image, each pixel is characterized by x and y coordinates, and three luminances: red luminance, blue luminance and green luminance (VR, VB, VG). By combining these three colors, you can get a large number of different shades.

Note that if at least one of the characteristics of the image is not a number, then the image belongs to the type of analog. Examples of analog images are holograms and photographs. There are special methods for working with such images, in particular, optical transformations. In some cases, analog images are converted into digital form. This task is performed by ImageProcessing.

The color of any pixel in a bitmap is stored using a combination of bits. The more bits are used for this, the more color shades can be obtained. The brightness gradation is usually allocated 1 byte (256 gradations), with 0 being black and 255 being white (maximum intensity). In the case of a color image, it is allocated one byte to the gradation of brightness of all three colors. It is possible to encode the brightness gradations with a different number of bits (4 or 12), but the human eye is only able to distinguish 8 bits of gradation per color. 24-bit colors provide over 16 million colors available and are often referred to as natural colors.

In color palettes, each pixel is described by a code. The link between this code and the 256-cell color table is maintained. The bit capacity of each cell is 24 bits. The output of each cell is 8 bits for red, green and blue.

The color space formed by the intensities of red, green and blue is represented as a color cube (see Fig. 1.).

Figure 1- Color Cube

The vertices of the cube A, B, C are the maximum intensities of green, blue and red, respectively, and the triangle they form is called Pascal's triangle. The perimeter of this triangle corresponds to the most saturated colors. The maximum saturation color always contains only two components. The segment OD contains shades of gray, with current O corresponding to black, and point D to white.

Types of rasters.

A raster is the order in which points (raster elements) are arranged. Figure 2 shows a raster, the elements of which are squares, such a raster is called rectangular, it is these rasters that are most often used.

Figure 2 - Raster with square elements

Although it is possible to use another shape as a raster element: a triangle, a hexagon; meeting the following requirements:

- all figures must be the same;

- must completely cover the plane without collision and holes.

So as a raster element it is possible to use an equilateral triangle (see Fig. 3), a regular hexagon (hexahedron) (see Fig. 4) You can build rasters using irregular polygons, but there is no practical sense in such rasters.

Figure 3- Triangular raster

Let's consider the ways of drawing lines in a rectangular and hexagonal raster.

Figure 4 - "Hexagonal raster"

In a rectangular raster, a line is drawn in two ways:

) The result is an eight-connected line. Adjacent pixels of the line can be in one of eight possible (see Fig.5a) positions

) The result is a four-connected line. Adjacent pixels of the line can be in one of four possible (see Fig. 5b) positions. The disadvantage is an excessively thick line at an angle of 45 °.

Figure 5 - Building a line in a rectangular raster

In a hexagonal raster, the lines are six-connected (see Fig. 6); such lines are more stable in width; the line width variance is less than in a square raster.

Figure 6 - Building a line in a hexagonal raster

One of the methods for evaluating a raster is transmission over a communication channel of an encoded image, taking into account the used raster, with subsequent restoration and visual analysis of the achieved quality.

Modeling a hexagonal raster. It is possible to build a hexagonal raster on the basis of a square one. For this, the hexagon is represented as a rectangle.

Vector graphics.

Vector graphics describe images using straight and curved lines, called vectors, and parameters that describe colors and positions. For example, the image of a tree leaf (see Fig. 7.) is described by the points through which the line passes, thereby creating the outline of the leaf. The color of the leaf is set by the color of the outline and the area within this outline.

Figure 7 - Example of vector graphics

Unlike raster graphics in vector graphics, the image is built using mathematical descriptions of objects, circles and lines. While this may seem more complicated at first glance than using raster arrays, for some types of images, using mathematical descriptions is easier.

The key to vector graphics is that it uses a combination of computer instructions and mathematical formulas for an object. This allows computing devices to calculate and place real points in the desired location when drawing these objects. This feature of vector graphics gives it a number of advantages over raster graphics, but at the same time is the reason for its disadvantages.

Vector graphics are often referred to as object-oriented graphics or drafting graphics. Simple objects such as circles, lines, spheres, cubes and the like are called primitives and are used to create more complex objects. In vector graphics, objects are created by combining different objects.

To create vector drawings, you must use one of the many illustration packages. The advantage of vector graphics is that the description is simple and takes up little computer memory. However, the disadvantage is that the detailed vector object can be too complex, it may not be printed as expected by the user, or not printed at all if the printer misinterprets or does not understand vector commands.

When editing vector graphics elements, the parameters of the straight and curved lines that describe the shape of these elements are changed. You can move elements, change their size, shape and color, but this will not affect the quality of their visual presentation. Vector graphics are resolution independent, i.e. can be displayed in a variety of output devices at different resolutions without loss of quality.

Vector representation consists in the description of image elements by mathematical curves, indicating their colors and occupancy.

Another advantage is high-quality scaling in any direction. An increase or decrease in objects is performed by increasing or decreasing the corresponding coefficients in mathematical formulas. Unfortunately, the vector format becomes disadvantageous when transferring images with a lot of shades or small details (for example, photographs). After all, each smallest glare in this case will not be represented by a collection of single-colored dots, but by a complex mathematical formula or a collection of graphic primitives, each of which is a formula. This makes the file heavier. In addition, converting an image from a raster to a vector format (for example, using AdobeStrimeLine or Corel OCR-TRACE) leads to the latter inheriting the impossibility of correctly scaling up. The increase in linear dimensions does not increase the number of details or shades per unit area. This limitation is imposed by the resolution of the input devices (scanners, digital cameras, etc.).

The concept of a fractal and the history of the appearance of fractal graphics.

You, probably, often saw quite clever pictures in which it is not clear what is depicted, but still the unusualness of their forms fascinates and attracts attention. As a rule, these are ingenious forms that do not lend themselves, it would seem, to any mathematical description. You, for example, saw patterns on glass after frost or, for example, ingenious blots left on a sheet with an ink pen, so something like that can be written down in the form of some algorithm, and, therefore, it is easy to communicate with a computer. Such sets are called fractal. Fractals are not similar to the figures we are familiar with, known from geometry, and they are built according to certain algorithms, and these algorithms can be displayed on the screen with the help of a computer. In general, if you simplify everything a little, then fractals are a kind of transformation that has been repeatedly applied to the original figure.

The first ideas of fractal geometry emerged in the 19th century. Cantor, using a simple recursive (repetitive) procedure, turned the line into a set of unconnected points (the so-called Cantor's Dust). He took the line and removed the center third and then repeated the same with the remaining segments. Peano drew a special kind of line (see Figure 8). To draw it, Peano used the following algorithm.

Figure 8- Drawing algorithm

At the first step, he took a straight line and replaced it with 9 segments 3 times shorter than the length of the original line (Part 1 and 2 of Figure 1). Then he did the same with each segment of the resulting line. And so on ad infinitum. Its uniqueness is that it fills the entire plane. It is proved that for each point on the plane, one can find a point belonging to the Peano line. Peano's Curve and Cantor's dust went beyond ordinary geometric objects. They did not have a clear dimension. Cantor's dust seemed to be built on the basis of a one-dimensional straight line, but consisted of points, and the Peano curve was built on the basis of a one-dimensional line, and the result was a plane. In many other areas of science, problems appeared, the solution of which led to strange results, like those described (Brownian motion, stock prices).

Until the 20th century, there was an accumulation of data on such strange objects, without any attempt to systematize them. That was until Benoit Mandelbrot, the father of modern fractal geometry and the word fractal, took on them. While working for IBM as a mathematical analyst, he studied noise in electronic circuits that could not be described using statistics. Gradually comparing the facts, he came to the discovery of a new direction in mathematics - fractal geometry.

Mandelbrot himself derived the word fractal from the Latin word fractus, which means broken (divided into parts). And one of the definitions of a fractal is a geometric figure made up of parts and which can be divided into parts, each of which will represent a reduced copy of the whole (at least approximately).

As soon as Mandelbrot discovered the concept of a fractal, it turned out that we are literally surrounded by them. Fractal ingots of metal and rocks, fractal arrangement of branches, patterns of leaves, capillary system of plants; circulatory, nervous, lymphatic systems in animal organisms, fractal river basins, cloud surfaces, lines of sea coasts, mountainous relief ...

To imagine a fractal, consider the example given in the book by B. Mandelbrot "The Fractal Geometry of Nature" which has become a classic - "What is the length of the coast of Britain?" The answer to this question is not as simple as it seems. It all depends on the length of the tool we will be using. By measuring the shore with a kilometer ruler, we get some length. However, we will skip many small coves and peninsulas that are much smaller than our lineup. By reducing the size of the ruler to, say, 1 meter, we will take into account these details of the landscape, and, accordingly, the length of the coast will become larger. Let's go ahead and measure the length of the coast using a millimeter ruler, here we will take into account details that are more than a millimeter, the length will be even greater. As a result, the answer to such a seemingly simple question can baffle anyone - the length of the coast of Britain is infinite.

The main property of fractals is self-similarity. Any microscopic fragment of a fractal in one way or another reproduces its global structure. In the simplest case, a part of a fractal is simply a reduced whole fractal.

Hence the basic recipe for constructing fractals: take a simple motif and repeat it, constantly decreasing in size. Eventually, a structure will emerge that reproduces this motive on all scales. (fig. 9)

Figure 9 - The motive of the repetition of the fractal

We take a segment and break its middle third at an angle of 60 degrees. Then we repeat this operation with each of the parts of the resulting broken line - and so on ad infinitum. As a result, we get the simplest fractal - the triad curve, which was discovered in 1904 by the mathematician Helga von Koch.

If at each step you not only reduce the main motif, but also displace and rotate it, you can get more interesting and realistic looking formations, for example, a fern leaf or even their entire thickets. Or you can build a very plausible fractal terrain and cover it with a very nice forest. In 3D StudioMax, for example, a fractal algorithm is used to generate trees. And this is no exception - most of the terrain textures in modern computer games are fractals. The mountains, forest and clouds in the picture are fractals.

Fractal image files have the fif extension. Usually, fif files are slightly smaller than jpg files, but it also happens vice versa. The fun begins when you look at pictures with increasing magnification. Files in jpg format almost immediately demonstrate their discrete nature - the notorious ladder appears. But fif files, as befits fractals, with increasing magnification show a new level of structure detailing, preserving the aesthetics of the image.

Geometric fractals.

It was with them that the history of fractals began. This type of fractal is obtained by simple geometric constructions. Usually, when constructing these fractals, one does the following: a "seed" is taken - an axiom - a set of segments, on the basis of which the fractal will be constructed. Then a set of rules is applied to this "seed", which transforms it into some kind of geometric figure. Next, the same set of rules is applied to each part of this figure. With each step, the figure will become more and more complex, and if we carry out an infinite number of transformations, we will get a geometric fractal.

The previously considered Peano curve is a geometric fractal. Figure 10 shows other examples of geometric fractals (Koch Snowflake, Liszt, Sierpinski Triangle).

Figure 10- Snowflake Koch

Figure 11-Sheet

Figure 12 - Sierpinski Triangle

Of these geometric fractals, the Koch snowflake is very interesting and rather famous. It is built on the basis of an equilateral triangle. Each line of which is replaced by 4 lines each 1/3 long of the original. Thus, with each iteration, the length of the curve increases by a third. And if we do an infinite number of iterations, we get a fractal - a Koch snowflake of infinite length. It turns out that our infinite curve covers a limited area.

The dimension of a Koch snowflake (when a snowflake grows 3 times its length increases 4 times) D = log (4) / log (3) = 1.2619 ...

The so-called L-Systems are well suited for constructing geometric fractals. The essence of these systems is that there is a specific set of system symbols, each of which denotes a specific action and a set of rules for character conversion.

Algebraic fractals.

The second large group of fractals is algebraic. They got their name because they are built on the basis of algebraic formulas that are sometimes very simple. There are several methods for obtaining algebraic fractals. One of the methods is a multiple (iterative) calculation of the function Zn + 1 = f (Zn), where Z is a complex number and f is some function. The calculation of this function continues until a certain condition is met. And when this condition is fulfilled, a point is displayed on the screen. In this case, the values ​​of the function for different points of the complex plane can have different behavior:

- tends to infinity in the course of time;

- tends to 0;

- takes several fixed values ​​and does not go beyond them;

–Behavior is chaotic, without any tendencies.

To illustrate algebraic fractals, let us turn to the classics - the Mandelbrot set.

Figure 13 - Mandelbrot set

To construct it, we need complex numbers. A complex number is a number consisting of two parts - real and imaginary, and it is denoted a + bi. The real part a is the usual number in our representation, and bi is the imaginary part. i is called an imaginary unit, because if we square i, we get -1.

Complex numbers can be added, subtracted, multiplied, divided, raised to a power and root, you cannot just compare them. A complex number can be depicted as a point on a plane, where the X coordinate is the real part of a, and Y is the coefficient of the imaginary part of b.

Functionally, the Mandelbrot set is defined as

1 = Zn * Zn + C.

To construct the Mandelbrot set, we will use the BASIC algorithm. A = -2 to 2 "for all real a from -2 to 2b = -2 to 2" for all imaginary b from -2 to 2

"Belongs to Mandelbrot set = True

"Repeat 255 times (for 256 color mode)

For iteration = 1 to 255 = Z0 * Z0 + C

"Checked - not owned abs (Zn)> 2 then Lake = False: Exit For0 = Zn

"Drawn a black dot belonging to Mandelbrot's" lake ".

If Lake = True Then PutPixel (a, b, BLACK)

"Drawn a point that does not belong to the set or lies on the border.

Else PutPixel (a, b, iteration)

Now let's describe the program in words. For all points on the complex plane in the range from -2 + 2i to 2 + 2i, perform a fairly large number of times Zn = Z0 * Z0 + C, each time checking the absolute value of Zn. If this value is greater than 2, we draw a point with a color equal to the iteration number at which the absolute value exceeded 2, otherwise we draw a black point. The whole set of Mandelbrot is in full glory before our eyes.

The black color in the middle shows that at these points the function tends to zero - this is the Mandelbrot set. Outside this set, the function tends to infinity. And the most interesting thing is the boundaries of the set. They are then fractal. At the boundaries of this set, the function behaves unpredictably - chaotically.

By changing the function, the conditions for exiting the cycle, you can get other fractals. For example, taking instead of the expression С = a + bi the expression Z0 = a + bi, and assigning arbitrary values ​​to С, we get the Julia set, also a beautiful fractal.

For the Mandelbrot set, self-similarity also manifests itself.

Stochastic fractals

A typical representative of this class of fractals "Plasma".

Figure14-Plasma

To construct it, take a rectangle and define a color for each corner. Next, we find the center point of the rectangle and paint it in a color equal to the arithmetic mean of the colors at the corners of the rectangle plus some random number. The larger the random number, the more "ragged" the drawing will be. If, for example, we say that the color of a point is the height above sea level, then we get instead of plasma - a mountain range. It is on this principle that mountains are modeled in most programs. Using an algorithm similar to plasma, a height map is built, various filters are applied to it, and a texture is applied.

computer graphics vector animation

Conclusion

In this course work, such an issue as the history of the development of computer graphics was studied, concepts were given to the main types of computer graphics, and the possibilities of computer graphics were considered.

Having studied the literature on this topic, we can conclude that the history of graphics does not stand still, but is developing rapidly.

In the future, you can consider in more detail the types of computer graphics and consider the programs of work in computer graphics.

The scope of computer graphics is not limited to artistic effects alone. All branches of commercial management use computer-generated diagrams, graphs and diagrams.

List of sources used

1 Development of electronic educational publications. Creation and use of information teaching aids: textbook. manual / N.D. Izergin, [and others]. - M .: Kolomna, 2006 .-- 160 p. - ISBN 5-89-5-89-655-8974-0.

Festival of Pedagogical Ideas "Open Lesson". Creation of an electronic textbook / ed. Tregubova O.P. - M .: Russia. - Access mode: http://festival.1september.ru/articles/526252/. - 20.06.2011.

What should be an electronic textbook. / V.B. Yasinsky // Electronic journal: RESEARCHED IN RUSSIA, 2000. - Access mode: http://zhurnal.ape.relarn.ru/articles/2001/011.pdf. - 06.21.2011.

Pankratova, LP. Knowledge control in informatics: Tests, control tasks, examination questions, computer projects / E.N. Chelak. SPb .: BHV-Petersburg. 2004 .-- 448 p. - ISBN 5-94157-371-5.

Russian Federation standard for primary vocational education. Computer operator. OST 9PO 02.1.9 2002.48 p.

Ugrinovich, N.D. Informatics and information technology. textbook / N.D. Ugrinovich. Moscow ..: Publishing house BINOM. Lab. knowledge, 2005 .-- 512 p. - ISBN 5-94774-001-8.

Informatics: textbook. manual / A.V. Mogilev. - 2nd ed., Erased. - Moscow ..: Academy, 2008 .-- 336 p. - ISBN 978-5-7695-4771-3.

Workshop on informatics: textbook. manual / A.V. Mogilev. Moscow. Publishing house Academy, 2001. 608 p. ISBN 5-7695-2247-X.

Computer science. Textbook / V.A. Ostreykovsky. 2nd ed., Erased. - M .: Higher. shk., 2004 .-- 511 p. - ISBN 5-06-003533-6.

11 Microsoft Office Word 2003. allowance / B. Hislop. Moscow. Dialectics, 2004.784 p. ISBN 5-8459-0646-6, 0-7645-3971-X.

12 Microsoft Office 2003. Textbook. manual.O.A. Mezhenny. - M .: Dialectics, 2004.368 p. ISBN 5-8459-0838-8.

Working on a personal computer (PC) in the office: training course / O.S. Stepanenko. Moscow. Williams Publishing. 3rd ed., 2006. - 768 p. - ISBN 5-8459-0974-0.

Zakharova, L.A. Microsoft Word 2003. Practical manual series "Step by step" (+ CD-ROM) / L.А. Zakharova. - M.: SP ECOM, 2005 .-- 384 p. - ISBN 5-9790-0005-4.

Bedet, A. Glossary of computer terms / D. Burdhardt, A. Cumming, [and others]. - 10th ed., M .: Publishing house: Williams, 2002 .-- 432 p. - ISBN 5-8459-0363-7, 0-2017-7629-4.

Gukin, D. Illustrated computer dictionary / D. Gukin, S.Kh. Gukin. - 4th ed., Moscow. Williams Publishing House, 2005. - 512 p. - ISBN 5-8459-0207-X, 0-7645-0732-X;

The starting point for the development of computer graphics can be considered 1930, when in the United States our compatriot Vladimir Zvorykin, who worked at Westinghouse, invented a cathode ray tube (CRT), which for the first time allows you to get images on a screen without using mechanical moving parts.

The beginning of the era of proper computer graphics can be considered December 1951, when the first display for the computer "Whirlwind" was developed at the Massachusetts Institute of Technology (MIT) for the air defense system of the US Navy. The inventor of this display was MIT engineer Jay Forrester.

One of the founding fathers of computer graphics is Ivan Sotherland, who in 1962, at the same MIT, created a computer graphics program called Sketchpad. This program could draw fairly simple shapes (points, lines, arcs circles), could rotate figures on the screen.

Under the leadership of T. Mofett and N. Taylor, Itek developed a digital electronic drawing machine. In 1964, General Motors introduced the DAC-1 computer-aided design system, developed in conjunction with IBM.

In 1965, IBM released the first commercial graphics terminal called the IBM-2250 (Figure 5).

In 1968, a group led by N. N. Konstantinov created a computer mathematical model of the cat's movement. The BESM-4 machine, executing the written program for solving differential equations, drew the cartoon "Kitty" (Fig. 7), which was a breakthrough for its time. An alphanumeric printer was used for visualization.

In 1977, Commodore released its PET (Personal Electronic Recorder) and Apple created the Apple II. The advent of these devices gave rise to mixed feelings: the graphics were terrible and the processors were slow. However, PCs have spurred the development of peripheral devices: inexpensive plotters and graphics tablets.

By the late 1980s, software was available for all areas of application, from control systems to desktop publishing systems. At the end of the eighties, a new market direction arose for the development of hardware and software scanning systems, automatic digitization. The original impetus in such systems should have been created by the magic machine Ozalid, which would scan and automatically vectorize the drawing on paper, converting it into standard CAD / CAM formats. However, the emphasis has shifted towards processing, storing and transmitting scanned pixels.

In the 90s, the distinction between CG and image processing was erased. Computer graphics often deal with vector data, and pixel information is the basis for image processing.

Until a few years ago, each user required a workstation with a unique architecture, and now the workstation processors are fast enough to manage both vector and raster information. In addition, it becomes possible to work with video. Add audio capabilities and you have a multimedia computer environment.

All areas of application - whether it be art, engineering and scientific, business / entertainment and - are the scope of CG. The growing potential of PCs and their huge number - ensures the steady growth of the industry in this industry.

Formation of general concepts of computer graphics

World Computer Graphics Day is celebrated annually on December 3. The date was chosen for a reason: this day in the English version is 3 December, that is, a key combination of its kind is obtained - 3D December, or 3D.

The proposal to create a holiday came in 1998 from the American company Alias ​​Systems (acquired by Autodesk), the developer of Maya, a 3D modeling and animation package. Then such giants as Adobe Systems, NVIDIA, Wacom, etc. joined the event.

At first, the holiday was celebrated only by those who are directly related to the creation of three-dimensional images, a little later all other spheres related to computer graphics in general joined. The Russian-speaking community calls the event in its own way - "Day of the 3D-Schnick".

Major industry players spend the entire first decade of December holding all kinds of events, presentations, seminars and master classes. We, in turn, will try to outline the general picture of the formation and development of computer graphics. There is no point in pretending to be complete in describing the history, but it is still possible to outline the main milestones by providing a superficial glance.

1950s: from text images to a graphical console

In the middle of the last century, computers were not just big, but huge, and precious mainframe machine time was used exclusively for military and industrial needs. However, one of the bored programmers came up with the idea of ​​using printing devices to display pictures and photographs. It's simple: the difference in the density of alphanumeric characters is quite suitable for creating images on paper - even if they are mosaic, they are quite acceptable for perception by sight at a distance.

ASCII graphics have been around since the late 19th century, when typists competed for the best drawing on a typewriter.
Illustration: jackbrummet.blogspot.com.

In 1950, Ben Laposky, a mathematician, painter and draftsman, began experimenting with drawing on an oscilloscope. The dance of light was created with the most complicated settings on this cathode-ray device. High-speed photography and special lenses were used to capture the images, later pigmented filters were added to fill the images with color.

Ben Laposki next to an oscilloscope, for which he has found unusual use.
Illustration: Sanford Museum.

Later, the "oscillons" became colored due to the use of light filters.
Illustration: Sanford Museum.

Laposki's "Visual Rhythms and Harmonies of Electronic Abstract Art" matched perfectly with audio synthesized by Robert Moog, the pioneer of electronic music.

In 1951, the Massachusetts Institute of Technology (MIT) completed the Whirlwind for the United States Air Force, the first computer with a video terminal (actually an oscilloscope) to output data in real time.

Whirlwind computer: magnetic core memory (left) and operator console.
Illustration: Wikimedia.

In 1952, the first visual computer game appeared - OXO, or tic-tac-toe, developed by Alexander Douglas for the EDSAC computer as part of his Ph.D. thesis as an example of human-machine interaction. The data were entered using a disk dialer, and the output was performed by a matrix cathode-ray tube.

OXO Tic Tac Toe in EDSAC Emulator for Mac OS X.
Illustration: Wikimedia.

In 1955, the light pen was born. At the tip of the pen is a photocell that emits electronic pulses and simultaneously responds to the peak glow corresponding to the moment the electron beam passes. It is enough to synchronize the pulse with the position of the electron gun to determine exactly where the pen is pointing.

Light pens were used heavily in computing terminals from the 1960s.

IBM 2250. The light pen at that time acted as an analogue of a computer mouse.
Illustration: Wikimedia.

In 1957, a team led by Russell Kirsch developed a drum scanner for the 1950 SEAC computer at the US National Bureau of Standards, which produced the world's first digital photograph. The image, which captures the scientist's three-month-old son, turned out to be 5 × 5 cm in size with a resolution of 176 × 176 pixels. The computer independently isolated the contours, counted the objects, recognized the symbols and displayed a digital image on the oscilloscope screen.

In 1958, MIT launched the Lincoln TX-2 computer, the first to use a graphical console. From that moment on, computer graphics acquired a real application of techniques and developments - a vector display.

Workstation TX-2.
Illustration: MIT.

Around this time, John Whitney, the pioneer of computer animation, was experimenting with a mechanical analog computer he himself created from the anti-aircraft fire control device - the Kerrison predictor. Collaboration with designer Saul Bass was the spirographic splash screen for Alfred Hitchcock's 1958 film Vertigo.

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1960s: from "Album" to animation

It is believed that the term "computer graphics" was coined in 1960 by William Fetter, a designer at Boeing Aircraft, although he himself claims that the authorship belongs to his colleague Verne Hudson. At that time, there was a need for a means of describing the structure of the human body, and at the same time with high accuracy and in a form suitable for change. Computer graphics were perfect for solving this problem.

Boeing Man. Computer graphics helped a lot to save time and effort in the design of aircraft.
Illustration: Boeing.

Although the first computer games were already implemented, the first real video game should be considered "Star Wars" (Spacewar!). The toy was embodied in 1962 by MIT student Steve Russel and his colleagues, and it was run on a DEC PDP-1 computer using the notorious oscilloscope as a display.

In 1963, Ivan Sutherland, another MIT student, wrote a computer program called Sketchpad for the TX-2. It, at that time rightfully revolutionary, gave machine graphics a huge push forward, served as a prototype for computer-aided design (CAD) systems, and for the first time described elements of modern user interfaces and object-oriented programming languages.

The "Album" by means of a light pen allowed drawing vector shapes on the display, saving them, and accessing ready-made primitives. The key was the use of the concept of "objects" and "instances": the master drawing could be copied many times, changing each of the sketches to your liking, and if changes were made to the original drawing, its duplicates were rebuilt accordingly.

Ivan Sutherland demonstrates "The Album" on the TX-2 graphics console. For his program, in 1988, he received the Alan Turing Prize, which in the computer world is comparable in importance to the Nobel Prize.
Illustration: MIT.

Another important invention of "Album" were tools for automatic drawing of geometric shapes: it is enough to indicate the location and dimensions of, for example, a square so that it can be drawn - there was no need to worry about exact right angles.

At the same time, Edward Zajac, a scientist at Bell Telephone Laboratories, prepared an animated film "Simulation of a two-gyro gravitational control system" on the IBM 7090 mainframe, in which he showed the spatial movement of a satellite orbiting the Earth.

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In parallel, Ken Knowlton, an employee of the same company, came up with BeFlix (from Bell Flicks), the first dedicated computer animation language based on Fortran. He, working with "graphic primitives" like drawing a line, copying an area, filling a zone, scaling, etc., allowed to create images with eight halftones and a resolution of 252 × 184 pixels.

Between 1965 and 1971, the Evans & Sutherland animation series was created based on BeFlix by experimental director Stan VanDerBeek. It was formed by the well-known Ivan Sutherland and David Evans, who closely study the aspects of the visual interaction of a computer with a person.

The laboratory was equipped with a comprehensive focus on computer generated imaging (CGI) - including real-time hardware, 3D acceleration and printer languages ​​- and was powerful enough to attract a cohort of promising talent.

So, among those who joined were Edwin Catmull, who realized that animation should be shifted to the shoulders of computers, John Warnock, co-founder of Adobe Systems and developer of the concept of the revolutionary PostScript page description language in publishing, James Clark ), co-founder of Silicon Graphics and Netscape Communications.

Ed Catmell, he is considered the father of computer animation. He is now president of Walt Disney and Pixar, a world leader in the practical implementation of computer graphics in the film industry.
Image courtesy of Flickr / Jeff Heusser.

In 1968 the cartoon "Cat" was filmed in the USSR, which became the first in which a computer-animated character appeared.

A group of specialists led by mathematician Nikolai Konstantinov turned to the BESM-4 computer, which, with a sufficient degree of realism, simulated the movements of a cat through a system of second-order differential equations. Each frame was output to a printer, then they were all combined into a tape.

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In the second part of our immersion into the history of computer graphics, we will analyze the questions of algorithms.!

The first computers did not have separate means for working with graphics, but they were already used to obtain and process images. By programming the memory of the first electronic machines, built on the basis of a matrix of lamps, it was possible to obtain patterns.

In 1961, programmer S. Russell led the project to create the first computer game with graphics. The creation of the game ("Spacewar!") Took about 200 man-hours. The game was created on a PDP-1 machine.

In 1963, American scientist Ivan Sutherland created the Sketchpad software and hardware complex, which allowed him to draw points, lines and circles on a tube with a digital pen. Basic actions with primitives were supported: moving, copying, etc. In fact, this was the first vector editor implemented on a computer. Also, the program can be called the first graphical interface, and it was such even before the appearance of the term itself.

In the mid-1960s. there were developments in industrial applications of computer graphics. Thus, under the leadership of T. Mofett and N. Taylor, Itek has developed a digital electronic drawing machine. In 1964, General Motors introduced the DAC-1 computer-aided design system, developed in conjunction with IBM.

In 1964, a group led by N.N.Konstantinov created a computer mathematical model of a cat's movement. The BESM-4 machine, executing the written program for solving differential equations, drew the cartoon "Kitty", which was a breakthrough for its time. An alphanumeric printer was used for visualization.

In 1968, computer graphics experienced significant progress with the emergence of the ability to memorize images and display them on a computer display, a cathode-ray tube.

In the late 60s - early 70s, new companies began to work in the field of computer graphics. If earlier, to perform any work, customers had to install unique equipment and develop new software, then with the advent of various software packages that facilitate the process of creating images, drawings and interfaces, the situation has changed significantly.

Over the decade, systems have become so sophisticated that they have almost completely isolated the user from software problems.

In the late 70s, significant changes took place in computer graphics. Now you can create raster displays that have many advantages: output of large data sets, stable, flickering image, work with color. For the first time, it became possible to obtain a color gamut. Raster technology became clearly dominant in the late 1970s. The most significant event in the field of computer graphics was the creation of the personal computer in the late 70s. In 1977, Apple created the Apple II. The introduction of this device gave rise to mixed feelings: the graphics were terrible and the processors were slow. However, personal computers have stimulated the development of peripheral devices. Of course, personal computers have evolved as an important part of computer graphics, especially with the introduction in 1984 of the Apple Macintosh with its graphical user interface.

The original area of ​​application of the personal computer was not graphics applications, but working with word processors and spreadsheets, but its capabilities as a graphics device prompted the development of relatively inexpensive programs in the field of CAD / CAM and in the more general areas of business and art. By the late 1980s, software was available for everything from control systems to desktop publishing. In the late 80s, a new market direction arose for the development of hardware and software scanning systems, automatic digitization. The original impetus in such systems was to create the magic machine Ozalid, which would scan and automatically vectorize the drawing on paper, converting it to standard formats.

However, the focus has shifted towards processing, storing and transmitting scanned pixel images.

In the 90s, the distinction between computer graphics and image processing was erased. Computer graphics often deal with vector data, and pixel information is the basis for image processing. Until a few years ago, each user required a workstation with a unique architecture, and now the workstation processors are fast enough to manage both vector and raster information.

In addition, it becomes possible to work with video. Add audio capabilities and you have a PC multimedia environment. The growing potential of personal computers and their enormous number - about 100 million - ensures the steady growth of the industry in the industry. Graphics are increasingly penetrating into business - today there are virtually no documents created without the use of any graphic element.

Scientific graphics

The first computers were used only for solving scientific and industrial problems. In order to better understand or present the results obtained, they were processed graphically (they built graphs, diagrams, drawings of the calculated structures). The first graphics on the machine were obtained in the mode of symbolic printing.

Business graphics

Business graphics is an area of ​​computer graphics designed to visualize various indicators of the work of institutions. Planned indicators, reporting documents, statistical summaries - these are the objects for which illustrative materials are created using business graphics. Business graphics software is included in spreadsheets.

Design graphics

It is used in the work of design engineers, architects, inventors of new technology. This type of computer graphics is an indispensable element of CAD (design automation systems). By means of design graphics, it is possible to obtain both flat images (projections, sections) and spatial three-dimensional images. This type of computer graphics is a must-have CAD element.

Illustrative graphics

Freehand drawing and drawing with a computer. Illustrative graphics packages are general purpose application software. The simplest illustrative graphics software is called graphics editors.

It became popular largely thanks to television. With the help of a computer, commercials, cartoons, computer games, video tutorials, video presentations, etc. are created. Graphic packages for these purposes require large computer resources in terms of speed and memory. A distinctive feature of these graphics packages is the ability to create realistic images and "moving pictures".

Obtaining drawings of three-dimensional objects, their rotations, approximation, removal, deformation is associated with a large amount of computation. The transfer of the illumination of an object depending on the position of the light source, on the location of shadows, on the surface texture, requires calculations that take into account the laws of optics.

Computer animation

Capture a moving image on the display screen. There are many software products in which the artist creates drawings on the screen of the initial and final position of moving objects, all intermediate states are calculated and displayed by the computer, performing calculations based on the mathematical description of this type of movement. The resulting drawings, displayed sequentially on the screen with a certain frequency, create the illusion of movement.

Multimedia is a combination of high-quality image on the monitor screen with sound. The most widely used multimedia systems are in the field of education, advertising, cinema, entertainment, etc.

Graphics for the web

The advent of the global Internet has led to the fact that computer graphics have become an integral part of it. More and more methods of transmission of visual information are being improved, more advanced graphic formats are being developed, there is a palpable desire to use three-dimensional graphics, animation, the whole range of multimedia.

The history of the development of computer graphics

Historically, the first interactive systems are considered computer-aided design (CAD) systems... Example: AutoCAD, KOMPAS, etc.
Are becoming more and more popular now geographic information systems (GIS)... This is a relatively new type of interactive computer graphics systems for mass users.
Typical for any GIS are such operations - input and editing of objects, taking into account their location on the Earth's surface, the formation of various digital models, writing to databases, executing various queries to databases. An important operation is the analysis, taking into account the spatial, topological relations of a set of objects located on a certain territory.

Types of computer graphics

Computer graphics is a branch of informatics that studies the means and methods of creating and processing graphic images using computer technology. Although there are many classes of software for working with computer graphics, there are four types of computer graphics. These are raster graphics, vector graphics, 3D and fractal graphics. They differ in the principles of image formation when displayed on a monitor screen or when printed on paper.

Raster graphics are used in the development of electronic (multimedia) and printing publications. Bitmap illustrations are rarely created by hand using computer programs. Most often, scanned illustrations prepared by the artist on paper or photographs are used for this purpose. Recently, digital cameras and video cameras have been widely used to enter raster images into a computer. Accordingly, most graphic editors designed to work with raster illustrations are focused not so much on creating images as on processing them. On the Internet, raster illustrations are used in cases where it is necessary to convey the full range of shades of a color image.

On the contrary, software tools for working with vector graphics are intended primarily for creating illustrations and, to a lesser extent, for processing them. Such tools are widely used in advertising agencies, design bureaus, editorial offices and publishing houses. Design work based on the use of fonts and the simplest geometric elements is much easier to solve using vector graphics. There are examples of highly artistic works created with vector graphics, but they are the exception rather than the rule, since artistic preparation of illustrations using vector graphics is extremely difficult.

Three-dimensional graphics are widely used in engineering programming, computer modeling of physical objects and processes, in animation, cinematography and computer games.

Fractal graphics software is designed to automatically generate images using mathematical calculations. Creating a fractal art composition is not about painting or decoration, but programming. Fractal graphics are rarely used to create printed or electronic documents, but they are often used in entertainment programs.

Raster graphics

The main (smallest) element of the bitmap is a point. If the image is on-screen, then this point is called a pixel. Each pixel of a bitmap has properties: location and color. The larger the number of pixels and the smaller their dimensions, the better the image looks. Large amounts of data are a major problem when using raster images. For active work with large-sized illustrations such as a magazine page, computers with extremely large RAM sizes (128 MB or more) are required. Of course, such computers must also have high-performance processors. The second disadvantage of raster images is associated with the impossibility of enlarging them to view details. Since the image consists of dots, enlarging the image only causes these dots to become larger and resemble a mosaic. No additional detail can be seen when the bitmap is enlarged. Moreover, enlarging the raster pixels visually distorts the illustration and makes it rough. This effect is called pixelation.

Vector graphics

As in raster graphics, the main element of the image is a point, so in vector graphics, the main element of the image is a line (it does not matter if it is a straight line or a curve). Of course, lines also exist in raster graphics, but there they are treated as combinations of points. For each point of a line in raster graphics, one or more memory cells are allocated (the more colors the points can have, the more cells are allocated to them). Accordingly, the longer the raster line, the more memory it takes up. In vector graphics, the amount of memory occupied by a line does not depend on the size of the line, since the line is represented in the form of a formula, or rather, in the form of several parameters. Whatever we do with this line, only its parameters, stored in memory cells, change. The number of cells remains unchanged for any line.

A line is an elementary vector graphics object. Everything in a vector illustration is made up of lines. The simplest objects are combined into more complex ones, for example, a quadrilateral object can be viewed as four connected lines, and a cube object is even more complex: it can be viewed as either twelve connected lines or six connected quadrangles. Because of this approach, vector graphics are often referred to as object-oriented graphics. We said that vector graphics objects are stored in memory as a set of parameters, but we must not forget that all images are still displayed on the screen as dots (simply because the screen is designed this way). Before displaying each object on the screen, the program calculates the coordinates of the screen points in the object's image, therefore vector graphics are sometimes called computed graphics. Similar calculations are performed when outputting objects to the printer. Like all objects, lines have properties. These properties include: the shape of the line, its thickness, color, the nature of the line (solid, dashed, etc.). Closed lines have a filling property. The inner area of ​​the closed path can be filled with color, texture, map. The simplest line, if not closed, has two vertices, which are called nodes. Nodes also have properties that determine how the top of the line looks and how two lines fit together.