The Greek philosophers-Pythagoreans stated that the whole world ? number. And if concerning the whole world, probably, philosophers also exaggerated value of number concerning computer technologies they appeared, certainly, are right: all computer world ? number.
Now it is developed and it is successfully applied two main principles of representation of images ? the pointwise (raster) drawing and vector graphics.
At the heart of that and other method mathematical models lie, for the pointwise drawing is an array (matrix) of the numbers describing color parameters of each point (???????), and for vector graphics is a mathematical formula, using which vectorial program every time enumerates all points of a circuit, proceeding from new values of coordinates of several points.
Acquaintance to bases of a numeral drawing and color helps to understand principles of coding of the graphic information and it is better to use all possibilities of the program of adobe Illustrator for more adequate implementation of the creative intentions.
Adobe Illustrator program is an image editor, consisting in the basis from objects ? vectorial circuits by which after their creation parameters ??????? and parameters of filling can be appropriated. Circuits are in turn described by mathematical formulas the so-called Bezier curve named in honor of French mathematician Pierre Beze (? Bezier) which applied mathematical curves and surfaces in the course of construction of a body of the car of Renault, in particular, is used.
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Nota Bene. Actually mathematical theory on which basis there was a possibility to use curves in various application areas, has been formulated at the beginning of the century by the Russian and Soviet mathematician academician Sergey Natanovichem Bernstein (1880?1968) who, by the way, in 1899 ended the Parisian university. |
As the formula which would be enough simple (from the point of view of the mathematician), general-purpose (from the point of view of the programmer) and geometrically evident (from the point of view of the user ? the artist or the designer), uses the mentioned Bezier curve more often. Actually, this whole family of curves from which the special case with a cubic level, i.e. the curve of the third order described by a following parametric equation is used
R (t) = Po (l-t) 3 + P1t (l-t) 2 + P2t2 (l-t) + ?3t3, where 0 < t < 1.
The general view of the elementary Bezier curve is presented on fig. 4.1. Such curve can be constructed, if coordinates of four points named the control are known.
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| Rice 4.1. The General view of the elementary Bezier curve |
From four test points the curve transits only through two, therefore these points are called as reference ? anchor points (differently they are called as nodes (nodes), as the elementary curves with each other "connect" to form a uniform difficult circuit).
Two other test points do not lie on a curve, but their layout defines curvature of a curve, therefore these points differently are called as controlling points, and the lines connecting controlling and reference points, controlling line (in popular speech named by "levers").
The Bezier curve is a smooth curve, i.e. it has no ruptures and continuously fills a segment between initial and finite points.
The curve begins in the first reference point, concerning a segment of the controlling line, and comes to an end in the last reference point, also concerning a segment of the controlling line. It allows to connect smoothly two Bezier curves with each other: controlling lines are allocated along one straight line which is a tangent to turned out curve (fig. 4.2).
The curve lies in the convex jacket created by controlling lines (fig. 4.3). It testifies to stability ("well-behaved behavior") a curve.
The Bezier curve is symmetric, i.e. it saves the form if to change a direction of a vector of a curve on opposite ("to change in places" initial and finite reference points). This property finds the application at creation of composite circuits. Look about it in chapter 7.
Bezier curve, using mathematical language, "affinely it is invariant", i.e. it saves the form at scaling (fig. 4.4). This property is the base of freedom of a manipulation objects of vector graphics.
If exists only two test points (reference point) or controlling lines are collinear (lie on one straight line), the curve turns to a direct segment.
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| Rice 4.2. Smooth connection of two Bezier curves |
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| Rice 4.3. A convex jacket of curve Bez |
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| Rice 4.4. Scaling of a Bezier curve does not change its form |
Position change at least one of test points conducts to change of the form of all Bezier curve. This property ? a source of the infinite variety of forms of vectorial objects.
The circuit of the arbitrary form and the arbitrary complexity (restrictions appear in specific applications and specific technical systems) is made of set of such elementary curves.
Each element of vector graphics ? a circuit ? represents independent object which can be moved, scaled, changed indefinitely. Vector graphics often name also an object-oriented drawing.
The vector graphics were widely adopted because of the numerous advantages
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It is economical in respect of volumes of the disk space necessary for storage of images: it is connected by that the image but only some specification, in particular, coordinates of reference and controlling points, using which the program every time anew is saved not recreates the image. Besides, the description of color characteristics not strongly increases file size as the data about color is identical for all object. |
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Objects of vector graphics are easily transformed also by them easily to manipulate that does not render almost any influence on image quality in view of that image rasterization (space or linear sampling of elements is an inevitable stage) happens at the moment of an output to the exterior device (the screen or the printing device). |
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In those areas of a drawing where the basic value has saving of clear and accurate circuits, for example, in font compositions, in creation of logos, logos and other, vectorial programs are absolutely irreplaceable. |
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The vector graphics as much as possible use possibilities of resolution capability of any output device (the image will always look it so qualitative the given device how much allows). |
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The vector graphics can include and images of a pointwise drawing, and editors of vector graphics offer more and more various possibilities on their handling, including various filters. |
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Nota Bene. It is necessary to mean only that it essentially increases file volume. |
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Important advantage of programs of vector graphics is developed integration of vector images and the text, the uniform approach to them, and as consequence, ? possibility of creation of an end-product (unlike programs of a pointwise drawing). Therefore editors of vector graphics are irreplaceable in the field of design, technical drawing, for ??????????????????? and design operations. |
However, on the other hand, the vector graphics have also a row of lacks which should be meant.
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The most essential lack is program dependence as there is no the basic possibility to create a uniform standard format which would allow to open freely any vectorial document in any vectorial program. |
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The vector graphics can seem excessively hardish and as though "plywood". It is really restricted in purely picturesque means, in vector graphics programs it is almost impossible (or is unusually labor-consuming) to create photo-realistic images. Introduction of objects of new type ? a graded-index grid (gradient mesh) and objects with various types of a transparency is some attempt of overcoming of this lack. |
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Besides, the vectorial principle of the description of the image does not allow to automate graphic information input as it is done by the scanner or a numeral photocamera for the pointwise drawing. |
Vector graphics elements started to be used in programs of a pointwise drawing as auxiliary means for creation of a difficult circuit of the selected area, creation ???????????? a circuit.
The principle of coding of the graphic information in pointwise (raster, bit) to the schedule strongly differs from the vectorial.
It has been invented and used by people many centuries prior to computers, monitors and scanners. It and drawing "on sections" ? a productive method of transfer of the image from a preparatory cardboard on a wall intended for a fresco. It and such directions monumental and applied art, as a mosaic, a stained-glass window, an embroidery: in each of the enumerated techniques the image is under construction of discrete and, as a rule, color elements.
All point images are not set of separate objects, and a mosaic from very small elements ? ????????, characterized by position in a so-called bit card (the table, a matrix) and color characteristics. Everyone ?????? as the stone in a mosaic, is independent from each other.
The pointwise drawing in comparison with vectorial, strangely enough, has not enough advantages.
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The main advantage simplicity and, as consequence, a technical realizability of automation of input (digitization) of the graphic information is represented. There is a developed system of exterior devices for input of photos, slides, pictures, water colors and other graphic originals, scanners concern them, videocameras, numeral photocameras. These exterior devices are continuously improved, giving possibility of more and more adequate conversion of images on the material carriers (a paper, a film and etc.) in the numeral form. |
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He less important advantage of a pointwise drawing is possibility to create and process photo-realistic images. It is possible to receive picturesque effects, for example a fog or to a smoke, to achieve the most thin ??????????? color, to create perspective depth and blur, blur, ????????????? and etc. |
However essential lacks are inherent in the pointwise drawing also.
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The lack which is found out to draw at the first attempt something in the program of a pointwise drawing, consists that prior to the beginning of drawing she demands introduction of specific values of resolution (an amount of points on unit of length) and depths of color (an amount of color bits on ??????). Certainly, then these values can be changed, but, as a rule, it leads to those or other errors, and it is impossible to do it repeatedly and in very broad range. |
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The second lack does not decelerate to be shown at attempt to scan not so big photo with the maximum resolution and depth of color. The volume of a file for point image storage is defined ?????. Guiding of its area on resolution and on depth of color (if they are led to uniform dimensionality). Therefore the software of any scanner in a state to calculate this value and to predict volume for image saving. It is thus absolutely not important that is displayed on ?????????: a white snow landscape with a lonely figure in the distance, or a scene of a rock concert with an abundance of color and forms. If three parameters are identical ? the file size (without compression) in both cases will be almost identical. |
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The third lack floats at attempt slightly to turn the image, for example, with accurate thin vertical lines on a small corner. At once it is found out that accurate lines turn to "steps". It means that at any transformations (turns, scaling, inclinations and other) in the pointwise drawing it is impossible to do without distortions (it is dictated by the discrete nature of the image). It is possible even to tell that the pointwise drawing is easier for deforming, than to transform. Therefore in programs of a pointwise drawing the majority of filters ? various noise, blurs, waves, ripples (in the program of adobe Photoshop 6.0 it is included about hundred filters, half from them is presented and in Adobe Illustrator program) if to them to get accustomed, represent not that other as conscious distortion, i.e. the distortion made a principle, and art effect it is simple reception of an abstraction of attention. However, it is characteristic for any of arts. The information on filters of a pointwise drawing look in chapter 12. |
The pointwise drawing operates with elements (?????????), having certain color value and the unambiguous layout in a grid of a bit card (fig. 4.5).
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| Rice 4.5. The Point image and its fragment at the big magnification |
With such images pointwise graphics editors, for example, Adobe Photoshop work. Similar images turn out as a result of operation of command Rasterize (????????????) menu Object (Object) in Adobe Illustrator program.
At a choice of this command dialog box Rasterize (rasterization Parameters) (fig. 4.6) in which it is required to define all key parameters of the point image opens:
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Color model ? in uncovered list Color Model (Color model); |
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Resolution ? switch Resolution (Resolution). |
At setting of flag Create Clipping Mask (to Create ??????????? a mask) the point image forms with - the transparent background. Such images can appear useful at switching-on in the illustrations intended for layout in network WWW.
The vector graphics operate with mathematical objects which are independent of parameters of the exterior device (the monitor, the printer) (fig. 4.7).
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| Rice 4.6. ??????????? window Rasterize |
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| Rice 4.7. ?????????? the image and its fragment at the big magnification |
At editing of a pointwise drawing color of certain set ???????? changes. Color change has the result change of the form of represented subjects. The ratio of color and the form in the pointwise drawing can be defined as follows:
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Color and the form are nonseparable; |
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??? it is primary; |
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The form ? derivative of color; |
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In the pure state the form does not exist. |
Process of creation of images of a pointwise drawing, short of computer specificity, is almost identical to operation of the artist which at the expense of layout on a plane of dabs of color creates the illusory validity ? a space metaphor.
At vector graphics editing the object form changes first of all, and color plays a supporting role. The ratio of color and the form in vector graphics can be defined as follows:
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Color and the form are independent from each other; |
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The form is primary; |
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Color ? simply filler of the form; |
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In the pure state color does not exist. |
Process of creation of images of vector graphics, short of computer specificity, reminds operation of the artist-applikatista which of a white paper cuts forms, then colors their color or prints on them a cliche, decomposes them on a plane (including superimposing some of them) and by that creates a decorative composition.
Point images are good for creation of photo-realistic images with thin and various color passages.
Vector images are used for display of objects with a clear boundary and clear details, for example, fonts, logos, graphic signs, ornaments, decorative compositions in advertizing and polygraphic production.
To the user who is engaged in a computer (numeral) drawing, imposition of issuings, a composition, it is necessary to imagine precisely merits and demerits of two methods of representation of the graphic information, with advantage to use advantages and as far as possible to avoid lacks.