İstatiksel verilerin iki boyutlu grafiksel gösterimi

Abstract

Bu çalışmada, eğri ve nesne çizimlerine yönelik olarak, verilerin oluşturulması, analizi ve oluşturulan bu değerlerden yararlanılarak, eğri ve objelerin çizimi ile ilgili çeşitli algoritmalar kullanılmıştır. Verilerin oluşturulması ve analizi aşamasında; bir serinin alacağı değerlerin oluşturulması, bu değerlerin analizinde yardımcı olacak istatistiksel hesaplanmaların yapılması ile ilgili yöntemler uygulanmıştır. Aynı zamanda verilen bir fonksiyonun, bilgisayar tarafından incelenmesi (parse) ve yorumlanması da yapılmıştır. Çalışmada ayrıca, eğri çizimi ile ilgili özellik ve yöntemlerle, obje çizimi ile ilgili matematiksel dönüşümler kullanılarak, bunların bir görüntü ortamında çizimini yapan algoritmalar gerçekleştirilmiştir. Bu çalışma sırasında geliştirilen uygulamada, nesneye yönelik programlama yardıma bir araç olarak kullanılmış ve daha sonraki grafik çizimi ve veri analizi uygulamalarına temel teşkil edebilecek bir sistem kurulmaya çalışılmıştır.

In this study, a computer program is developed in order to show some statistical data, graphical on computer screen or printer. For this purpose, some commercial computer program package can be found, but the program developed in this study is different from them. It is very specific, easy to use, and user-friendly. The thesis is divided into five main parts. 1. Introduction 2. Computer sceen components 3. Graphics transformation methods for two-dimensional case 4. Statistical data and their relations 5. Drawing series and objects Computer Screen Components The display medium for computer graphics-generated pictures has become widely diversified. Typical examples are cathode ray tube (CRT) displays, flat panel displays, pen-and-ink plotters, dot matrix, electrostatic or laser printer plotters and film. In addition to display devices, image capture devices are becoming of increasing importance. The three most common types of CRT display technologies are direct-view storage tube (line drawing), calligraphic (line drawing) refresh and raster scan (point plotting) refresh displays. The most common types of flat panel displays include plasma-gas discharge, electroluminescent, liquid crystal and light-emitting diode technologies. With recent advances, an individual display may incorporate more than one technology. In discussing the various displays we take a user's, or conceptual, point of view; i.e., we are generally concerned with functional capabilities. Storage Tube Graphics Displays The direct- view storage tube1 is conceptually the simplest of the CRT displays. The storage tube displays, also called a bistable storage tube, can be considered a CRT 1 Storage tube graphics displays are no longer manufactured However, there are still literally thousands of them in use, hence the discussion. vıı with a long-persistence phosphor. A line or character remains visible (up to an hour) until erased. Calligraphic Refresh Graphics Displays In contrast to the storage tube displays, a calligraphic (line drawing or vector) refresh CRT display uses a very short persistence phosphor. These displays are frequently called random scan displays. Because of the short persistence of the phosphor, the picture painted on the CRT must be repainted or refresh many times each second. The minimum refresh rate is at least 30 times each second, with a recommended rate of 40 to 50 times each second. Refresh rates much lower than 30 times each second result flickering image. The effect is similar to that observed when a movie film is run too slowly. The resuting picture is difficult to use and disagreeable to look at. The basic calligraphic refresh display requires two elements in addition to the CRT. These are the display buffer and the display controller. The display buffer is contiguous computer memory containing all the information required to draw the picture on the CRT. The display controller's function is to repeatedly cycle through this information at the refresh rate. Two factors which limit the complexity (number of vectors displayed) of the picture are the size of the display buffer and the speed of the display controller. Raster Refresh Graphics Displays Both the storage tube CRT display and the calligraphic refresh displays are line drawing devices. That is, a straight line can be drawn directly from any addressable point to any other addressable point. In contrast, the raster CRT graphics display is a point plotting device. A raster graphic device can be considered a matrix of discrete cells, each of which can be made bright. It is not possible, except in special cases, to directly draw a straight line from one addressable point or pixel (picture element), in the matrix to another addressable point or pixel. The line can be approximated by a series of dots (pixels) close to then path of the line. The most common method of implementing a raster CRT graphics device uses a frame buffer. A frame buffer is a large, contiguous piece of computer memory. As a minimum there is a one memory bit for each pixel in the raster. This amount of memory is called a bit plane. A 512x512 element square raster requires 218 (29 = 512; 218 = 512x512) or 262,144 memory bits a single bit plane. The picture is built up in the frame buffer 1 bit at a time. Since a memory bit has only two states (binary 0 or 1) a single bit plane yields a black-and-white (monochrome) display. Since the frame buffer is a digital device, while the raster CRT is an analog device, conversion from a digital representation to an analog signal must take place when information is read from the frame buffer and displayed oh the raster CRT graphics device. This is accomplished by a digital-to-analog converter (DAC). Each pixel in the frame buffer must be accessed and and converted before it is visible on the raster CRT. vm Drawing Object and Series Drawing can be considered in in two groups: showing statistical series and drawing objects. Statistical Graphics: In this case, one or more data series can be show as a graphic on a computer screen. Statistical graphics can be line, bar, area, xy scatter or pie. These graphics have different properties depending on data types. For example pie graphs shows the percentage of elements in the total value of the series. Therefore, it can not be used the second series in pie graphs. In this study, the graphics are considered as an object, and subdivided some useful objects; graph titles, horizontal axis titles, vertical axis titles, series titles and graph area. Graph area is also subdivided into three objects which they are x-axis, y-axis and series. In the developed program each object draws itself, and chooses its own window location. xu Cathode Ray Tube Basics A frame buffer as described above is not itself a display device. It is simply used to assemble and hold a digital representation of the picture. The most common display device used with a frame buffer is a video (TV) monitor. An understanding of the raster displays, and to some extent line drawing refresh displays, requires a basic understanding of CRT's display techniques. It is at this point that line drawing displays, both storage and refresh, and raster scan displays differ. In a line drawing display the electron beam may be deflected directly from an arbitrary position to any other arbitrary position on the face of the CRT. A perfectly straight line results. In contrast, in a raster scan display the beam is deflected in a set, rigidly controlled pattern. This pattern comprises the video picture. Color CRT Raster Scan Basics A color raster scan CRT is a similar to then standard black-and-white CRT described in the previous section. In the color raster scan CRT there are three electronic guns, one for each of the primary colors, red, green and blue. The electronic guns are frequently arranged in a triangular pattern corresponding to a similar triangular pattern of red, green and blue phosphor dots on the face of the CRT. Graphics Transformation Methods for Two-Dimensional Case Points and lines which join them, along with an apporpiate drawing algorithm, we used to represent objects or to display information graphically. When visualing an object, it may be desirable to scale, rotate, translate, distort or develop a perspective view of the object. Representation of Points A point is represented in two dimensions by its coordinates. These two values are specified as the elements of a 1-row, 2-column matrix: [X] = [xy] In three dimensions a 1 x 3 matrix [X] = [xyz] is used. Alternately, a point is represent by a 2-row, 1 -column matrix [x], in two dimensions or by IX Cathode Ray Tube Basics A frame buffer as described above is not itself a display device. It is simply used to assemble and hold a digital representation of the picture. The most common display device used with a frame buffer is a video (TV) monitor. An understanding of the raster displays, and to some extent line drawing refresh displays, requires a basic understanding of CRT's display techniques. It is at this point that line drawing displays, both storage and refresh, and raster scan displays differ. In a line drawing display the electron beam may be deflected directly from an arbitrary position to any other arbitrary position on the face of the CRT. A perfectly straight line results. In contrast, in a raster scan display the beam is deflected in a set, rigidly controlled pattern. This pattern comprises the video picture. Color CRT Raster Scan Basics A color raster scan CRT is a similar to then standard black-and-white CRT described in the previous section. In the color raster scan CRT there are three electronic guns, one for each of the primary colors, red, green and blue. The electronic guns are frequently arranged in a triangular pattern corresponding to a similar triangular pattern of red, green and blue phosphor dots on the face of the CRT. Graphics Transformation Methods for Two-Dimensional Case Points and lines which join them, along with an apporpiate drawing algorithm, we used to represent objects or to display information graphically. When visualing an object, it may be desirable to scale, rotate, translate, distort or develop a perspective view of the object. Representation of Points A point is represented in two dimensions by its coordinates. These two values are specified as the elements of a 1-row, 2-column matrix: [X] = [xy] In three dimensions a 1 x 3 matrix [X] = [xyz] is used. Alternately, a point is represent by a 2-row, 1 -column matrix [x], in two dimensions or by IX Drawing Object and Series Drawing can be considered in in two groups: showing statistical series and drawing objects. Statistical Graphics: In this case, one or more data series can be show as a graphic on a computer screen. Statistical graphics can be line, bar, area, xy scatter or pie. These graphics have different properties depending on data types. For example pie graphs shows the percentage of elements in the total value of the series. Therefore, it can not be used the second series in pie graphs. In this study, the graphics are considered as an object, and subdivided some useful objects; graph titles, horizontal axis titles, vertical axis titles, series titles and graph area. Graph area is also subdivided into three objects which they are x-axis, y-axis and series. In the developed program each object draws itself, and chooses its own window location.