In an axiomatic system, which category do points, lines, and planes belong to?
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Point plotting is accomplished by converting a single coordinate position furnished by an application program into appropriate operations for [he output device in use. With a CRT monitor, for example, the electron beam is turned on to illuminate the screen phosphor at the selected location. How the electron beam is positioned depends on the display technology. A random-scan (vector) system stores point-plotting instructions in the display list, and coordinate values in these instructions are converted to deflection voltages that position the electron beam at the screen locations to be plotted during each refresh cycle. For a blackand- white raster system, on the other hand, a point is plotted by setting the bit value corresponding to A specified screen position within the frame buffer to 1. Then, as the electron beam sweeps across each horizontal scan line, it emits a burst of electrons (plots a point) whenever a value of I is encounted in the sMian3-1 frame buffer. With an RGB system, the frame buffer is loaded with the color Pointsand hnes codes for the intensities that are to be displayed at the s m n pixel positions. Line drawing is accomplished by calculating intermediate positions along the line path between two specified endpoint positions. An output device is then directed to fill in these positions between the endpoints. For analog devices, such as a vector pen plotter or a random-scan display, a straight line can be drawn smoothly from one endpoint to the other. Linearly varying horizontal and vertical deflection voltages are generated that are proportional to the required changes in the x and y directions to produce the smooth line. Digital devices display a straight line segment by plotting discrete points between the two endpoints. Discrete coordinate positions along the line path are calculated from the equation of the line. For a raster video display, the line color (intensity) is then loaded into the frame buffer at the corresponding pixel coordinates. Reading from the frame buffer, the video controller then "plots" the screen pixels. Screen locations are xeferenced with integer values, so plotted positions may only approximate actual Line positions between two specified endpoints. A computed line position of (10.48,20.51), for example, would be converted to pixel position (10,211. Tlus rounding of coordinate values to integers causes lines to be displayed with a stairstep appearance ("the jaggies"), as represented in Fig 3-1. The characteristic stairstep shape of raster lines is particularly noticeable on systems with low resolution, and we can improve their appearance somewhat by displaying them on high-resolution systems. More effective techniques for smoothing raster lines are based on adjusting pixel intensities along the line paths. For the raster-graphics device-level algorithms discussed in this chapter, obp- t positions are specified directly in integer device coordinates. For the time being, we will assume that pixel positions are referenced according to scan-line number and column number (pixel position across a scan line). This addressing scheme is illustrated in Fig. 3-2. Scan lines are numbered consecutively from 0, starting at the bottom of the screen; and pixel columns are numbered from 0, left to right across each scan line. In Section 3-10, we consider alternative pixel addressing schemes. To load a specified color into the frame buffer at a position corresponding to column x along scan line y, we will assume we have available a low-level procedure of the form Figure 3-1 Staintep effect (jaggies) produced when a line is generated as a series of pixel positions. Line Number - Plxd Column Number Figure 3-2 Pie1 positions referenced by scanline number and column number. We sometimes will also want to be able to retrieve the current framebuffer intensity setting for a specified location. We accomplish this with the low-level fundion getpixel (x, y )