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Note for Computer Graphics - CG by Firoj Ahammed

  • Computer Graphics - CG
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  • Computer Science Engineering
  • B.Tech
  • 8 Topics
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Electrostatic deflection of the electron beam in a CRT An electron gun emits a beam of electrons, which passes through focusing and deflection systems and hits on the phosphor-coated screen. The number of points displayed on a CRT is referred to as resolutions (eg. 1024x768). Different phosphors emit small light spots of different colors, which can combine to form a range of colors. A common methodology for color CRT display is the Shadow-mask meth

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Illustration of a shadow-mask CRT The light emitted by phosphor fades very rapidly, so it needs to redraw the picture repeatedly. There are 2 kinds of redrawing mechanisms: Raster-Scan and Random-Scan 1.2.2 Raster-Scan The electron beam is swept across the screen one row at a time from top to bottom. As it moves across each row, the beam intensity is turned on and off to create a pattern of illuminated spots. This scanning process is called refreshing. Each complete scanning of a screen is normally called a frame. The refreshing rate, called the frame rate, is normally 60 to 80 frames per second, or described as 60 Hz to 80 Hz. Picture definition is stored in a memory area called the frame buffer. This frame buffer stores the intensity values for all the screen points. Each screen point is called a pixel (picture element). On black and white systems, the frame buffer storing the values of the pixels is called a bitmap. Each entry in the bitmap is a 1-bit data which determine the on (1) and off (0) of the intensity of the pixel. On color systems, the frame buffer storing the values of the pixels is called a pixmap (Though nowadays many graphics libraries name it as bitmap too). Each entry in the pixmap occupies a number of bits to represent the color of the pixel. For a true color display, the number of bits for each entry is 24 (8 bits per red/green/blue channel, each channel 28=256 levels of intensity value, ie. 256 voltage settings for each of the red/green/blue electron guns).

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1.2.3 Random-Scan (Vector Display) The CRT's electron beam is directed only to the parts of the screen where a picture is to be drawn. The picture definition is stored as a set of line-drawing commands in a refresh display file or a refresh buffer in memory. Random-scan generally have higher resolution than raster systems and can produce smooth line drawings, however it cannot display realistic shaded scenes. Display Controller For a raster display device reads the frame buffer and generates the control signals for the screen, ie. the signals for horizontal scanning and vertical scanning. Most display controllers include a color map (or video look-up table). The major function of a color map is to provide a mapping between the input pixel value to the output color. Anti-Aliasing On dealing with integer pixel positions, jagged or stair step appearances happen very usually. This distortion of information due to under sampling is called aliasing. A number of ant aliasing methods have been developed to compensate this problem. One way is to display objects at higher resolution. However there is a limit to how big we can make the frame buffer and still maintaining acceptable refresh rate. Drawing a Line in Raster Devices 1.3 DDA Algorithm In computer graphics, a hardware or software implementation of a digital differential analyzer (DDA) is used for linear interpolation of variables over an interval between start and end point. DDAs are used for rasterization of lines, triangles and polygons. In its simplest implementation the DDA Line drawing algorithm interpolates values in interval [(xstart, ystart), (xend, yend)] by computing for each xi the equations xi = xi−1+1/m, yi = yi−1 + m, where Δx = xend − xstart and Δy = yend − ystart and m = Δy/Δx. The dda is a scan conversion line algorithm based on calculating either dy or dx. A line is sampled at unit intervals in one coordinate and corresponding integer values nearest the line path

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are determined for other coordinates. Considering a line with positive slope, if the slope is less than or equal to 1, we sample at unit x intervals (dx=1) and compute successive y values as Subscript k takes integer values starting from 0, for the 1st point and increases by until endpoint is reached. y value is rounded off to nearest integer to correspond to a screen pixel. For lines with slope greater than 1, we reverse the role of x and y i.e. we sample at dy=1 and calculate consecutive x values as Similar calculations are carried out to determine pixel positions along a line with negative slope. Thus, if the absolute value of the slope is less than 1, we set dx=1 if i.e. the starting extreme point is at the left. The basic concept is: - A line can be specified in the form: y = mx + c - Let m be between 0 to 1, then the slope of the line is between 0 and 45 degrees. - For the x-coordinate of the left end point of the line, compute the corresponding y value according to the line equation. Thus we get the left end point as (x1,y1), where y1 may not be an integer. - Calculate the distance of (x1,y1) from the center of the pixel immediately above it and call it D1 - Calculate the distance of (x1,y1) from the center of the pixel immediately below it and call it D2 - If D1 is smaller than D2, it means that the line is closer to the upper pixel than the lower pixel, then, we set the upper pixel to on; otherwise we set the lower pixel to on. - Then increatement x by 1 and repeat the same process until x reaches the right end point of the line. - This method assumes the width of the line to be zero 1.4 Bresenham's Line Algorithm This algorithm is very efficient since it use only incremental integer calculations. Instead of calculating the non-integral values of D1 and D2 for decision of pixel location, it computes a value, p, which is defined as: p = (D2-D1)* horizontal length of the line if p>0, it means D1 is smaller than D2, and we can determine the pixel location accordingly However, the computation of p is very easy: The initial value of p is 2 * vertical height of the line - horizontal length of the line.

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