Bresenham's Line Algorithm
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Bresenham's Line Algorithm
Bresenham's line algorithm is a line drawing algorithm that determines the points of an ''n''-dimensional raster that should be selected in order to form a close approximation to a straight line between two points. It is commonly used to draw line primitives in a bitmap image (e.g. on a computer screen), as it uses only integer addition, subtraction and bit shifting, all of which are very cheap operations in commonly used computer instruction sets such as x86_64. It is an incremental error algorithm, and one of the earliest algorithms developed in the field of computer graphics. An extension to the original algorithm may be used for drawing circles. While algorithms such as Wu's algorithm are also frequently used in modern computer graphics because they can support antialiasing, Bresenham's line algorithm is still important because of its speed and simplicity. The algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards. It can also be fou ...
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Line Drawing Algorithm
In computer graphics, a line drawing algorithm is an algorithm for approximating a line segment on discrete graphical media, such as pixel-based displays and printers. On such media, line drawing requires an approximation (in nontrivial cases). Basic algorithms rasterize lines in one color. A better representation with multiple color gradations requires an advanced process, spatial anti-aliasing. On continuous media, by contrast, no algorithm is necessary to draw a line. For example, cathode-ray oscilloscopes use analog phenomena to draw lines and curves. List of line drawing algorithms The following is a partial list of line drawing algorithms: * Naive algorithm * Digital Differential Analyzer (graphics algorithm) — Similar to the naive line-drawing algorithm, with minor variations. *Bresenham's line algorithm — optimized to use only additions (i.e. no division Multiplications); it also avoids floating-point computations. *Xiaolin Wu's line algorithm — can perform s ...
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Graphics Card
A graphics card (also called a video card, display card, graphics adapter, VGA card/VGA, video adapter, display adapter, or mistakenly GPU) is an expansion card which generates a feed of output images to a display device, such as a computer monitor. Graphics cards are sometimes called discrete or dedicated graphics cards to emphasize their distinction to Graphics processing unit#Integrated graphics, integrated graphics. A graphics processing unit that performs the necessary computations is the main component of a graphics card, but the acronym "GPU" is sometimes also used to refer to the graphics card as a whole. Most graphics cards are not limited to simple display output. The graphics processing unit can be used for additional processing, which reduces the load from the central processing unit. Additionally, computing platforms such as OpenCL and CUDA allow using graphics cards for General-purpose computing on graphics processing units, general-purpose computing. Applications o ...
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Pixel Center
In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device. In most digital display devices, pixels are the smallest element that can be manipulated through software. Each pixel is a sample of an original image; more samples typically provide more accurate representations of the original. The intensity of each pixel is variable. In color imaging systems, a color is typically represented by three or four component intensities such as red, green, and blue, or cyan, magenta, yellow, and black. In some contexts (such as descriptions of camera sensors), ''pixel'' refers to a single scalar element of a multi-component representation (called a ''photosite'' in the camera sensor context, although ''sensel'' is sometimes used), while in yet other contexts (like MRI) it may refer to a set of component intensities for a spatial position. Etymology The w ...
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Slope
In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is used for slope, but its earliest use in English appears in O'Brien (1844) who wrote the equation of a straight line as and it can also be found in Todhunter (1888) who wrote it as "''y'' = ''mx'' + ''c''". Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical – as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan. The ''steepness'', incline, or grade of a line is measured by the absolute ...
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Octant (plane Geometry)
A circular sector, also known as circle sector or disk sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, where the smaller area is known as the ''minor sector'' and the larger being the ''major sector''. In the diagram, is the central angle, r the radius of the circle, and L is the arc length of the minor sector. The angle formed by connecting the endpoints of the arc to any point on the circumference that is not in the sector is equal to half the central angle. Types A sector with the central angle of 180° is called a '' half-disk'' and is bounded by a diameter and a semicircle. Sectors with other central angles are sometimes given special names, such as quadrants (90°), sextants (60°), and octants (45°), which come from the sector being one 4th, 6th or 8th part of a full circle, respectively. Confusingly, the arc of a quadrant (a circular arc) can also be termed a quadrant. Compass Traditionally wind ...
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Bresenham
Jack Elton Bresenham (born 11 October 1937, Clovis, New Mexico, US) is a former professor of computer science. Biography Bresenham retired from 27 years of service at IBM as a Senior Technical Staff Member in 1987. He taught for 16 years at Winthrop University and has nine patents. He has four children: Janet, Craig, Linda, and David. Bresenham's line algorithm, developed in 1962, is his most well-known innovation. It determines which points on a 2-dimensional raster should be plotted in order to form a straight line between two given points, and is commonly used to draw lines on a computer screen. It is one of the earliest algorithms discovered in the field of computer graphics. The midpoint circle algorithm shares some similarities to his line algorithm and is known as ''Bresenham's circle algorithm''. * Ph.D., Stanford University, 1964 * MSIE, Stanford University, 1960 * BSEE, University of New Mexico, 1959 See also * List of computer scientists * Bresenham's line algorit ...
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Association For Computing Machinery
The Association for Computing Machinery (ACM) is a US-based international learned society for computing. It was founded in 1947 and is the world's largest scientific and educational computing society. The ACM is a non-profit professional membership group, claiming nearly 110,000 student and professional members . Its headquarters are in New York City. The ACM is an umbrella organization for academic and scholarly interests in computer science ( informatics). Its motto is "Advancing Computing as a Science & Profession". History In 1947, a notice was sent to various people: On January 10, 1947, at the Symposium on Large-Scale Digital Calculating Machinery at the Harvard computation Laboratory, Professor Samuel H. Caldwell of Massachusetts Institute of Technology spoke of the need for an association of those interested in computing machinery, and of the need for communication between them. ..After making some inquiries during May and June, we believe there is ample interest to ...
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IBM 1401
The IBM 1401 is a variable-wordlength decimal computer that was announced by IBM on October 5, 1959. The first member of the highly successful IBM 1400 series, it was aimed at replacing unit record equipment for processing data stored on punched cards and at providing peripheral services for larger computers. The 1401 is considered to be the Ford Model-T of the computer industry, because it was mass-produced and because of its sales volume. Over 12,000 units were produced and many were leased or resold after they were replaced with newer technology. The 1401 was withdrawn on February 8, 1971. History The 1401 project evolved from an IBM project named World Wide Accounting Machine (WWAM), which in turn was a reaction to the success of Bull Gamma 3 (fr). The 1401 was operated as an independent system, in conjunction with IBM punched card equipment, or as auxiliary equipment to IBM 700 or 7000 series systems. Monthly rental for 1401 configurations started at US$2,500 (wort ...
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Calcomp Plotter
Calcomp plotters (sometimes referred to as CalComp plotters) were the best known products of the California Computer Products company ( Calcomp or CalComp). Overview The Calcomp 565 drum plotter, introduced in 1959, was one of the first computer graphics output devices sold. The computer could control in increments the rotation of an wide drum, and the horizontal movement of a pen holder over the drum. The pen was pressed by a spring against paper scrolling across the drum. A solenoid could lift the pen off the paper. This arrangement allowed line drawings to be made under computer control. Later, Calcomp manufactured its model 563, which was very similar but had a wide drum. The paper rolls were long. A metal bar above the take-up reel allowed a finished plot to be torn off and removed. The drum would then be advanced using the manual controls and the fresh paper end taped to the take-up reel. The standard pen was a ball-point, but liquid ink pens were available, and typi ...
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National Institute Of Standards And Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical science laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards. History Background The Articles of Confederation, ratified by the colonies in 1781, provided: The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States. Article 1, section 8, of the Constitution of the United States, ratified in 1789, granted these powers to the new Congr ...
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Jack Elton Bresenham
Jack Elton Bresenham (born 11 October 1937, Clovis, New Mexico, US) is a former professor of computer science. Biography Bresenham retired from 27 years of service at IBM as a Senior Technical Staff Member in 1987. He taught for 16 years at Winthrop University and has nine patents. He has four children: Janet, Craig, Linda, and David. Bresenham's line algorithm, developed in 1962, is his most well-known innovation. It determines which points on a 2-dimensional raster should be plotted in order to form a straight line between two given points, and is commonly used to draw lines on a computer screen. It is one of the earliest algorithms discovered in the field of computer graphics. The midpoint circle algorithm shares some similarities to his line algorithm and is known as ''Bresenham's circle algorithm''. * Ph.D., Stanford University, 1964 * MSIE, Stanford University, 1960 * BSEE, University of New Mexico, 1959 See also * List of computer scientists * Bresenham's line alg ...
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Graphics Hardware
Graphics hardware is computer hardware that generates computer graphics and allows them to be shown on a display, usually using a graphics card (video card) in combination with a device driver to create the images on the screen. Types Graphics cards The most important piece of graphics hardware is the graphics card, which is the piece of equipment that renders out all images and sends them to a display. There are two types of graphics cards: integrated and dedicated. An integrated graphics card, usually by Intel to use in their computers, is bound to the motherboard and shares RAM(Random Access Memory) with the CPU, reducing the total amount of RAM available. This is undesirable for running programs and applications that use a large amount of video memory. A dedicated graphics card has its own RAM and Processor for generating its images, and does not slow down the computer. Dedicated graphics cards also have higher performance than integrated graphics cards. It is possi ...
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