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A circle of radius 23 drawn by the Bresenham algorithm. In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. It is a generalization of Bresenham's line algorithm. The algorithm can be further generalized to conic sections. [1] [2] [3]
An extension to the original algorithm called the midpoint circle 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.
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. [3] [4] Ph.D., Stanford University, 1964; MSIE, Stanford University, 1960; BSEE, University of New Mexico, 1959
Midpoint_circle_algorithm,_radius_23.png (589 × 589 pixels, file size: 3 KB, MIME type: image/png) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
Raskin invited Atkinson to visit him at Apple Computer; Steve Jobs persuaded him to join the company immediately as employee No. 51, and Atkinson never finished his PhD. [3] [4] Atkinson was the principal designer and developer of the graphical user interface (GUI) of the Apple Lisa and, later, one of the first thirty members of the original Apple Macintosh development team, [5] and was the ...
Midpoint circle algorithm; Minimum bounding box; Minimum bounding box algorithms; Minimum bounding rectangle; Minimum-diameter spanning tree; Minkowski addition; Minkowski Portal Refinement; Möller–Trumbore intersection algorithm; Monotone polygon; Multiple line segment intersection
English: An illustration of two octants of the w:Midpoint circle algorithm (also known as Bresenham's circle algorithm). Vector version of public domain image w:File:Bresenham_circle3.png on English Wikipedia.
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that