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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]
The Bresenham Line-Drawing Algorithm by Colin Flanagan; National Institute of Standards and Technology page on Bresenham's algorithm; Calcomp 563 Incremental Plotter Information; Bresenham Algorithm in several programming languages; The Beauty of Bresenham’s Algorithm — A simple implementation to plot lines, circles, ellipses and Bézier curves
A good description of what I think is the correct midpoint circle drawing algorithm (in its more general form for ellipses) is given in this paper: Jerry R. Van Aken: An Efficient Ellipse-Drawing Algorithm. IEEE Computer Graphics and Applications 4(9): 24-35 (1984) Note that use of the midpoint is an essential part of the method.
In pseudocode, this algorithm would look as follows. The algorithm does not use complex numbers and manually simulates complex-number operations using two real numbers, for those who do not have a complex data type. The program may be simplified if the programming language includes complex-data-type operations.
A simple way to parallelize single-color line rasterization is to let multiple line-drawing algorithms draw offset pixels of a certain distance from each other. [2] Another method involves dividing the line into multiple sections of approximately equal length, which are then assigned to different processors for rasterization. The main problem ...
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 ...
Force-directed graph drawing algorithms assign forces among the set of edges and the set of nodes of a graph drawing.Typically, spring-like attractive forces based on Hooke's law are used to attract pairs of endpoints of the graph's edges towards each other, while simultaneously repulsive forces like those of electrically charged particles based on Coulomb's law are used to separate all pairs ...
In geometry, the Steiner inellipse, [1] midpoint inellipse, or midpoint ellipse of a triangle is the unique ellipse inscribed in the triangle and tangent to the sides at their midpoints. It is an example of an inellipse .