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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
The Rytz’s axis construction is a basic method of descriptive geometry to find the axes, the semi-major axis and semi-minor axis and the vertices of an ellipse, starting from two conjugated half-diameters. If the center and the semi axis of an ellipse are determined the ellipse can be drawn using an ellipsograph or by hand (see ellipse).
Algorithms used in Computer graphics. See also Category:Computer graphics data structures . Wikimedia Commons has media related to Computer graphic algorithms .
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 ...
This algorithm requires log 2 (d) iterations of point doubling and addition to compute the full point multiplication. There are many variations of this algorithm such as using a window, sliding window, NAF, NAF-w, vector chains, and Montgomery ladder.
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.