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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]
Asymptote is also notable for having a graphical interface coded in Python (and the Tk widget set), xasy.py – this allows an inexperienced user to quickly draw up objects and save them as .asy source code which can then be examined or edited by hand. The program's syntax was originally described by using a Yacc compatible grammar.
The algorithm selects one point p randomly and uniformly from P, and recursively finds the minimal circle containing P – {p}, i.e. all of the other points in P except p. If the returned circle also encloses p, it is the minimal circle for the whole of P and is returned. Otherwise, point p must lie on the boundary of the result circle.
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.
The algorithm consists of drawing pairs of pixels straddling the line, each coloured according to its distance from the line. Pixels at the line ends are handled separately. Lines less than one pixel long are handled as a special case. An extension to the algorithm for circle drawing was presented by Xiaolin Wu in the book Graphics Gems II ...
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
The language contains predefined basic linear objects: line, move, arrow, and spline, the planar objects box, circle, ellipse, arc, and definable composite elements. Objects are placed with respect to other objects or absolute coordinates. A liberal interpretation of the input invokes default parameters when objects are incompletely specified.
A workplane is plane with an origin for the new sketch where the SolveSpace draws entities. Users can make it active and draw basic primitives such as lines, circles, arcs, dots, and other points of references on the workplane, and constrain them to specific dimensions and relations. [15] SolveSpace can split intersecting entities via a ...