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Circle Drawing 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. Summary This algorithm draws all eight octants simultaneously, starting from each cardinal direction (0°, 90°, 180°, 270°) and extends both ways to reach the nearest multiple of 45° (45°, 135°, 225°, 315°). It can determine where to stop because, when = , it has reached 45°. The reason for using these angles is shown in the above picture: As increases, it neither skips nor repeats any value until reaching 45°. So during the ''while'' loop, increments by 1 with each iteration, and decrements by 1 on occasion, never exceeding 1 in one iteration. This changes at 45° because that is the point where the tangent is =. Whereas before and after. The second part of the problem, the determinant, is far trickier. This determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Midpoint Circle Algorithm Animation (radius 23)
In geometry, the midpoint is the middle point (geometry), point of a line segment. It is Distance, equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It Bisection, bisects the segment. Formula The midpoint of a segment in ''n''-dimensional space whose endpoints are A = (a_1, a_2, \dots , a_n) and B = (b_1, b_2, \dots , b_n) is given by :\frac. That is, the ''i''th coordinate of the midpoint (''i'' = 1, 2, ..., ''n'') is :\frac 2. Construction Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction. The midpoint of a line segment, embedded in a Plane (geometry), plane, can be located by first constructing a Lens (geometry), lens using circular arcs of equal (and large enough) radius, radii centered at the two endpoints, then connecting the cusp (singularity), cusps of the lens (the two points where the arcs intersect). The point where th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |