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Nearest-X: Objects are sorted by their first coordinate ("X") and then split into pages of the desired size. Packed Hilbert R-tree: variation of Nearest-X, but sorting using the Hilbert value of the center of a rectangle instead of using the X coordinate. There is no guarantee the pages will not overlap.
Animation of Fortune's algorithm, a sweep line technique for constructing Voronoi diagrams. In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface to solve various problems in Euclidean space. It is one of the critical techniques in computational ...
Above: monochrome screening; below: Gupta-Sproull anti-aliasing; the ideal line is considered here as a surface. In computer graphics, a line drawing algorithm is an algorithm for approximating a line segment on discrete graphical media, such as pixel-based displays and printers. On such media, line drawing requires an approximation (in ...
Thus, a non-leaf node in the Hilbert R-tree contains at most C n entries of the form (R, ptr, LHV) where C n is the capacity of a non-leaf node, R is the MBR that encloses all the children of that node, ptr is a pointer to the child node, and LHV is the largest Hilbert value among the data rectangles enclosed by R. Notice that since the non ...
In this algorithm, one recursively draws a line to split the vertices into two sets. The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line. Using some clever tricks, the merge operation can be done in time O( n ) , so the total running time is O( n log n ) .
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary parameter value. The algorithm is numerically stable [ 1 ] when compared to direct evaluation of polynomials.
As Fortune describes in ref., [1] a modified version of the sweep line algorithm can be used to construct an additively weighted Voronoi diagram, in which the distance to each site is offset by the weight of the site; this may equivalently be viewed as a Voronoi diagram of a set of disks, centered at the sites with radius equal to the weight of the site. the algorithm is found to have ...