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AN O(n log log n)TIME ALGORITHM FOR TRIANGULATING A SIMPLE POLYGON
, 1988
"... Given a simple nvertex polygon, the triangulation problem is to partition the interior of the polygon into n2 triangles by adding n3 nonintersecting diagonals. We propose an O(n log logn)time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that tria ..."
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Cited by 37 (4 self)
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Given a simple nvertex polygon, the triangulation problem is to partition the interior of the polygon into n2 triangles by adding n3 nonintersecting diagonals. We propose an O(n log logn)time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that triangulation is not as hard as sorting. Improved algorithms for several other computational geometry problems, including testing whether a polygon is simple, follow from our result.
An Efficient Filling Algorithm for Nonsimple Closed Curves Using the Point Containment Paradigm
, 1997
"... . The Point Containment predicate which specifies if a point is part of a mathematically defined shape or not is one of the most basic notions in raster graphics. This paper presents a technique to counteract the main disadvantage of Point Containment algorithms: their quadratic time complexity wi ..."
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. The Point Containment predicate which specifies if a point is part of a mathematically defined shape or not is one of the most basic notions in raster graphics. This paper presents a technique to counteract the main disadvantage of Point Containment algorithms: their quadratic time complexity with increasing resolution. The implemented algorithm handles complex geometries such as selfintersecting closed curves. 1 Introduction The Point Containment paradigm is a natural way to perform raster graphics operations such as filling and stroking. However, Point Containmentbased algorithms generally have been judge to be too slow [14]. In [9], Forrest expressed the need for an eficient and robust algorithm to decide if a given point is part of a mathematically defined shape. Such an algorithm was later developed by Corthout et al. [2, 3, 4, 5] and implemented in dedicated silicon, the Pharos chip fabricated by Philips, on support of the PostScript page description language. The most ...