Triangulating a convex polygon with fewer number of non-standard bars

Triangulating a convex polygon with fewer number of non-standard bars

For a given convex polygon with inner angle no less than 3π and boundary edge bounded by [l, αl] for 1 ≤ α ≤ 1.4, where l is a given standard bar’s length, we investigate the problem of triangulating the polygon using some Steiner points such that (i) the length of each edge in triangulation is bounded by [βl, 2l], where β is a given constant and meets 0 < β ≤ 1 2 , and (ii) the number of non-s...

Triangulating a Convex Polygon with Small Number of Non-standard Bars

For a given convex polygon with inner angle no less than 2 3 π and boundary edge bounded by [l, αl] for 1 ≤ α ≤ 1.4, where l is a given standard bar’s length, we investigate the problem of triangulating the polygon using some Steiner points such that (i) the length of each edge in triangulation is bounded by [βl, 2l], where β is a given constant and meets 0 < β < 1 2 , and (ii) the number of no...

Triangulating a Polygon in Parallel

In this paper we present a.n efficient pa.ra.Ilel algorithm. for polygon tria.ngu.Ia.tion. The algo-rithm we present runs in O(logn) time using D(n) processors, which is optimal if the polygon is allowed to contain holes. This improves the previous parallel complexity bounds for this problem by a log n factor. If we are also given a trapezoidal decomposition of the polygon as input, then we can...

Triangulating a Simple Polygon in Linear Time

Triangulating a simple polygon has been one of the most outstanding open problems in two-dimensional computational geometry. It is a basic primitive in computer graphics and, generally, seems the natural preprocessing step for most nontrivial operations on simple polygons [5,13]. Recall that to triangulate a polygon is t o partition it into triangles without adding any new vertices. Despite its...

Translating a convex polygon to contain maximum number of points