Milenkovic, V.J.: Rotational polygon containment and minimum enclosure using only robust 2d constructions. Computational Geometry 13 (1999) 3--19  Home/Search   Document Details and Download   Summary   Related Articles   Check

....it can be applied to optimize the sampling of the parameterizations constructed by our method. Charts packing in texture space. Finding the optimal packing of the charts in texture space is known as the bin packing problem. It has been studied by several authors, such as Milenkovic (see, e.g. [21]) but the resulting algorithms take a huge amount of time since the problem is NP complete. To speed up these computations, several heuristics have been proposed in the computer graphics community. In the case of individual triangles, such a method is described by several authors (see, e.g. ....

....non convex polygons, we want to find a non overlapping placement of the polygons in such a way that the enclosing rectangle is of minimum area. The so obtained texture coordinates are then re scaled to fit the size of the texture. The packing problem is known to be NP complete (see, e.g. [21] and [22] Approaches based on computational geometry show good performances in terms of minimization of lost area, but are not efficient enough for large and complex data sets. For this reason, several heuristics have been proposed in computer graphics. For instance, in the method proposed by ....

V. Milenkovic. Rotational polygon containment and minimum enclosure using only robust 2D constructions. Computational Geometry, 13(1):3--19, 1999.

....densely. Their approach achieves packing efficiencies close to those of human experts, but the nature of the medium (cloth) dictates that the polygons must follow the grain of the cloth and not be rotated. Even so, packing arbitrary polygons into a rectangular container is an NP hard problem [11]. The polygons in our problem are simpler, but must be rotated, so our goals are different. Moreover, we seek approximate, aesthetically pleasing packings; we do not need maximum density packings. Photomosaics [3, 12] approach the problem representing an image with coarse tiles by using ....

Milenkovic, V. Rotational Polygon Containment and Minimum Enclosure. Proceedings of the 14th Annual Symposium on Computational Geometry, (June 1998): 1-8.

....face. And, we prevent overlaps by checking for intersections using a spatial hash table. The next step is to arrange the chart images inside the unit square. Packing a set of non convex polygons into a given 2D domain is a well studied problem in computational geometry known as pants packing [11] due to its application in the clothing industry. Since the problem is NP hard, an exact solution cannot generally be computed. Heuristic algorithms for arranging on the order of a hundred polygons with no initial layout produce significantly worse results than a trained human. Therefore, we let ....

MILENKOVIC, V. J. Rotational polygon containment and minimum enclosure. Proc. of the 14th Annual Symp. on Computational Geometry, ACM (June 1998).

....Similarly, it intersects U 1 with the range of w 1 and U hi;j;i 0 ;i 1 i with the range of w hi;j;i 0 ;i 1 i . This last case involves only the intersection of convex polygonal regions with non convex polygonal regions. We implement this operation in oating point using nearest pair rounding [13]. Let R 0 be the range of w 0 in the relaxed problem. Since U 0 is already the intersection of a convex set with H 0 (Equation 5) it suces to replace U 0 with R 0 H 0 (instead of R 0 U 0 ) The intersection of a convex polygonal region with H 0 can at worst have multiple connected components, ....

V. J. Milenkovic. Rotational polygon containment and minimum enclosure using only robust 2d constructions. Computational Geometry: Theory and Applications, 13:3-19, 1999.

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Milenkovic, V.J.: Rotational polygon containment and minimum enclosure using only robust 2d constructions. Computational Geometry 13 (1999) 3--19

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V. Milenkovic. Rotational polygon containment and minimum enclosure using only robust 2D constructions. Computational Geometry, 13(1):3--19, 1999. 3

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