37 research outputs found

    On Deletion in Delaunay Triangulation

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    This paper presents how the space of spheres and shelling may be used to delete a point from a dd-dimensional triangulation efficiently. In dimension two, if k is the degree of the deleted vertex, the complexity is O(k log k), but we notice that this number only applies to low cost operations, while time consuming computations are only done a linear number of times. This algorithm may be viewed as a variation of Heller's algorithm, which is popular in the geographic information system community. Unfortunately, Heller algorithm is false, as explained in this paper.Comment: 15 pages 5 figures. in Proc. 15th Annu. ACM Sympos. Comput. Geom., 181--188, 199

    A novel optical granulometry algorithm for ore particles

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    This paper proposes a novel algorithm to detect the particle size distribution of ores with irregular shapes and dim edges. This optical granulometry algorithm is particularly suitable for blast furnace process control, so its result can be used directly as a reliable basis for control system dynamics optimization. The paper explains the algorithm and its concept, as well as its method, which consists of five steps to detect ore granularity and distribution. A series of comparative experiments under industrial environments proved that this novel algorithm, compared with conventional ones, improves the accuracy of granulometry

    Improved Incremental Randomized Delaunay Triangulation

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    We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the triangulation of a small sample of the levels below. Point location is done by marching in a triangulation to determine the nearest neighbor of the query at that level, then the march restarts from that neighbor at the level below. Using a small sample (3%) allows a small memory occupation; the march and the use of the nearest neighbor to change levels quickly locate the query.Comment: 19 pages, 7 figures Proc. 14th Annu. ACM Sympos. Comput. Geom., 106--115, 199

    Convex Tours of Bounded Curvature

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    We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with nn vertices. We present an O(m+n) time algorithm finding the path, going around the obstacle, whose curvature is the smallest possible.Comment: 11 pages, 5 figures, abstract presented at European Symposium on Algorithms 199
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