37 research outputs found
On Deletion in Delaunay Triangulation
This paper presents how the space of spheres and shelling may be used to
delete a point from a -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
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New algorithms for minimum-measure simplices and one-dimensional weighted Voronoi diagrams
We present two new algorithms for finding the minimum-measure simplex determined by a set of n points in R^d for arbitrary d >/= 2. The first algorithm runs in time O(n^d log n) using O(n) space. The only data structure used by this algorithms a stack. The second algorithm runs in time O(n^d) using O(n^2) space, which matches the best known time bounds for this problem in all dimensions and exceeds the previous best space bounds for all d > 3. We also present a new optimal algorithm for building one-dimensional multiplicatively weighted Voronoi diagrams that runs in linear time if the points are already sorted
A novel optical granulometry algorithm for ore particles
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
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
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 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