Symbolic Treatment of Geometric Degeneracies
Symbolic Treatment of Geometric Degeneracies
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In our eReader you can find the full English version of the book. Read Symbolic Treatment of Geometric Degeneracies Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Symbolic Treatment of Geometric Degeneracies
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Clearly the combinatorial structure of the perturbed Voronoi diagram is different from the original Voronoi diagram. So, in the combinatorial sense, the problem would not seem stable. Another attempt at trying to show that the problem is stable is this: use the Hausdorff metric on closed point sets. Unfortunately a small perturbation may introduce an infinite Hausdorff distance between the two Voronoi di- agrams. [Consider the diagram of two points p = (-1, 0) and q = ( + 1, 0) and then perturb... one of the points top' = {6 - 1, 0) for all 0. ] Now suppose our goal is to use this Voronoi diagram to compute an obstacle-avoiding path for a unit disc between two specified points P and Q, viewing these sites as obstacles. (It follows from [15], that to find such a path, it is sufficient to look for one path in which the center of the disc lies in the Voronoi diagram. ) Let the set of n sites be represented by a £ f^ (where d = 2n and £"'' is the Euclidean d-dimensional space). It is natural to measure the 'connection width' between any two points P and Q in the plane by the quantity C(P, Q;a) > defined as the maximum value attained by the clearance of some path from P to Q in the presence of obstacles defined by a.
What to read after Symbolic Treatment of Geometric Degeneracies?
You can find similar books in the "Read Also" column, or choose other free books by Chee K Yap to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Clearly the combinatorial structure of the perturbed Voronoi diagram is different from the original Voronoi diagram. So, in the combinatorial sense, the problem would not seem stable. Another attempt at trying to show that the problem is stable is this: use the Hausdorff metric on closed point sets. Unfortunately a small perturbation may introduce an infinite Hausdorff distance between the two Voronoi di- agrams. [Consider the diagram of two points p = (-1, 0) and q = ( + 1, 0) and then perturb... one of the points top' = {6 - 1, 0) for all 0. ] Now suppose our goal is to use this Voronoi diagram to compute an obstacle-avoiding path for a unit disc between two specified points P and Q, viewing these sites as obstacles. (It follows from [15], that to find such a path, it is sufficient to look for one path in which the center of the disc lies in the Voronoi diagram. ) Let the set of n sites be represented by a £ f^ (where d = 2n and £"'' is the Euclidean d-dimensional space). It is natural to measure the 'connection width' between any two points P and Q in the plane by the quantity C(P, Q;a) > defined as the maximum value attained by the clearance of some path from P to Q in the presence of obstacles defined by a.
What to read after Symbolic Treatment of Geometric Degeneracies?
You can find similar books in the "Read Also" column, or choose other free books by Chee K Yap to read onlineMoreLess
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