The Shortest Watchtower And Related Problems for Polyhedral Terrains
The Shortest Watchtower And Related Problems for Polyhedral Terrains
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In our eReader you can find the full English version of the book. Read The Shortest Watchtower And Related Problems for Polyhedral Terrains 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 The Shortest Watchtower And Related Problems for Polyhedral Terrains
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Let e = ab be an edge of S. For each Ostrsl define u(t)= (l-/)a + tb € e, and v(r) = the point on L lying directly above w(f). Let F t (t)= |«(r)v(r)|. It is easily checked that F e is a piecewise linear convex function of t (where breakpoints on F e occur when v(f) lies on an edge of L). It therefore has a global minimum which is attained either at a breakpoint or in some subinterval of e between adjacent breakpoints. Moreover, given any point u(t) on e, if we know the corresponding point v(»)... and the face of L on which it lies, then we can deter- mine, in constant additional time, on which side of u (t) the minimum of F e is attained, or that this minimum is attained at t itself. (Note also that finding v(f), given «(f), can be done in 0(log n) time, by locating the projection u*(t) of u(t) in the map L* . ) To elaborate this observation, let 0
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To quickly assess the difficulty of the text, read a short excerpt:
Let e = ab be an edge of S. For each Ostrsl define u(t)= (l-/)a + tb € e, and v(r) = the point on L lying directly above w(f). Let F t (t)= |«(r)v(r)|. It is easily checked that F e is a piecewise linear convex function of t (where breakpoints on F e occur when v(f) lies on an edge of L). It therefore has a global minimum which is attained either at a breakpoint or in some subinterval of e between adjacent breakpoints. Moreover, given any point u(t) on e, if we know the corresponding point v(»)... and the face of L on which it lies, then we can deter- mine, in constant additional time, on which side of u (t) the minimum of F e is attained, or that this minimum is attained at t itself. (Note also that finding v(f), given «(f), can be done in 0(log n) time, by locating the projection u*(t) of u(t) in the map L* . ) To elaborate this observation, let 0
What to read after The Shortest Watchtower And Related Problems for Polyhedral Terrains?
You can find similar books in the "Read Also" column, or choose other free books by Micha Sharir to read online
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