Shortest Paths for Line Segments
Shortest Paths for Line Segments
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In our eReader you can find the full English version of the book. Read Shortest Paths for Line Segments 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 Shortest Paths for Line Segments
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To quickly assess the difficulty of the text, read a short excerpt:
Lemma 6 Let P = (0, 0, 0) and Q = (x. Y. A) be two placements such that 0 q/2.
Proof: Take an optimal motion from P to Q. We continue this motion by a rotation of an angle of (tt — a) around (j, y). We arrive at a placement Q' antiparallel to P. We have d2(Q, Q') d. IP. Q) + d2(Q, Q') > do(P, Q') > wfl =^ d->{P, Q) > q/2.
D It is easy to see that lower bound of the preceding lemma is attained by any pure rotation through an angle of at most n about any point of the line segment. This answ...ers the question posed in the introduction to this section: Corollary 3 Any pure rotation through an angle of at most w about any point of the line segment AB is optimal.
We are now able to construct shortest paths between any two placements P, Q that are sufficiently close together: Definition 6 Two placements P, Q are said to be near to each other if mP]-B[Q]\\
What to read after Shortest Paths for Line Segments?
You can find similar books in the "Read Also" column, or choose other free books by Christian Icking to read online
To quickly assess the difficulty of the text, read a short excerpt:
Lemma 6 Let P = (0, 0, 0) and Q = (x. Y. A) be two placements such that 0 q/2.
Proof: Take an optimal motion from P to Q. We continue this motion by a rotation of an angle of (tt — a) around (j, y). We arrive at a placement Q' antiparallel to P. We have d2(Q, Q') d. IP. Q) + d2(Q, Q') > do(P, Q') > wfl =^ d->{P, Q) > q/2.
D It is easy to see that lower bound of the preceding lemma is attained by any pure rotation through an angle of at most n about any point of the line segment. This answ...ers the question posed in the introduction to this section: Corollary 3 Any pure rotation through an angle of at most w about any point of the line segment AB is optimal.
We are now able to construct shortest paths between any two placements P, Q that are sufficiently close together: Definition 6 Two placements P, Q are said to be near to each other if mP]-B[Q]\\
What to read after Shortest Paths for Line Segments?
You can find similar books in the "Read Also" column, or choose other free books by Christian Icking to read online
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