Implicitly Representing Arrangements of Lines Or Segments
Implicitly Representing Arrangements of Lines Or Segments
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In our eReader you can find the full English version of the book. Read Implicitly Representing Arrangements of Lines Or 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 Implicitly Representing Arrangements of Lines Or Segments
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To quickly assess the difficulty of the text, read a short excerpt:
Lemma 3. 12 Let S be a spiral from p to q. Any line intersects the outer chain at least as often as the inner chain.
Proof: If the spiral is short, then the conclusion holds. Thus we will cut a long spiral into several short spirals by the following process. Consider walking along the inner chain from p to q, maintaining a point w on the inner chain and a ray that is tangent to the inner chain at w and opposite the direction of the walk. As we walk on the inner chain from p, this ray sweeps a p...oint w' on the outer chain.
Figure 4: Cutting a long spiral along a ray At the beginning of the walk, choose a direction d — perhaps the direction of the first edge on the walk. Whenever our walk faces direction d or —d, we cut the spiral along the edge {w, w'). See Figure 4. Since w' is a convex angle, we form a short spiral from p to w that includes edge {w, w') on the outer chain. Since the cut is tangent to the inner chain at w, we have a spiral from w' to q with edge {w, w') on the inner chjiin.
What to read after Implicitly Representing Arrangements of Lines Or Segments?
You can find similar books in the "Read Also" column, or choose other free books by Herbert Edelsbrunner to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Lemma 3. 12 Let S be a spiral from p to q. Any line intersects the outer chain at least as often as the inner chain.
Proof: If the spiral is short, then the conclusion holds. Thus we will cut a long spiral into several short spirals by the following process. Consider walking along the inner chain from p to q, maintaining a point w on the inner chain and a ray that is tangent to the inner chain at w and opposite the direction of the walk. As we walk on the inner chain from p, this ray sweeps a p...oint w' on the outer chain.
Figure 4: Cutting a long spiral along a ray At the beginning of the walk, choose a direction d — perhaps the direction of the first edge on the walk. Whenever our walk faces direction d or —d, we cut the spiral along the edge {w, w'). See Figure 4. Since w' is a convex angle, we form a short spiral from p to w that includes edge {w, w') on the outer chain. Since the cut is tangent to the inner chain at w, we have a spiral from w' to q with edge {w, w') on the inner chjiin.
What to read after Implicitly Representing Arrangements of Lines Or Segments?
You can find similar books in the "Read Also" column, or choose other free books by Herbert Edelsbrunner to read onlineMoreLess
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