Separating Two Simple Polygons By a Sequence of Translations
Separating Two Simple Polygons By a Sequence of Translations
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Hence P — Q is 3. Polygonal region, each of whose edges has the form p — q, where either p is an edge of P and ^ is a vertex of 2 or P is a vertex of P and 5 is an edge of Q. Since there are at most 2mn such differences, it follows that the boundary of P — Q is contained in the union of these 2mn segments. Moreover, each comer oi P — Q must be either the difference of a vertex of P and a vertex of Q, or a point of intersection of two of the above segments. Since there are plainly at most mn com...ers of the first kind and 0{w}rp-) comers of the second kind, the claim follows.
(b) It is plain that P — Q \s connected, so that the boundary of any connected component of {P — QY must be connected. □ Before continuing we present two examples which help to calibrate the worst case combinatorial complexity otP - Q and of C, .
Example 1: This example shows that in the worst case P — Q can have ^{w}n^) connected components (and thus also n(m^n^) comers). In this -7- example, as illustrated in Fig.
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To quickly assess the difficulty of the text, read a short excerpt:
Hence P — Q is 3. Polygonal region, each of whose edges has the form p — q, where either p is an edge of P and ^ is a vertex of 2 or P is a vertex of P and 5 is an edge of Q. Since there are at most 2mn such differences, it follows that the boundary of P — Q is contained in the union of these 2mn segments. Moreover, each comer oi P — Q must be either the difference of a vertex of P and a vertex of Q, or a point of intersection of two of the above segments. Since there are plainly at most mn com...ers of the first kind and 0{w}rp-) comers of the second kind, the claim follows.
(b) It is plain that P — Q \s connected, so that the boundary of any connected component of {P — QY must be connected. □ Before continuing we present two examples which help to calibrate the worst case combinatorial complexity otP - Q and of C, .
Example 1: This example shows that in the worst case P — Q can have ^{w}n^) connected components (and thus also n(m^n^) comers). In this -7- example, as illustrated in Fig.
What to read after Separating Two Simple Polygons By a Sequence of Translations?
You can find similar books in the "Read Also" column, or choose other free books by Richard Pollack to read onlineMoreLess
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