86 lines
2.4 KiB
Plaintext
86 lines
2.4 KiB
Plaintext
Definition of a bend
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Ends of the line should always be bends, otherwise not
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all line vertices are covered by bends (definition elsewhere).
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Gentle inflection at the end of the bend
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The article does not specify how many vertices should be included when
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calculating the end-of-bend inflection. We chose the iterative approach -- as
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long as the angle is "right" and the distance is (greedily) decreasing, keep
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going.
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Self-line crossing when cutting a bend
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The self-line-crossing may happen after a few bends have been skipped. E.g.
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ends of A<->B cross the line, but "swallow" a few more in between:
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,______
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/ \
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|___A | \ \
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\ | B\ | __
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\ | | | / \
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/ | | |___,---,___/A |
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/ | \_________________|
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\ |
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\ | \ \
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/ / B\ | _ __
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----/ / | | / \ / \
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/ ,____/ | |___/ \___/A |
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/ B| \_________________|
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If a bend with 180+ deg sum of inflection angles is found, its line between
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inflection angles (AB in our examples) must be crossed with all the other bends
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to detect a possible line-crossing. This is O(N*M), where N is the total number
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of line segments, and M is the number of qualifying bends. It is expensive.
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Also, there is another way to remove self-crossing, without removing most of
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the bend. E.g. from:
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\ /
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B\ | __
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| |____/A |
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\__________|
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Instead of:
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\ /
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\/ A'
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B
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To:
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\ \_
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B\ `-,_.__
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| A' \
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\__________|
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But perhaps it doesn't look quite as natural. I will trust the original
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article to do the right thing here and remove the bend altogether.
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The Context of a Bend
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Similar bends:
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> For example, if bend 1 has four unit areas and bend 2 has six unit areas, the
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> average size is five units, and the normalized areas of bends 1 and 2 are
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> 4/5=0.8 and 6/5=1.2, respectively.
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My comment: everything until this sentence is clear. However, "unit areas" is
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misleading: there is little reason to normalize areas, but leave the distances
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intact (if we'd like to normalize areas, it would make sense to square-root
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them).
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Removing that removes changes the meaning of the sentence that **euclidean
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distance** is normalized (the composite of the bend properties), rather than
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a single component.
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