stud/IV/notes.txt

Definition of a bend
--------------------

Ends of the line should always be bends, otherwise not
all line vertices are covered by bends (definition elsewhere).

Gentle inflection at the end of the bend
----------------------------------------

The article does not specify how many vertices should be included when
calculating the end-of-bend inflection. We chose the iterative approach -- as
long as the angle is "right" and the distance is (greedily) decreasing, keep
going.

Self-line crossing when cutting a bend
--------------------------------------

The self-line-crossing may happen after a few bends have been skipped. E.g.
ends of A<->B cross the line, but "swallow" a few more in between:

     ,______
    /       \
    |___A   |    \  \
        \   |    B\ |             __
         \  |     | |            /  \
         /  |     | |___,---,___/A  |
        /   |     \_________________|
        \   |
         \  |    \  \
         /  /    B\ |     _       __
    ----/  /      | |    / \     /  \
   / ,____/       | |___/   \___/A  |
  / B|            \_________________|
     |



If a bend with 180+ deg sum of inflection angles is found, its line between
inflection angles (AB in our examples) must be crossed with all the other bends
to detect a possible line-crossing. This is O(N*M), where N is the total number
of line segments, and M is the number of qualifying bends. It is expensive.

This may be simplified: if other bend's endpoints (A' and B') are in the same
sub-plane as divided by AB, then the bend can be skipped from checking if it
intersects with AB. Some intersections may be missed (see the last example),
but they will be eliminated by joining A and B anyway.

Also, there is another way to remove self-crossing, without removing most of
the bend. E.g. from:

  \  /
  B\ |      __
   | |     /  \
   | |____/A  |
   \__________|

Instead of:

  \  /
   \/ A'
  B

To:

  \  \_
  B\   `-,_.__
   |       A' \
   |          |
   \__________|

But perhaps it doesn't look quite as natural. I will trust the original
article to do the right thing here.