# Triangulations of multilaterals

• I'm adding user text sercxjo (sighs) https://ru.stackoverflow.com/a/167434/177188 )

1. If the number of vo = 3 is completed
2. Choose the first top as the current (N)
3. If there is no diagonal inside the polygon at point N+2, the current becomes the next, etc. on the ring. I think I can. To prove that this cycle is not endless.
4. "Let's cut" the triangle from the multiangle, the peaks become one less by deleting the top of N+1.
5. We turn to paragraph 1

It's probably convenient to use the contact list.

Determining whether the diagonal inside the polyangle passes.

Determine in which direction a multi-angle is put, by or against the clockwise. Next, if the triangle N+1 N+2 is in In the opposite direction, it means our diagonal is not outside. Right. Otherwise, there's a possibility of a diagonal option. to the outside in whole or in part because of other internal corners.

For N+3 and N-1 points, we need to check that these angles are at these peaks. were more than the corresponding angles of the cut-off triangle. I mean. The top lies on the other side of the diagonal relative to the top of N+1, or the angle at the top is more depressed.

For the remaining parties, it is necessary to check whether they intersect. Diagonal.

Determination of the direction of the lateral bypass

Walking from one top A1 vector to all the remaining A1-stateA2, A1-stateA3, ... A1-national. We consider the sum of N-1 vectors of neighbouring vectors In order, we're only intercepted by coordinate z. This module amount The figure is doubled, and the sign indicates the direction of the circumference.

== sync, corrected by elderman ==

These words do not understand:

Otherwise, another option is possible when the diagonal is outside.

For N+3 and N-1 points, we need to check that these angles are at these peaks. were more than the corresponding angles of the cut-off triangle. I mean. The top lies on the other side of the diagonal relative to the top of N+1, or the angle at the top is more depressed.

For the remaining parties, it is necessary to check whether they intersect. Diagonal. Full or partly due to other inner angles.

Since this verification is not performed, very complex figures are not being processed correctly.

Please explain this in other words.

• If a multi-angle is swell, his triangulation is trivial.
Non-pollutant multi-angles differ from the swelling of only one characteristic: the presence of angles exceeding the depressed (180 degrees). Since this angle is not possible in the triangle, it is easier to link a triangle with it. For practical purposes (location, moments, centre of gravity, etc.), the processing of algorithms to allow the deductions to be accounted for is not difficult.

What's important is that they don't cross. And if the cut-off is in the order of the "inverted" angle, the process of presenting an unpopular multiangle in the form of a swelling multiangle and a lot of triangles is not a problem.

If classical triangulation is required, a large number of triangles and many extracts can be formed and each triangle can be expected to cross with each extract. If changes are made, remove the reference triangle and add the result to the end of the triangle list. Repeat cycles are not necessary, but the triangle deduction function is not complex (the triangle has no diagonals) and is written once.

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