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Say you have a set of points and joining lines as show below:

t junctions are at D, F, and E

In this diagram of triangles, T-(or Y-like) junctions are at D, F, and E.

At vertex F for example, there is a triangle FDE, but no line FJ. If there was a line FJ, then there would be no T junction at F. Two triangles would be formed instead out of triangle-ACJ as tri-AFC and tri-FCJ.

How do you find the vertices that form "T" (or Y-like) junctions?

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    I don't know much on this, but you would like to read this: http://books.google.co.in/books?id=DU8QUqIoxlIC&pg=PA40&lpg=PA40&dq=T-Junctions+in+an+array+of+triangles&source=bl&ots=9tlj9szu68&sig=286k43H-RQ2njkbapCV6ujYMECI&hl=en&ei=7eyDTMWnNI7OvQOkxpi5Cg&sa=X&oi=book_result&ct=result&resnum=6&ved=0CCsQ6AEwBQ#v=onepage&q&f=false2010-09-05
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    This on the other hand would probably have to be treated as a graph theory problem.2010-09-05

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My first stab at it is to consider each triangle in the diagram, as well as all its adjacent triangles.

Consider tri-FEC first. FEC is adjacent to ACJ, but only one vertex is shared (C). If there is to be no T-junction, then two vertices should have been shared between adjacent triangles.