well unless there is something unconventional in you features, perhaps converting them back to points and regenerating the triangulation would be a good first test
In think Dan Patterson has the key. Be sure to check the point location (optional) settings in the tool for the one that matches your need. Also, note that an Advanced license level is required to run the tool.
Some other thoughts:
If you need to clean up your line data first, consider running a Integrate and then Dissolve in preparation for Feature Vertices to Points. Note that what settings you use for each of these will depend on how your data is organized.
Note that if there are two or more geoprocessing tools that need to be run in sequence that they can be run together using Modelbuilder or Python.
Also, Geodatabase Topology can be of help in getting the linework coincident.
Then of course, the final tool, once points have been derived
Chris Donohue, GISP
I'm considering trying this technique. But I'm wondering this... I want to create one polygon for each group of lines that share an attribute. When I convert the lines to points, I'll end up with multiple points that represent each line...and I'm thinking I should dissolve those points into multi-part point features based on the attribute I'm interested in. But the Create Thiessen Polygons tool creates one polygon for each input point...so how does it handle multi-part point features? I don't see this addressed on the help page for the tool. Does it create one polygon for each point within a multi-part feature, or create one polygon for the entire multi-part feature? I suppose I could try it and find out, but that may take a while since I have a large data set.
They should be single part features, multiparts will either fail as inputs or they will be exploded. As well, you should remove duplicate points (ie points shared by polygons). Thiessen Polygons (as are Voronoi diagrams, Delaunay triangulations, TINS and other spatial delination methods) are all about the points not your attributes... you will deal with that through spatial associations done after the fact.
You might also want to try a small sample to see if you get the triangulation you want first
OK, then I'm thinking that if the attribute I need from the lines is carried over to the points and then to the polygons that are generated from the points...then I will be able to dissolve the Thiessen polygons by that attribute and that will give me the result I need. This would be nice if it works... Thanks!