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Can someone provide a precise definition of what a "non-noded intersection" is? There are various GIS platforms and toolkits that have errors with this text, and Google search results for this tend to fall in the category of "drop some precision and all your problems go away" without any real explanation of what's going wrong. Given two valid geometries, why would this error occur?

References to documentation would be most helpful.

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It means that nodes can not be in the same spatial space during intersection. I drew you a picture. enter image description here

These are the same lines, but intersected.

If you noticed, if had dropped the node in the middle (since it isn't needed) that the bottom diagram would be impossible.

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So if this is the case, why would it be an error condition? –  FMM Dec 19 '12 at 22:39
    
I can't comment toward your particular error condition, but I would suspect that it might have something to do with finding the distance between two points and then dividing by that amount. See finding a point along a line article: physicsforums.com/showthread.php?t=419561 –  user13395 Dec 19 '12 at 22:44
    
So why would this be an error condition, for instance, when intersecting two valid geometries? –  FMM Dec 19 '12 at 23:19
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As much as I hate to say it, you gotta throw something. The package you are using could experience a divide by zero error. The program would then throw the error divide-by-zero to you. You would find this error most confusing since it really gives you no methodology to fix the error. Instead the programmer detects this an throws a non-noded intersection so you have some chance of fixing it. Again, I am guessing at a lot of things here since various toolkits and various tools can be used. A geometry can be valid and still have a non-noded intersection and a node-intersection. –  user13395 Dec 19 '12 at 23:37
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