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I am using 10.2 but had no issues clipping your TIN. Your polygon is not a 3D feature so you may have incorrectly set the Height Field parameter which by default is, in this case, set to iD - this will force to clip the TIN at that height which is 0. Set the Height Field to NONE and run it again: The resulting TIN will be clipped as follows:


Could it be that the tool you're using calls the InterpolateShape function under the hood, the docs of which are: http://resources.arcgis.com/en/help/main/10.1/index.html#/Interpolate_Shape/00q90000006m000000/ The sample_distance parameter which: By default, this is a raster's cell size or a TIN's natural densification. In the GUI tool you use, is there ...

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