I have created a TIN for all the polygons in a block and then converted it to a feature layer in order to be able to delete the triangles that fall in the polygons. Now I want to remove triangles that fall into the concave but exterior part of polygons. But I don't know how to do it in ArcGIS. This condition makes triangles with all three vertices located on the same object to be removed from consideration. The screenshot of part of my data is as the first picture. And I want to remove exterior white triangle as shown in the second picture. And My final purpose is to form a skeleton graph for each street block, like the third picture. In other words, I want to implement Thiessen polygon for polygons instead of points but I don't know how to do it. If I would be able to implement Thiessen polygon for polygon objects, it would be used instead.

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    Thiessen polygons around polygons? Use the Euclidean Allocation tool in ArcToolbox-Spatial Analyst Tools-Distance-Euclidean Allocation. Convert the resulting raster to polygons if necessary.
    – GBG
    Commented Feb 26, 2018 at 19:24
  • Can you delete the Polygons that have a Vertex count of 3?
    – klewis
    Commented Feb 26, 2018 at 19:43
  • Select ones that are completely inside and delete or switch selection and delete.
    – FelixIP
    Commented Feb 27, 2018 at 5:07
  • @GBG I tried the way you stated but the results are not satisfactory as some of the Thiessen polygons around polygons intersect with polygon boundary
    – parastoo
    Commented Feb 27, 2018 at 5:51
  • @klewis I don't understand what you mean. All the triangles have vertex count of 3.
    – parastoo
    Commented Feb 27, 2018 at 5:53

1 Answer 1


You can build the convex hull of the polygons, then select by location the triangles that "are within" the convex hull and remove them. In order to create convex hull, you can use the minimum bounding geometry tool (see this post for more details).

As a remark, a quick and dirty method to achieve your "thiessen polygons" for polygons is to 1) densify the polygons with a distance smaller than the distance between two polygons, 2) convert polygon vertices to points, 3) create thiessen polygons for points and 4) dissolve based on the attributes of the original ID of the polygons. But, this is not an exact solution.

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