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I have GIS data for which I would like to calculate where curvature is present. Anyone has done this before, please help.

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You will need to be much more specific about your data and use case. – glennon Aug 20 '10 at 8:01
I would change the question into: "How to compute curvature for polylines?" – julien Aug 20 '10 at 8:53
How do you know the question is about polylines? Perhaps these "GIS data" are a DEM. – whuber♦ Aug 20 '10 at 14:51
KESHINE, could you rephrase the question to be clear what kind of data you're working with? We cannot appropriately answer it as-is, thanks! – scw Aug 20 '10 at 18:50

closed as not a real question by whuber♦ Aug 20 '11 at 1:17

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

1 Answer

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Curvature is defined for curves that can be derived 2 times. The problem is that polylines are not derivable everywhere. So, the curvature cannot be computed and has to be approximated.

I know a perfect document that gives an exhaustive state of the art of methods to compute curvature approximations for polylines but... it is in French...!

See annexes, pp 16 to 24, of this document: Barrault Mathieu, 1998, Résolution d'un problème à forte combinatoire et présentant un grand nombre de contraintes variées : le placement cartographique des écritures

Most of these methods are based on the distribution theory.

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ien: How are distributions related to estimating the curvature of polylines? – whuber♦ Aug 20 '10 at 14:52