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    <p>well, it all depends on how you define tortuosity. there is a <a href="http://en.wikipedia.org/wiki/Tortuosity" rel="nofollow">wikipedia article regarding tortuosity</a>, which may shed some light on the subject.</p> <p>an interesting sentence in the article tells us that: <code>"roughness (or tortuosity) could be measured by relative change of curvature"</code>. that makes a good starting point. </p> <p>your polyline is made of adjacent line segments. you can compute the angle between each adjacent line segment. using this information you can get a good idea of tortuosity for your polyline. for example, let <code>seg(n)</code> be the line segment between point <code>n</code> and point <code>n+1</code>: </p> <pre><code>tortuosity = sum(abs(angle(seg(n), seg(n+1))) for n in 1 to number of segment) </code></pre> <p><em>(computing the angle between 2 line segments is left as an exercise, but does not require a degree in mathematics)</em></p> <p>the above measure is not scaled: the more points you have, the higher the value might be. you can easily scale this result according to the number of line segments you have:</p> <pre><code>unit_tortuosity = tortuosity / (n * pi) </code></pre> <p><em>(the maximum angle between 2 line segments is <code>pi</code>, adjust your <code>angle()</code> function so that it returns a result between <code>0</code> and <code>pi</code>. so your tortuosity would be at most <code>n*pi</code>, hence the above scaling factor which allows to have a value between <code>0</code> and <code>1</code> with <code>0</code> representing a perfectly straight polyline)</em></p>
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    1. POCompute the tortuosity of a polyline
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    1. POCompute the tortuosity of a polyline
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    1. COYes, I have reading articles but I want mantain the question as open as I can ;) What do you think about (total track lenght)/(straight distance among start and end point)?
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    2. CO@Mariano: `(total track lenght)/(straight distance among start and end point)` seems to be a gross estimation, and may give surprising results in some cases. for example: imagine a track of someone going straight ahead, then coming back on its path to end at its starting point. it will have the same result as someone performing zig-zags for going somewhere, although the first track is straight but not the second.
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    3. COYes, you've right, I have said a a wrong thing. I haven't understand why you consider pi/2 (90 degrees) as maximum.
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