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I know some biologist that are taking curvature measurements on photos with softwares to understand the variation on beak morphology.

I'm wondering if there is a way to build a mechanical tool (or if one exist already) to measure the curvature of a circle's (or ellipse) arc. The arc is not always of the same length, so it would need to be adjustable.

There is a constrain (see the grey line): enter image description here

I can't fit a big calliper on the bird's head.

I want to know:

  1. the radius of the circle that correspond to the beak curvature
  2. how "steep" is that curvature (probably a lack of vocabulary on my side but see the image down to see what I mean by "steep")

enter image description here

You can see this image as the different birds in the image above. Bird #4 would have a flatter beak than bird #1.

I need to be able to calculate the "steepness" even if the x, y or z are not of the same length.

The idea of bringing a mechanical tool is to calculate rapidly and conveniently a number and add it directly to a dataset. It's much faster than to look at photos and analyse with a software. So if there is a mechanical tool designed for this, it would be super useful.

Again, the image is just a visualization of the problem. I would like to measure the beak of different birds on the field.

M. Beausoleil
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  • To what class of curves are you constraining this question? E.g., are you asking about tools for determining the major and minor radii of an ellipse based on a sample segment? – feetwet Jul 18 '16 at 21:26
  • Software is a tool. Did you mean a mechanical tool? – do-the-thing-please Jul 19 '16 at 03:05
  • Yep, I mean a mechanical tool. – M. Beausoleil Jul 19 '16 at 03:07
  • @feetwet see the image in the question that I edited. You'll see that it's segments (arc) of a circle attached to a bird's head. – M. Beausoleil Jul 19 '16 at 03:21
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    There are also Digital Radius Gauges which can measure small arcs (~10mm) http://www.cutwel.co.uk/measuring-tools/small-tool-instruments/miscellaneous-gauges/insize-digital-radius-gauge-2183-series?utm_source=google&utm_medium=shopping&utm_campaign=purenet_feed&VariantId=2183&gclid=CjwKEAjwn7e8BRCUqZiP_vnrtBkSJAC_lp4HZdoiTLI8lmAI6p1BbZQq1Dd8J7dQVCB9ml7Yx7SMlhoCQeLw_wcB – atom44 Jul 19 '16 at 10:15
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    It's not clear to me what class of curves a bird's head can be assumed to follow, so your question is still unclear: Is it an arbitrary curve? Or are you interested in the "best fit" *circular* segment? – feetwet Jul 19 '16 at 14:54
  • Why the insistence on non-software tool? Unless you're doing a historical reconstruction, that makes no sense. – Carl Witthoft Jul 19 '16 at 19:00
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    @CarlWitthoft there are heaps of valid reasons people might want measuring tools that don't depend on software. For example if you need to do the measurements in the field where there is no power available for long periods of time or if you need to produce a large number of gauges so volunteers can help collect data. In most simple cases, it's also much easier to validate a non-software solution. – Ethan48 Jul 20 '16 at 13:21
  • @Ethan48 The number of no-power field situations is rapidly approaching zero. In any case, the OP is asking about sets of drawings, which is hardly a exo-laboratory situation. – Carl Witthoft Jul 20 '16 at 14:34

2 Answers2

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For a circle, yes. Such a tool exists: Digital Radius Caliper

There are also Digital Radius Gauges, which may be useful for smaller curves.

For a general curve, you can't measure the curvature exactly since it varies continuously along the curve. You could perhaps assume a region is approximately circular and measure that. But depending on the size of the tool and the rate of curvature change this could be wildly inaccurate.

atom44
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  • For larger curves, there are also radius gauges like https://www.zoro.com/baileigh-industrial-inside-radius-gauge-irg-3600/i/G8479186/?gclid=CjwKEAjw_LG8BRDb1JTxm8uP_UwSJADu_8pWrTfKMTzFiI3nBxdg_s9yDb2sc-pQba9YrxDF38BrBRoCxdLw_wcB&gclsrc=aw.ds – Ethan48 Jul 19 '16 at 00:40
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How about a Contour Gauge: Contour Gauge

And here: Wikipedia Article

  1. Make your measurement
  2. Trace it
  3. Scan/digititize it
  4. Analyze it (spline/curve fit) with some type of CAD software.
GisMofx
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  • They are used to *record* the curvature, not *measure* it. They don't tell you e.g. "the radius is 250mm". – AndyT Jul 19 '16 at 11:01
  • @AndyT Yes, Record it, trace and digitize it, & then measure it or curve-fit with some CAD software. – GisMofx Jul 19 '16 at 11:19
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    Measuring it with CAD software means that this is not a mechanical measuring tool. I could take a photo, and load that into CAD software, that doesn't mean my camera is a mechanical measuring tool. – AndyT Jul 19 '16 at 11:26
  • @AndyT photos are more prone to error because you must get the projection right. – joojaa Jul 20 '16 at 14:43
  • @joojaa - Doesn't matter, for the purposes of this question. My point is that this answer misses a fundamental point of the OP's question. Quote from the question (emphasis mine): "I'm wondering if there is a way to build a **mechanical tool**" – AndyT Jul 20 '16 at 14:50
  • I merely proposed an option to obtain a measurement. If they are researching and collecting data, in this day and age, computers will be used. Likely a bird beak is not a perfect radius and will have multiple radii or be spline-like, so this may or may not be a viable solution for them to record the beaks' curvatures in the field and come back to the lab and analyze them. Let the OP weigh in. – GisMofx Jul 20 '16 at 14:59
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    @AndyT but this is a mechanical tool that can be built ;) Just because the OP suggested to use it for scan purposes does not mean you need to do it. This provides a much better documentation than a point sample. But you may object to the fact that it is a lot of work, sure. – joojaa Jul 20 '16 at 15:06
  • @GisMofx - Fair enough on wanting the OP to weigh in. Following your comment, I have just checked the question, and he has edited it, which I believe clearly covers this: "The idea of bringing a mechanical tool is to calculate rapidly and conveniently a number and add it directly to a dataset. It's much faster than to look at photos and analyse with a software. So if there is a mechanical tool designed for this, it would be super useful." – AndyT Jul 20 '16 at 15:14