topic Re: Roundness calculations in LabVIEW

Roundness calculations

Alain_S — Tue, 02 Jun 2009 06:36:38 GMT

Hi there,

Roundness can be defined by means of different methods. So far I found MRS or MZC, MIC, MCC and LSC.
Complete description in the VI as comment 🙂

So far I managed to calculate LSC because LV provide a VI for it 🙂

Can someone please help me with the other ones?

I can't finad a way to determine the radius and offset of the maximum inscribed circle and minimum circumscribed circle.

Does anyone has the formulas to calculate those circles?

Thanks a lot

Alain

Re: Roundness calculations

elset191 — Tue, 02 Jun 2009 14:26:29 GMT

For MIC and MCC I took the center as the (x0,y0,z0) that was returned by LSC. Then found the closest and farthest points from that point and used those as the radii for MIC and MCC.

It should be noted that I don't know if this is an official way to do the calculation. It made sense in my head though.

Message Edited by elset191 on 06-02-2009 09:26 AM

Re: Roundness calculations

Alain_S — Tue, 02 Jun 2009 14:41:15 GMT

Thanks for the effort Tim but taking the center point from the LSC circle as zero point for MIC & MCC circles is not right 😞

And that's my problem, how to find the middle point of those circles.

I think there is a formula to determine them but I can't find them on the web 😞

I found formulas for area and gravity point but not for MIC & MCC 😞

Anyway, thanks for your work so far.

I can't open your VI, I have V8.5 instead of V8.6

Regards

Alain

Re: Roundness calculations

elset191 — Tue, 02 Jun 2009 14:47:20 GMT

Well, if you find a way to find the proper center, you just have to switch two wires. I've attached my VI in 8.5 so you can see it.

Re: Roundness calculations

Alain_S — Tue, 02 Jun 2009 14:54:51 GMT

Half of the job is done 🙂

I'll keep looking for the other half

Thanks for the V8.5 vi.

Regards

Alain

Re: Roundness calculations

Cory_K — Tue, 02 Jun 2009 15:00:49 GMT

Since (0,0) isnt the center, how about this.

Center x-value = [(max x-value)+(min x-value)] / 2

Center y-value = [(max y-value) + (min y-value)] / 2

Then your center will be (center x, center y)

Re: Roundness calculations

Cory_K — Tue, 02 Jun 2009 15:03:24 GMT

And to find out how round the circles are:

(largest diameter in y-direction) - (largest diameter in x-direction)

As this difference approaches 0, the circle is more and more circular (less eliptical)

Re: Roundness calculations

elset191 — Tue, 02 Jun 2009 15:09:17 GMT

The ellipse doesn't necessarily have it's axes aligned with the X and Y axes.

Re: Roundness calculations

Cory_K — Tue, 02 Jun 2009 15:13:18 GMT

That shouldnt be a problem.

Find your maximum and minimum for both x and y values.

Find the difference between your max-y and min-y. This will be 1 diameter (in y-direction)

Find the difference between your max-x and min-x. This will be the other diameter (in x-direction)

If you subtract one of these differences from the other, you should get a (hopefully small) value.

Edit: Oh wait, you mean if the ellipse is off to an angle..... then you are correct.

Let me see if I can think of a solution to that

Message Edited by Cory K on 06-02-2009 10:13 AM

Re: Roundness calculations

elset191 — Tue, 02 Jun 2009 15:16:05 GMT

You can just do a rotation of all the points (or the axes themselves. I've done something like this before. ) if you can figure out the angle. Then treat it like it's aligned properly.

Re: Roundness calculations

Cory_K — Tue, 02 Jun 2009 15:18:48 GMT

elset191 wrote:
You can just do a rotation of all the points ...

That sounds a little easier said than done.

Is there an easy way to do that?

Re: Roundness calculations

elset191 — Tue, 02 Jun 2009 15:22:27 GMT

Mathematics -> Geometry -> 2D Cartesian Coordinate Rotation.

Of course when I did it way back when I didn't know about this VI so wrote it myself.

Re: Roundness calculations

Alain_S — Tue, 02 Jun 2009 15:47:05 GMT

Hi Cory,

I think that with

Center x-value = [(max x-value)+(min x-value)] / 2

Center y-value = [(max y-value) + (min y-value)] / 2

you wil calculate the center point of the minimum circumscribed BOX, not circle!

If by any luck, your box is a square then it's ok but I'm pretty sure that it will never be the case 😞

Message Edited by Alain S on 06-02-2009 10:47 AM

Re: Roundness calculations

DSPGuy — Tue, 02 Jun 2009 22:00:04 GMT

You should be able to pose this as a sort of constrained optimization problem. The LS circle is just the unconstrained solution (minimize the LS distance between the datapoints and the circle). For the maximum inscribed circle the constraint is that no datapoint should lie inside the circle (distance from any datapoint to the circle center must be greater than the circle radius). For the minimum circumscribed circle all datapoints should lie inside the circle (distance from any datapoint to the circle center must be less than the circle radius). The constrained nonlinear optimization.vi should be able to solve this problem.

Re: Roundness calculations

Alain_S — Wed, 03 Jun 2009 05:40:58 GMT

I found a way to calculate MCC

Start the VI and.......................have a break 🙂

So now I need a) a super computer or b) valuable data reduction

I'll go for the last one and also a way to find MIC & MZC, keep you posted guys ... ... ...

I took a rough look at the constrained nonlinear optimization.vi but I don't know yet how to translate the constraints you mentioned into LV code 😞

Can you help a little bit more DSPGuy?

Regards

Alain

Re: Roundness calculations

DSPGuy — Wed, 03 Jun 2009 20:17:45 GMT

Okay, I implemented a first pass at the MCC and MIC using the constrained optimization VI. I modified your original VI, and now display the MCC and MIC on the same graph as the same graph as the data and the LS circle. I commented the model functions so the mapping is clearer (I hope). Performance seems pretty good, with both circles being found within 700 mS or so on my desktop machine.

Re: Roundness calculations

Alain_S — Thu, 04 Jun 2009 05:15:56 GMT

Thanks DSPGuy for your efforts!

I'll have to install V8.6 first, I have the CD's somewhere but......... can't find them right now

Forget about my version because there's an inadmissible error in the both centre point and radius.
it looks good on a graph but when zooming in it isn't anymore 😞

I have a dataset with known values for centerpoint and radius and the error I get is too large 😞

As soon as I have V8.6 installed I will test your code with the same dataset and let you know the outcome!

Thanks for your help so far

Regards

Alain

Re: Roundness calculations

DSPGuy — Thu, 04 Jun 2009 18:48:18 GMT

Reposting code saved for LabVIEW 8.21.

Re: Roundness calculations

Alain_S — Fri, 05 Jun 2009 05:16:22 GMT

Thanks for the "earlier" version but I already have 8.6 installed and translated to V8.5. I

also did some caculations.

A first sight it's ok but with some objects I don't get an answer for MIC or MCC or even both.

It seems that how the more unround a shape is or the more spread there is in the data, the more critical it is to set correct start parameters.

I'll make a vi with some datasets to explain the above.

To be continued... ...

Re: Roundness calculations

Alain_S — Fri, 05 Jun 2009 15:54:37 GMT

As promised a vi with some datasets that genereates errors instead of answers

I'll have a closer look at that vi in the week-end ...