Bulge Calculation

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Bulge Calculation

Postby jimandi5000 » Mon Nov 11, 2019 2:28 am

Hi all,

Looking for some help. before I do the deep dive on spending a bunch of time, I would ask... I am looking for the formula to calculate arc bulge. Anyone out there crossed that bridge?

This is what I have so far:
Code: Select all
function BulgeCalculator (Rad, Ang)
   return math.tan (math.rad(Ang) * Rad)
end
Thanks,
Jim
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Re: Bulge Calculation

Postby jimandi5000 » Mon Nov 11, 2019 4:39 am

Hi,

I wrote this and ran 30 to 40 test. I am thing it is working.

Code: Select all
function Arc2Bulge (p1, p2, Rad)
    local chord = math.sqrt(((p2.x - p1.x) ^ 2) + ((p2.y - p1.y) ^ 2))
    local seg = (Rad - (0.5 * (math.sqrt((4.0 * Rad^2) - chord^2))))
    local bulge = (2 * seg) / chord
    return bulge
end
Thanks,
Jim
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Re: Bulge Calculation

Postby vgraves » Mon Nov 11, 2019 6:46 pm

Not exactly sure what you mean by bulge, but I interpreted it to refer to circular segments. This may help you validate the results of your existing function.

https://en.wikipedia.org/wiki/Circular_segment

Van
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Re: Bulge Calculation

Postby jimandi5000 » Tue Nov 12, 2019 5:05 am

Hi Van,

Thanks for the reply. Here is what the SDK states on page 95.
Attachments
Annotation 2019-11-11 220048.jpg
Thanks,
Jim
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Re: Bulge Calculation

Postby armbrusterco » Thu Nov 14, 2019 1:01 pm

In geometry, the "bulge" is called a sagitta. Surveyors sometimes calculate the sagitta to use when staking out arcs.

If you know the radius and chord length of the arc, here are two links with the formula to calculate the length of the sagitta.
https://www.mathopenref.com/sagitta.html https://www.liutaiomottola.com/formulae/sag.htm

If you know the radius and the angle of the arc, here is a link with a formula to calculate the length of the sagitta.
https://planetcalc.com/1421/
Bob Armbruster
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Re: Bulge Calculation

Postby jimandi5000 » Fri Nov 15, 2019 8:19 am

Hi armbrusterco,

Not sure I agree. the SDK states
The bulge represents a ratio between the chord length of an arc and its height (bulge = (2*arc_height) / chord_length).
So you are somewhat correct we do need the sagitta but we need the ratio to the chord to the sagitta.

Thoughts?
Thanks,
Jim
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Re: Bulge Calculation

Postby armbrusterco » Sun Nov 17, 2019 5:06 am

You are correct. I missed the ratio. Oooops.
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Re: Bulge Calculation

Postby jimandi5000 » Sun Nov 17, 2019 5:43 pm

No Problem... I am just trying to learn as much as I can... ;)
Thanks,
Jim
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