Intersect curve and circle (workaround)? Any ideas?

Matt_ shared this question 7 years ago
Answered

Hello folks!


I am stuck in the middle of the construction of a file. I´m aiming to create gears with en evolvent profile.


The problem is that ggb doesn´t allow to intersect a curve and a circle. But I really need to, to proceed.

I´m hoping that someone has a good workaround for me, here is a list of the things I already tried (without success):


1) Calculate intersection in CAS (to then define a point from the list). Get wrong output.

2) Set several points on circle, create list, use polyline command. Still can´t intersect.

3) Set several points on evolvent curve, create list, use polyline. Still can´t intersect.

4) Re-create both (circle and evolvent) as polylines and intersect. Can´t intersect.

5) Calculated the evolvent as a function of x (by solving x=x(t) for t and substituting it in y=y(t)). Sadly the function I get has nothing to do with the evolvent...


I don´t know what else I could try.

I don´t know if it makes sense to try.


If you know for sure that I can´t proceed, you´re very welcome to let me know :)


Thanks a lot to whoever reads!

Thanks even more to whoever answers :smiley_cat:


Ciao!!

https://ggbm.at/565455

Comments (9)

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Hi

Try this for a workaround with lists and sequences


https://ggbm.at/565457


D@niel

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If you parameterize the circle as eg

    Curve[x(B) + rbase2 cos(t), y(B) + rbase2 sin(t), t, 0, 2 pi]


then you can just use the Intersect Tool :)

https://ggbm.at/565459

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For general purposes multiple intersections could be suitable, as per att'd screenshot.

Cheers

Philippe5af5f30b80307793c2893487ad2fca30

Files: 17.png
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For general purposes multiple intersections could be suitable


Just click twice (for non-polynomials)


http://wiki.geogebra.org/en...

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Very nice, thank you!bb53dbfe30d909fc31c9aa78a6e1acd0

Files: 19.png
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I love you all! :D


This is the first forum I signed it. And it is awesome!


Thanks a lot to everybody, this is a great software with even greater people using it :)


Cheers!! :D :D :D

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Actually...I have one question left :)


How did you pick the parametric values to use in the interception?


Intersect[j, b, 0.51647, 3.04972]


Are they random? Thanks :)

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Hi,

The numerical method uses a "guess interval".

Basically, by using the Tool and clicking on the intersection point of the two objects, GeoGebra does the same as the command

Intersect[ <Function>, <Function>, <Start x-Value>, <End x-Value> ] that yields the intersection point of the two functions in the given interval. In this case, a neighbourhood of the clicked point is taken as guess interval.

More information about Intersect command here, or here :smiley_cat:.

Cheers,

Simona

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Thanks Simona :)


Topic is now clear to me!


Have a good day,


Matt

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