Workaround: Arc tangent to two circles

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hulf2012
Posts: 716
Joined: Sat Nov 24, 2012 12:37 pm

Workaround: Arc tangent to two circles

Postby hulf2012 » Wed Jul 17, 2013 2:25 am

Hello:
In other topic, an user was asking for a method to conect to circles with a tangent.
The present workaround it's not perfect. It's not the solution.

The key is converting a path to a guide, because it gaves us an angle that can be copied. After that, just rotate the objects until a convenient arrangement.

I think it will be helpfull if I put here.



Any comment or critic is welcome
If you have problems:
1.- Post a sample (or samples) of your file please.
2.- Please check here:
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/index.html
3.- If you manage to solve your problem, please post here your solution.

Lazur
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Joined: Tue Jun 14, 2016 10:38 am

Re: Workaround: Arc tangent to two circles

Postby Lazur » Wed Jul 17, 2013 4:37 am

That's interesting!
You have two fixed circle AND a fixed radius for the tangent circle which is three independent input for a geometrical construction of a circle.
It is geometrically possible to do such, though I don't know right now how to do it exactly.
And even if there is a theoretically good construction, the result can be more inaccurate than an aproximation.

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druban
Posts: 1917
Joined: Fri Nov 20, 2009 10:48 pm

Re: Workaround: Arc tangent to two circles

Postby druban » Wed Jul 17, 2013 8:45 am

well, of course! :oops: Tangent to two circles=chord->center from chord. Duh!

Although you say it's a workaround and not exact, Hulf, your method is the bright idea that leads to a geometrically rigorous and absolutely correct construction.
In fact I think it can be extended to a construction that locates the centers of all tangent circles to two circles.
It becomes obvious when you put it so elegantly, Hulf! :applause:
Last edited by druban on Fri Jul 19, 2013 2:03 pm, edited 1 time in total.
Your mind is what you think it is.

hulf2012
Posts: 716
Joined: Sat Nov 24, 2012 12:37 pm

Re: Workaround: Arc tangent to two circles

Postby hulf2012 » Fri Jul 19, 2013 4:16 am

Hello:
Thanks for you comments!
Lazur: I don't understand what you say. It is not a good method?. In any case, it's just a workaround, a first step.
Druban: Many thanks, again

To all:
I'm thinking in developing more tutorials or workarounds. Do you have more ideas, about a tutorial, or something you want to know (maybe something more general, like pespective, or human figure, or geometric constructions)?.

To be honest, I took all this work, like a training, for something more ... concrete. whynot, Like a designing or art project.
If you have problems:
1.- Post a sample (or samples) of your file please.
2.- Please check here:
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/index.html
3.- If you manage to solve your problem, please post here your solution.

Lazur
Posts: 4717
Joined: Tue Jun 14, 2016 10:38 am

Re: Workaround: Arc tangent to two circles

Postby Lazur » Fri Jul 19, 2013 7:44 am

It is an effective method, but not an "exact", theoretically corect construction.
"Rotate until you see them to be tangent" is not a geometrical workaround, even if it's more screen-accurate.
It's hard to talk about accuracy when you use the right theory you get more inaccurate results then when you go by your perception.

hulf2012
Posts: 716
Joined: Sat Nov 24, 2012 12:37 pm

Re: Workaround: Arc tangent to two circles

Postby hulf2012 » Sat Jul 20, 2013 3:21 am

Thanks for your reply Lazur URH,
Let's see the first frame (top left).
- The three circles ARE tangents, because they only touch in One point each one, their quadrant points. I have to say here that I'm limitated by Inkscape's tools.
-When you do transformations, rotation, scaling, even translation, there is not possible (for me) to snap to special points.
I do all the rotations because I try to keep the tangency of the first frame. The inaccuracy comes when I try to locate, two of the three circles to a desired place. It's complicated for me to explain this point. When you try to join two circles, you have them in a specific position, where is hard to find the tangent circle to the others. But when the circles are aligned like in the first frame, it's easy to find the tangents.
If you have problems:
1.- Post a sample (or samples) of your file please.
2.- Please check here:
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/index.html
3.- If you manage to solve your problem, please post here your solution.

Lazur
Posts: 4717
Joined: Tue Jun 14, 2016 10:38 am

Re: Workaround: Arc tangent to two circles

Postby Lazur » Sat Jul 20, 2013 10:08 am

Took another look on the construction.
There is no need for obtaining the rough desired distance, you can construct it right:

SVG Image

That way of measuring the angle was clever!
Not geometrically correct, but works better.

hulf2012
Posts: 716
Joined: Sat Nov 24, 2012 12:37 pm

Re: Workaround: Arc tangent to two circles

Postby hulf2012 » Thu Aug 01, 2013 3:49 am

Hello:
Lazur, you are right,
At the end it seems that there is a easier and more general solution.

So I'm delivering the version 0.2 of this workaround:

The two first circles can be put in any place. The third circle, which is the tangent circle, try to be not so small or so big, allthoug if it's big enough a smooth transition can be drawn between circles.

If you have problems:
1.- Post a sample (or samples) of your file please.
2.- Please check here:
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/index.html
3.- If you manage to solve your problem, please post here your solution.

Lazur
Posts: 4717
Joined: Tue Jun 14, 2016 10:38 am

Re: Workaround: Arc tangent to two circles

Postby Lazur » Thu Aug 01, 2013 4:39 am

That looks decent!

Now, another workaround based on that would be, with more of an inkscape drawing aspect:
duplicating the c1 and c2 circles, and combining them,
adding a 2*R3 wide stroke,
converting the outline to path,
breaking it apart and deleting the smaller path,
then
adding a 2*R3 wide stroke to the bigger path,
converting it's outline to a path,
breaking it apart, and deleting the bigger one
-and it will result in the right path, hopefully.


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