I'm still fairly new to Inkscape and need help forming a unique shape consisting of a large circle and a small circle connected with tangent curves and then the internal sections of the circles removed. The picture shows the two circles and an approximation of the curves.



This may be the wrong approach for this, but I turned them into paths and added nodes on the large circle 45deg left and right from the bottom where I want the tangent lines to connect. I'm trying to find a way to draw a curve from one node to another, hopefully with a way to ensure they are tangent, but I've so far been unable to find a way.

Thanks in advance!

Hello there!

The things you want to achieve at the same time is impossible mathematically.
You want to connect selected nodes with a tangent curve -you can do that with a regular path, but it won't be circular.

If you want to stick with tangent circles,
keep in mind that you can construct a circle based on three independent input data.
For this construction you have two tangent lines and two points for the inputs,
which means one of those has to be left out.

For example those tangent circles you want to construct either have different tangents,
or different sizes of the basic circles.




In geometry you can find more information on such constuctions at Apollonian -tangent circle- constructions.

If you are more interested in drawing a tangent curve for the bulb in a less geometrical way, then I will write an example way for doing that.

Hello,

If you are more interested in drawing a tangent curve for the bulb in a less geometrical way, then I will write an example way for doing that.

Well, I think it's an interesting topic. I've managed to conect to circles with a tangen curve (the arc of another circle), but it's just for special cases. And other limitations.
Lazur, if you want please share that example. Later, I will try to show my method, but I can't promise it.
Greetings

Here is a topic that talks of tangent lines; tangent curves to two circles would necessarily be within the two tangent points of the line (for concave curves, naturally another set of convex tangent curves would be outside those points). You can control the slope/shape of the tangent line/curve, or the separation between the two circle centers or the relative sizes of the circles, but not all three! Also as Lazur has pointed out the tangent curve cannot ever be a circle

hulf2012 wrote:Hello,

If you are more interested in drawing a tangent curve for the bulb in a less geometrical way, then I will write an example way for doing that.

Well, I think it's an interesting topic. I've managed to conect to circles with a tangen curve (the arc of another circle), but it's just for special cases. And other limitations.
Lazur, if you want please share that example. Later, I will try to show my method, but I can't promise it.
Greetings

Well I was afraid that this has to be explained haha.
Here is the process in a nutshell:


It is much harder to describe step by step for someone new to inkscape as it is only complicated without some routine in the basic tools.
The idea behind is that the circle arches are as well defined for a 45° turn by two nodes as this tangent curve should be.
So it is an intuitive representation of such tangent curve -as you couldn't be sure with any path's curves, what do they really represent.

druban wrote:Here is a topic that talks of tangent lines; tangent curves to two circles would necessarily be within the two tangent points of the line (for concave curves, naturally another set of convex tangent curves would be outside those points). You can control the slope/shape of the tangent line/curve, or the separation between the two circle centers or the relative sizes of the circles, but not all three! Also as Lazur has pointed out the tangent curve cannot ever be a circle

It can be a circle but not in this case.
You can construct a tangent circle to two given circles and one point, or to two circles and a line,
or a tangent circle to three circles.
That last one is the hardest of those, I should read them upon as inversion is used for the construction.
Well it's theoretical, knowing that it wouldn't come out precisely in inkscape. Maybe with python?...

The wikipedia has some nice examples for those:

http://en.wikipedia.org/wiki/Apollonian_gasket

Didn't checked that mentioned post, I will look at it!

I only meant that I could not think of a method to construct a tangent circle to two overlapping circles. Did you find a way to do that

That is two independent input data; for the construction, you need three -or you can construct an infinite number of circles that would be tangent.
Like, in my first example there is a constructed tangent circle.
More precisely that is a tangent circle drawn to a circle and to a line and a point.
Only that is not matching exactly the original post, as that has 4 of those inputs:
start and end tangent lines, and starting and end points were all given.
One of them has to be left out.

Hello:

I placed a workaround here:
viewtopic.php?f=6&t=15711


Greetings

Here is a geometrical construction if one tangent point is fixed on one of the circles:

Actually it didn't came out too accurate in my opinion due to the differences between a geometrical circle and circular paths with 8 nodes.