Hi,

is there a script or something to ease the creation of a line tangent to say 2 circles or arcs or better wet, a couple of curves?

I know it's pretty basic, I had to it the other day and my memory failed me (again) and I had to do a search on the web to find the old way. For circles and arcs it's fairly easy but for curves it's another story.

Thanks in advance,
Felix

Hi Felix, there isn't any way to script that right now, the tan/tan mechanism relies on mouse input and looking for the shared tangent in the general area of your first and second points. You have to get your initial points somewhere in the general (like 50pixel or something) neighborhood of where the actual tan/tan line is at.


> For circles and arcs it's fairly easy but for curves it's another story.

Could you please post a 3DM file with a set of curves that are giving you trouble so I could take a look?

- Michael

There appear to be some tan,tan snaps for two circles, for the up to 4 tangent lines, when the
line starts "near" a tangent point....
There are 4 simultaneous equations, in the case of 2 circles...

http://www.cut-the-knot.org/Curriculum/Geometry/TangentTwoCirclesI.shtml#explanation


Even got tan,tan snap for a circle and a catenary... :-)

Michael,

here is a simple 2d drawing where I was trying to create the blue lines. For what I would call the "external" tangent lines, the solution is to create a circle inside the larger circle with a radius of R2-R1 then draw a line from the center of the small circle tangent to this circle we just created and translate this line to the edge of small circle (followind the perdendicular radius). Basically, it's the same for the "internal" tangent-tangent lines except this time you create a new circle with radius R1+R2.

I haven't tried any of this on curves yet maybe some day I'll have a need for it but my guess is it would be a little more complicated.

@bemfarmer: I got this idea from here http://mathworld.wolfram.com/Circle-CircleTangents.html

Thanks,
Felix

Hi Felix.

You pose an interesting question.

On google, found a way to construct the two centers of similitude, (There are 0, 1, or 2 such centers, depending) for
two circles, by copying the red line to the green line, and making construction lines.

http://www.cut-the-knot.org/Curriculum/Geometry/TangentTwoCirclesII.shtml

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





( The inner tangent line just happens to be close to the points where the red and green lines intersect the circle.)

Bemfarmer,

I understand there is a mathematical way of doing this and that we would need to solve some equations to do this via a script. But I didn't recall the way to do this by "construction" either.





In order to construct L1' one as to first construct the blue circle with a radius of R1+R2, then draw a line from C1 to P1 which is tangent to the blue circle, (Moi give us a snap point at P1) then we translate L1 from P1 to P1' along the radius line (cyan) from C2 to P1.

The process is basically the same to construct L2' except this time we create a circle (cyan) with a radius of R2-R1 instead.

Regards,
Felix

You can construct all this without any drawing anything! ;)
Just use helpers lines and the Line function !
Call Line function but draw only helper lines !
AB (center of each circle)
MM' (diameter perpendicular AB)
NN'
MN' (N' is hidden by the dialog box on this image :)
M'N
J is the intersection of MN' & M'N
JB then Reorient it ! (Rotate from J toward N - will be the same toward N' for another internal tangent)
Tangent Click first point
Tan / Tan on the circle = Click second Point
et voilà ;)
Seems the more easy for the moment before Michael makes a special script :D
Moi is fabulous for any 2D geometry's construction! (surelly the same in 3D ;)
here the image ;)

very neet Pilou!

Have you thought about the outside tangent lines?

Thanks,
Felix

Yes its the same even more easy!

Call Line
Now just helper lines
AB each center of circle
AN Radius perpendicular to AB (NN' if you want the 2 tangents extern)
BM Radius perpendicular to AB (MM' if you want the 2 tangents extern)
NM
AJ = intersection with NM
JA Reorient it (Rotate from J toward N Tan..gent : first click
Tangent on second circle : second click
et voilà :)
Here the image :) sorry for bad visibility it's my fault not Moi :)

Splendid work guys!

So we see, that's how sausage is made. ;-)

I opened the sample file and the tan/tan snap works for all of those blue lines? Maybe I'm missing something.

@ Burr
Yes but that was not the problem ;)
The problem was : that is complex and painful for obtain the blue lines ;)
Redraw a circle etc...
With my little new method above that is more easy ;)

PS : Precision: it's not my method, i had found it on the Net and adpated it for Moi ;)

I must be missing something. I refered to the sample file posted here:

http://moi3d.com/forum/index.php?webtag=MOI&msg=5253.4

And could delete all those lines and redraw them in a few seconds...

No circles? I am assuming the circles are in the file? Is the question about being abale to draw this type of shape without the circles there?

@Burr
No, i believe that is just for the method ;)
Felix wants not add more circles than existing for draw the tangents !

And wants even a special function : just click 2 circles and the tangents will drawn! (internal(s), external(s), both)
But don't know if Michael will make that ;)

""""""""""Felix wants not add more circles than existing for draw the tangents !"""""

Yeah, but the Tan/Tan snap does this.

"""""""""""just click 2 circles and the tangents will drawn! (internal(s), external(s), both)""""""""

Oh, ok. A script that automates it is the request.

Not this?

Hi Felix, maybe I'm a little bit lost with what you're discussing here, but like Burr says above, MoI does have a tan/tan snap that you can use to construct these kinds of lines without needing to do any of that additional extra work.

> here is a simple 2d drawing where I was trying to create the blue lines. For what I would call the "external"
> tangent lines, the solution is to create a circle inside the larger circle with a radius of R2-R1 then draw a
> line from the center of the small circle tangent to this circle we just created and translate this line to the
> edge of small circle (followind the perdendicular radius).

You don't need to do any of this additional circle construction and line translation - just draw in a single line and it will give you a tan/tan snap point that you can grab on to. It's a special snap that not only snaps the endpoint of the line but also moves the base point of the line as well. It also works on bendy curves as well, not just circles.

In order to use it make sure "Object Snap" is enabled in the bottom toolbar, and also make sure you have not disabled "tan/tan" snap type in the object snaps list, and then you just draw in a line nearby where the tan/tan line is and move your mouse until you find the snap point that is created, it is usually just a short distance away from the single end-point tangent line.

See here for a previous example:
http://moi3d.com/forum/index.php?webtag=MOI&msg=2788.4

EDIT: and I was going to do a video showing it on your same file too but it looks like Burr has done that already, thanks Burr!

So none of that extra work for constructing circles and moving lines is needed, just draw a single line in fairly close to where the tan/tan line is at and there will be a snap point created that you can move your mouse to which will then give you the tan/tan line, it works on curves as well.

- Michael

There's also a similar perp/perp snap that you can use to create a common perpendicular line between things in a similar way as the tan/tan snap:
http://moi3d.com/forum/index.php?webtag=MOI&msg=3042.13

- Michael

Hi Felix, so notice in Burr's video above how he just uses the line drawing tool and that's all that is needed for putting in tan/tan lines - he just places the line in nearby where the tan/tan line is, then there will be a snap point created on the second circle (or curve, it works on any bendy curve as well) right at the tan/tan location and if you put your mouse on it the tan/tan snap will engage which will also move the base point of the line. You can tell when that special tan/tan snap engages because a "Tan/Tan" tag will appear on not only the end point of the line but also the start point of the line as well - with that snap the start point of the line is also adjusted. Here's a previous video of this in action:



Move your mouse a little ways along the second curve until you find the tan/tan point and then you'll have these lines you need without doing any special extra construction work.

- Michael

Aaaaaaaaaaaaaaaahhhhhhhh :)
That is some magic! Never seen these 2 posts or did'nt remember this double move back !

Script was yet existing :)

So i had learnt the mehod for pencil and paper ! :)