I'll probably look at it again tonight, after work, unless someone else solves it.

Hi Martin, so the "tan" and "perp" snaps that you are seeing are line-based snaps, when you see them pop up they are showing you a tangent location on a line coming from the previous picked point which in your case here is the second picked point of the arc, not showing you the type of tangency that you're looking for which is more of an "full object" tangency.

That type of tangency is usually created by the Circle or Arc tangent command, and not by "Circle through 3 points", but circle and arc tangent are set up to make stuff tangent to 2 curves and through a point, or tangent to 2 curves with a specified radius, or tangent to 3 curves, but not tangent to one curve and through 2 points like you want to do here.

Pilou, I think your method will only work in the special case where the 2 points are equal distances away from the center line...


It looks like the link bemfarmer posted above has the answer in it, though.


- Michael

<< the special case where the 2 points are equal distances away from the center line...

There is always only one line between the 2 "upper circles" centers, so an only one middle, so always an only "special position" ;)

Try my method, it's a simple simplicity against the theory :)

Hi Pilou, how would your method work with points like this:



- Michael

So simple and works with any 2 points, circles...



And when you have drawn your circle 3 Points as I said just rotate as inverse :)

Hi Pilou, again you seem to be assuming that always the 2 points are equally spaced from one another.

Here I will exaggerate it a bit more, try with this example and with the attached file:





It is indeed simple if the 2 points are exactly balanced and form an isosceles triangle with the center of the circle as you keep showing, but that's just one special arrangement of points.

- Michael

This special case asks some reflexion! :)

Hi Pilou, the one that you are showing the solution for is the special case with points arranged in a particular configuration. I don't believe that your solution works for the more general case where the points are placed anywhere...

- Michael

Well here's my solution http://screencast.com/t/EngogKiRXu6C

I don't know if it's the same as the way shown in bemfarmer's link, as that was hard for me to follow, but somehow I got to work it out OK.

Martin (2)

Hi Martin, I'm glad that you got it solved. I will look into adding this case into the circle and arc tangent commands.

- Michael

So for your special case :) (I have made a general rotation for more practical explanation ;)




Cool movie solution of the mirror trick !

>>Hi Martin, I'm glad that you got it solved. I will look into adding this case into the circle and arc tangent commands.

>>- Michael

Michael.

That would be nice if you can do it and definitly appreciated by me - not because I perform this particular manoeuvre on a daily basis, but it would be one less interruption to hamper workflow when the need arises.

Well apart from this one case, I must say that I tried quite a few different tangent intersection scenarios and have come away very impressed with the logic built in to MoI and its ability to find the right solution. Most software seems to either give a null result or insist on jumping to the wrong side of the arc when doing one of the more unusual kinds of blend.

Thanks to all for helping.

Martin (2).

Martin(2), your mirror by midpoint method, with construction line and circle tangent command is very nice.
In your example, there are two circle solutions. There are other cases...




I've never studied inversion/reflection in a circle, nor radical axis, and haven't grasped it yet. Here are a couple of pdf's on the subject:

http://geometer.org/mathcircles/inversion.pdf

http://jwilson.coe.uga.edu/MATH7200/InversionCompanion/inversion/inversionSupplement.pdf

So what would a MoI command to invert some geometry, with some circle do?