When you say Curve 3 Points, you mean Arc 3 Points ?
Because if it's a curve you have an infinity of solutions!

Hi Psygorn, may be you can do it the (not so) hard way with 3pt circle ?

Sorry my bad! yes you are right I mean Arc 3 points. :-)

Your method sounds promising, However, I have to check it thoroughly. ( I mean I want to check if it yields true tangent point) needless to say it sounds promising.

One thing that made me suspicious about it is that when I zoom in I see two different crossing! ( I mean when I zoom in it seems the curve crosses the red line at two different points which means this method does not show the true tangent point)

I checked it using Trim method and it seems your method is correct way of finding the tangent point!

Hi Psygorn so if you do mean "Arc through 3 points", 3 non-collinear points already fully defines a single unique arc and so there isn't any way to set up a tangent additionally there.

I'm not sure that there is a built in tool in MoI currently that will generate a circle by tangent and 2 points on the circle. It can be calculated with this method:
https://www.emathzone.com/tutorials/geometry/equation-of-a-circle-given-two-points-and-tangent-line.html

- Michael

I'll be the first to say I'm not good at geometry. May be a simpler way.

This does seem to match your blue curve. Coincidence? Will it work in all cases? Don't know :)

Draw two small half circles (magenta)

Draw straight line to ends of circles (green)

Select both circles and Blend [Tangent G1, Bulge = 1] (cyan)

Pilou find apex trick (orange lines)

Draw Perp to Perp line from Blend apex to green line (black)

Draw 3-point arc from top to bottom of green line while snapping the center to the intersection of the black & red lines (blue)

Ed Ferguson

Perfect maybe...
So my little trick can help! :)

A curious problem who can have some solutions! :)

A perfect headache!

PS Alas your method don't work :( Big zoom shows 2 crossing curves!
Or i miss the verification...

Little half circles are well on the same line than the green one ?

The Circle tangent command can do circle tangent to 2 curves through a point, or tangent to 3 curves, but not tangent to one curve through 2 points like you want in this case.

- Michael

Hi Psygorn,

re:
> So, in MOI 3D, when you already have a line how could you draw a curve tangent to that line, quick and fast?

Circle Diameter can make a circle tangent to a line quick and fast, the problem is that you want not just a tangent circle quick and fast but also passing through 2 points.

- Michael

OK I believe i have found! :) Half only ! :( so...on the track!

And with my Apex trick! ;)

Just draw a little red arc circle 3 points! :)

Resists half to the big zoom! :)

Damned! It's good just on upper part! :(

https://moiscript.weebly.com/uploads/3/9/3/8/3938813/resist.3dm

What a fight!
With a little red, a big black, intersection with the 2 Apex on the green Vertical
quasi perfect but...the black arc is not totally under the green one always on the bottom part at atomic zoom size! :(

An another simple and quasi perfect but...

Another one quasi perfect! But...
(crossing to perpendicular)

Some geometric solutions at:
https://www.quora.com/How-do-you-construct-a-circle-passing-through-2-points-outside-line-L-and-tangent-to-line-L

- Michael

Pilou -

I zoomed in to the microscopic level on my model and indeed it's not tangent. Then I tried the Jfs (PAQUICINNO) method in his video (which I think is the better solution), and it also was not tangent. Of course these are visual checks.

I don't know the mathematical solution, or even if displayed curves are 100% visually accurate when zoomed in that far.

Practically speaking, the error I saw when zoomed in that far is below the resolution on my micrometer :)

But it would be nice to verify what the precise solution is.

Update - I see Michael has linked to a solution above. Who wants to test it? :)

Ed Ferguson

From https://www.quora.com/How-do-you-construct-a-circle-passing-through-2-points-outside-line-L-and-tangent-to-line-L?share=1

I think this one is the easiest:













Create circle/arc 3 pts through points A, B, P.

- Michael

Here's a video I made that demonstrates a reasonable way to make the tangent.
https://vimeo.com/545453177


Martin.

Nice solution Martin!

hi Martin

Nice vidéo; Very Clever !

Hi Ed,

I was suspicious about your solution. and yes I think PAQUICINNO's method works better maybe! ( yet it needs to be proved mathematically)

And I checked something when there is a line tangent to a circle and when you zoom in on atomic scale you see that there is a tiny gap between tangent line and the circle - which I believe it is normal to see such thing at such microscopic zooms - but there are no several crossings!

And feel free to check what I said in the attached file.