Arc tangent to line and arc

[AllenJessup]

I thought this would be simple but I can't get it to work.

I'm trying to draw an arc that's tangent to a line at a specific point and tangent to an arc. I drew the line, started the arc command, hit enter to force the arc tangent to the line at the endpont and then tried to use a Tangent OSnap to hit tangent to the arc. This is what I got. Note the Tangent snap at the midpoint of the arc.

If I accept the Tangent snap it does draw the new arc to the midpoint of the existing arc. Definitely not tangent.  Does this mean there is no solution? I think I'm missing something. I'm usually aiming for a set radius and have no trouble. This is kind of a Best Fit situation. The only criteria are that the new arc be tangent to the red line at the intersection with the yellow line and tangent to the red arc.

Allen

[doni49]

---

@AllenJessup wrote:

---

doni49 wrote:

When I used my lsp routine, and then do as you say, it produces a line that's "0.00000000001029" long.  When I use the graphical solution, I get a line that's "0.00000000000575".  So in my test case, the graphical solution was actually more accurate than the lisp routine version.

---

That's strange. Every time I use your Lisp I get zeros out to 14 places. Are you using Fillet to trim out the circle?

Allen

---

No I use TRIM (selecting the orig line and curve as the cutting elements).

[AllenJessup]

Matt,

Took me a while to duplicate your process. It looks like it has to be drawn in the order of tangent first then curve.

Thank you.

Allen

[AllenJessup]

I've done a little more testing and now see that the tangent osnap does not go to the midpoint of the Arc, The TAN Osnap hits the point where the Chord of the arc being drawn would be tangent to the destination arc. WHY?

Allen

[doni49]

It sounds like the osnap function doesn't take into account the type of object being drawn.  It assumes you're drawing a line -- in that case this WOULD be the correct location for the line.

[AllenJessup]

I swear I remember this working correctly in the way-back. I wish I had an old R12 (not 2012) AutoCAD to test it in.

Allen

[Joe-Bouza]

More importantly the curve and the tangent have to be drawn in the same direction, and when drawing the free curve follow suit

[Joe-Bouza]

helping with the graphical solution evidently

[nestly2 · Accepted solution]

Low-tech solution...

Above can be done without any construction geometry by re-orienting the UCS, but I though this was the best way to demonstrate how the center is found.

[Neilw_05]

Looks like you found another graphical solution. 1 kudo for you

[Anonymous]

Thats impressive. I cant follow the geomtry as to why it makes sense. If you were kind enough I greatly appreciate it

[Neilw_05]

The 2 solutions are nearly identical, just constructed in a different way.

In the attached screen capture you can see the 2 solutions overlaid on each other. The line colors help to see the lines that correspond to each solution. The phantom lines represent the overlaid lines from the opposite solution.

[Neilw_05]

After running a few more tests I can confirm the original solution is correct. There must have been an error in my geometry when I ran this first test. Likely I didn't place the copy of the line perpendicular to the tangent precisely on the center of the target arc.

[nestly2]

---

@Anonymous wrote:
Thats impressive. I cant follow the geomtry as to why it makes sense. If you were kind enough I greatly appreciate it

---

Maybe this is more clear

[Pointdump]

Nestly2 (Is there a Nestly1?),

OK, now I'm even more impressed and confused. I haven't a clue how that works, or why. What constraints did you use to copy the circle over to the perpendicular construction line? And how do you make those cool GIF's?

Dave

[nestly2]

Nestly2 (Is there a Nestly1?)

Due to circumstances beyond my control, I lost access to my original account.  😞

I haven't a clue how that works, or why. What constraints did you use to copy the circle over to the perpendicular construction line?

Copy the original circle/arc to the endpoint of the line, then move it's center to the intersection of it's perimeter and the perpendicular line. It is now tangent to the line at the endpoint of the line.  A line through the intersection of the two circles intersects the perpendicular (yellow) line at a point that is equal distance from both circles  (ie the centerpoint of the circle that will be tangent to both) 

And how do you make those cool GIF's?

Camtasia Studio

[AllenJessup]

Very good Nestly. This brings me back to compass and straight edge drafting. If I'd started thinking like a hand drafter or Surveyor I might have figured it out. But I kept trying to force the program to give me the answer. I still think it should without all this construction.

I haven't heard anything from Autodesk on the SR I opened regarding this. When I do. I'll post their answer.

Allen

[Pointdump]

Nestly2,

Thank you. Makes perfect sense now.

Dave

[AllenJessup]

After all this it's now been decided to hold the standard return curve radius on the curb and move the catch basin. A much better solution in my view. More expensive but better.

This thread was not a waste of time for me (and I hope others). I learned a lot and enjoyed exploring all the solutions.

BTW. The SR I opened on the subject on Nov 5th still has no reply. I don't know if I'm being ignored or Autodesk is confused. Or maybe just very busy at the moment.

Allen

[AllenJessup]

I got a reply about the SR. It's being forwarded to the Development Team.

Allen

[Anonymous]

Hi Allen

What was the SR for? the precision

IMHO this was one of the most elucidating threads on geometry. The graphic solutions are mint. I do have a like for the math solution but would most likely go graphical.