If I know the distances between a point and two space curve, how can I locate this point? is this point unique?

Hello everyone,

Here is the question. I have two space curves, and I want to find a point (location), with the known distance to the two curves. As the pic shows, the distances of the point to the short and long curve are 1.9 and 2 mm. Is this point unique? And How can I find this point (location)?

My idea is like this:
1, create perpendicular plane for each curve, then draw circle with the radius as the distance;
2, move the perpendicular planes (circles) along the curves until they have tangency.
I may do it manually, however, I don’t know how to realize it automaticaly.

The curves are here: spacecurves.3dm (29.2 KB)

Any suggestion and comments are so appreicated!


You can make a pipe with radius equal to your distance for both curves, and then intersect the 2 pipe surfaces.
In the picture, any point int the yellow curve is a valid result.
So, no, there is not an “unique” solution.
You might need to add another “rule” to the problem.

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Thank you, Riccardo, for your quick and nice answer!

You method is much better than mine. So I could change the question, how can I find the first point (from bottom to up)?

How accurate does it need to be?
You could divide the intersection curve and then sort for the Z key. (But you might be off by a small factor. That’s why I’m asking.)

Or maybe there is even a much easier solution, but I can’t think of one right now. :sweat_smile:

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Thank you, Luc, for your suggestion. Yes, I think that’s a good idea. I don’t need very accurate location.

Thank you all!

lowest intersection.gh (7.8 KB)

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That’s great, Riccardo!!

Thank you so much for your help and patience!

:clap: There is the easier solution …
Nicely done : )