How to find the tangent point on a planar curve throught another point in the same plane?

Hi,

I have solved this maths before using recursion with bi-section inside C# component inside grasshopper, but the speed seem to be quite slow if I want to yield a good result.

It seems that Rhino could snap to the tangent point while modelling. I looked through the help doc on rhinocommon but could find anything helpful.

Is there a powerful function out there which could solve this problem? or, Is there a cleverer way to solve this math in a more mathmatical way?(with less guessing, thus more suffienct)

Thanks,

-Jerome

Replies to This Discussion

Permalink Reply by Damien Alomar on May 29, 2011 at 6:58am

Nope. AFIAK recursion is the only way, and if it was too slow for you, then I would suggest revisiting. I remember putting together a function that did this and tracked mouse movements in Rhino so you could get realtime feedback. There was no lag and the response was pretty smooth, so I'd imagine a faster result is certainly possible.

You should be able to use some pretty light math to get this done. Just create a line from the tangent at a given point, then test the distance between the point and that infinite line (I believe there is a Rhino function that does this, although the math for it shouldn't be too outrageous). As that distance approaches zero, you've got something that's closer to intersecting. After that, its just a matter of structuring the recursion in a good manner.

I'll see if I can find where I did this, but I'm not really recalling many details about it other than what I mentioned above.

Permalink Reply by Jerome on May 29, 2011 at 7:19pm

Thanks, Damien

Yeah, your suggestion of combining the mouse movements to find the answer is a good way to go, I will try it these days. However, what I really what to achieve is the fully automatic finding without any human interference.

Damien, I don' quite understand the next process you mentioned. How to detect "distance approaches zero"? Maybe this would be another kind of robust calculations that would take time. or, Maybe I just misunderstand your method.

Thanks,

-Jerome

Permalink Reply by Tuan N. Tran on May 29, 2011 at 1:32pm

In this definition, I sample a line at some (t) parameter and find the Tangent vector (vector1) of the curve at that parameter. A vector (vector2) is created from this point on the curve to the point you want to draw the tangent line. Both vector1 and vector2 are unitized. I used Galapagos to minimize the distance between the these two unitized vector.

This took less than 15 seconds to find. I suppose this method needs tweaking if there are more than one possible tangential points on the curve.

Hope this helps.

Permalink Reply by Jerome on May 29, 2011 at 7:03pm

Thanks, Tuan

Galapagos is a way to go, but it seems that it needs a lot of tweaking before it could yeild a fast result. The first population in galapagos is just some random seed and this will consume a lot of time. Bi-section, however, it goes toward the answer from the beginning to the end. It took bi-secion less than 0.1 second to find the answer, but for me, too long. More mathmatical may be a better idea than these robust ways.

Thanks!

-Jerome

Permalink Reply by Firat Aydin on December 27, 2012 at 10:44pm