Construct a closest point with 2 parameters

Hello! Can anybody give some ideas to solve this? I have a point O, and have an algorithm to construct another point P, and I want point P to be as close as possible to O. Now this algorithm involves 2 variables. How can I determine the values of the 2 variables respectively, so that I can get the desired point P?

Hope this is clear enough to explain my problem. Thank you in advance for any help!

Replies to This Discussion

Permalink Reply by David Rutten on May 24, 2014 at 2:26am

Hi Lezhi,

what do the two variables represent? What are the constraints?

David Rutten

david@mcneel.com

Permalink Reply by Lezhi Li on May 24, 2014 at 9:00am

Hi David,

Thanks for the reply! What I'm trying to do is this:

I have a line 1 which originates from O1, I evaluate an A1 at a certain distance, from A1 I draw A1-O2 (the distance from A1 to O2 is predefined), keeping it perpendicular to line 1. Now I get O2, the origin of line 2.

To get the direction of line 2, I cross-multiply the vector O1-A1 and the vector A1-O2, and then rotate the cross-product around the axis A1-O2, the rotation angle is ALPHA.

Then I evaluate A2, keeping O2-A2 = O1-A1. From A2 I draw A2-O3, the distance of which equals to A1-O2. To get the direction of A2-O3, I rotate the direction of A1-O2 around the axis O2-A2, the rotation angle is BETA.

Then repeat the process to get line 3 and line 4. From line 4 I can get the position of O5 (O5 is the point P in my previous post), and I want O5 to be the same as O1 (or as close as possible).

The two parameters are ALPHA and BETA. Quite a complex process, hope the explanation is clear enough. Basically I just want to calibrate ALPHA and BETA so that O5 can be close enough to O1.

Permalink Reply by David Rutten on May 24, 2014 at 10:00am

[...] keeping it perpendicular to line 1. Now I get O2, the origin of line 2.

This is underdefined. There is an infinite amount of perpendicular directions away from a line in 3D space. If the operation is constrained to a 2D plane then there are only 2 possible perpendicular vectors.

Other than that the problem is now clear to me. There may well be a trigonometric exact solution to this problem, but perhaps you'd be happy with a solution using Galapagos?

David Rutten

david@mcneel.com

Permalink Reply by Lezhi Li on May 24, 2014 at 10:27am

Hi,

Thanks a lot! To clarify, the direction of A1-O2 is pre-defined, in other words it's a unique, determined value.

Yes there is a exact solution but it's quite difficult to calculate it manually. So you are talking about evolutionary algorithm? I was just thinking about it but didn't know there is a plugin for EA. Thanks for the information! I think I'll try to learn to use it and perhaps I will have other related questions to ask you later.

Permalink Reply by David Rutten on May 24, 2014 at 11:11am

If you upload the file you have with all the variable angles as sliders, I can hook it up to Galapagos for you.

David Rutten

david@mcneel.com

Permalink Reply by Lezhi Li on May 24, 2014 at 10:57pm

Hi David!

I'm not sure whether you are familiar with Hoopsnake. I want to do the process above with Hoopsnake, but had some problems, described here

http://www.grasshopper3d.com/group/hoopsnake/forum/topics/hoopsnake...

Do you have any solutions for that? You are already familiar with my problem so I think your suggestions will be valuable.

Thank you very much!

Permalink Reply by Lezhi Li on May 24, 2014 at 10:56am

Wow, amazing tool! The result is very satisfactory so far. Thank you very much!