Help needed....math problem

Sorry guys

I want to write a grasshopper definition where I can just draw circle and a random two points outside of circle to find a point on a circle that will give bisected angles in the image...

I'm not good at grasshopper :( Is this possible in grasshopper? can someone guide me through how to do this?

Thank you very much!

Attachments:

math_problem.jpg, 165 KB

Replies to This Discussion

Permalink Reply by David Rutten on April 6, 2011 at 1:30am

Hi kimu,

this is a lovely problem. While I'm thinking about how to solve it analytically, here's a Galapagos solution.

David Rutten

david@mcneel.com

Poprad, Slovakia

Attachments:

trigproblem_galapagos.ghx, 98 KB

Permalink Reply by Garcia del Castillo on April 6, 2011 at 2:02am

Hey David, the definition works fine, but you wrote it in GH 0.8.0008! hehe

Permalink Reply by David Rutten on April 6, 2011 at 2:07am

Darnit, I can't crack it. Either it's a lot trickier than it seems or my brain just isn't working today. If you have the solution on a napkin, I can probably tell you how to transfer it to a Grasshopper network.

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by benmo on April 6, 2011 at 10:46am

I'm sorry...I don't have solution......i don't know how to do it...

but would it possible in grasshopper where i can let it loop the points on circle and find out that one point where it will bisect that angles?

this is really frustrating...i really need to figure this out...and running out of helpp please help mee

Permalink Reply by David Rutten on April 6, 2011 at 11:16am

You might want to ask on a math forum somewhere. If they can write out the theory you'll probably find someone here to do the hooking up.

In the meantime, you can use the Galapagos file to get solutions, and you could also generate 10,000 points on the circle and find the best fit. Tot very elegant though.

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by benmo on April 6, 2011 at 11:33am

nicee!!! I tried to see the numeric value of each angle of the two angles in the galapagos file. and see where they match. because when those two angles become same that's when the angles (ones that i want) get bisected. it's not possible to find out when numerical value become exactly same in grasshopper??????

yess i'm trying to figure it out in mathematical way

Permalink Reply by benmo on April 6, 2011 at 9:01pm

is there anyway ithe gaapagos file you can use "equal" function or something that will get the exact value???

Permalink Reply by David Rutten on April 6, 2011 at 11:22pm

Hi Kimo,

I'm confused, what values are you looking to equalize and for what purpose?

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by benmo on April 6, 2011 at 11:39pm

in the galapogos file there is "angle" function two of them.

when they are exactly equal. that's when the angles that i want get bisected from the image that i uploaded earlier

and i was wondering if there was function that will adjust the number slider or something to give me equal numerical value of those two angles.........really desperate..

Attachments:

Image_1.jpg, 122 KB

Permalink Reply by Pieter Segeren on April 7, 2011 at 3:49pm

ARRRGH! This is breaking my head, very annoying indeed!
I might have found someone who will get us the answer. Maybe Larry already did..
Though I haven't found the solution in here just yet, I thought since you are the best man to spot the neccesary info in these very interesting clips, I'd just let you know.. hope you like it and even find the formula.

http://www.youtube.com/watch?v=tIEAQjrv8Os&feature=related

Permalink Reply by Chris Tietjen on April 7, 2011 at 9:44am

Here's a definition that let's you dial into a solution that might be accurate enough for some situations.

Chris

Attachments:

2PtsCircleBisector.3dm, 35 KB
2PtsCircleBisector.ghx, 183 KB

Permalink Reply by Larry Boxler on April 7, 2011 at 3:29pm

I dont have the chops to work out the math, but here's an idea that you may not have tried yet for an analytical formulation. Since you are finding the bisector here, the problem is analogous to a reflection problem for light which uses Fermat's principle to derive the light reflection path. See this illustration

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/fermat.html.

Your problem adds a bit of additional complexity in that the point x shown in the fermat principle diagram must lie on a circle of know radius r, but I believe that if you blend the equation of a circle and the equation from fermat's principle you can get it into an analytical form.