Circle by 3Points - Not tangent

Hi Guys,

I tried the "circle by 3points" GH function but since the function does not include tangency to curves the circles are not always included in the triangle (if not equilateral).
Would there be another way to get a circle from point AND tangency to curve ?

Many thanks,

Arthur

Replies to This Discussion

Permalink Reply by David Rutten on October 1, 2009 at 11:17am

Wikipedia page with triangle|Circle math.

I can add a component that takes a triangle and creates the circle, but until I do you'll have to transscribe one of those equations into either Grasshopper nodes or VB.NET.

--
David Rutten
david@mcneel.com
Seattle, WA

Permalink Reply by Arthur Mamou-Mani on October 1, 2009 at 12:10pm

Thanks a lot David,

I am actualy trying to draw the "incircles" using existing tools on GH.
On the wikipedia link it says: The "InCircles" center is located at the intersection point between the bisectors of the triangle's angle.
Is there any easy way to get the bisector line of an angle on GH ?

thanks again:)

Arthur

Permalink Reply by David Rutten on October 1, 2009 at 1:54pm

You can construct a bisector by taking the two departing vectors, unitizing them and adding them.

This, if you have a triangle defined by 3 points A, B & C, you can create two vector starting at corner A (AB and AC). Then you unitize both vectors (to make sure they are the same length) and add them together. The resulting vector points in the bisector direction.

The VectorSummation component has a boolean input parameter which will unitize the vectors for you, so you can skip that part.

I just wrote a component for this so it will be available in the next version.

--
David Rutten
david@mcneel.com
Seattle, WA

Permalink Reply by David Rutten on October 1, 2009 at 3:49pm

I also just added a Steiner Ellipse component. The cool thing about those is that two adjacent ellipses are both coincident and tangent halfway the triangle edges. So if you construct them from a grid of triangles they always line up:

--
David Rutten
david@mcneel.com
Seattle, WA

Permalink Reply by Arthur Mamou-Mani on October 2, 2009 at 6:07am

Hey David,
Thanks a lot! Made it!
I found the angle bisector using your advice but was wondering: What does "unitize vector" actualy do?

Permalink Reply by Damien Alomar on October 2, 2009 at 7:09am

It sets the vectors' length to 1...vectors can represent both direction and mangnitude, but if you have unitized vectors, then they are pretty much just a representation of direction.

Permalink Reply by Adelina on January 22, 2011 at 9:40am