Circle tangent to curve

Hello,

I'm looking for a grasshopper definition to make circles be tangent to a curve. The circles shoud not overlap the curve nor eachother and depend on the curve control-points.

Below is an example how it should look like. I prepared it manually in Rhino.

Replies to This Discussion

Permalink Reply by TheChosenOne on November 26, 2011 at 4:51am

Yeah, interesting little problem.

Permalink Reply by TheChosenOne on November 26, 2011 at 5:19am

Attachments:

circlesoncurve.gh, 11 KB

Permalink Reply by Jacek Jaskólski on November 26, 2011 at 5:43am

1. What do you mean by depend on the curve control-points?

2. If you want the radius of the circles to correspond to the curvature of the curve (like in your example), there're curvature components to help you with that.
3. If you want the circles to distribute evenly throughout the entire curve (no intersections & no gaps) then it's not that elementary anymore. I'd go with using the Kangaroo solver to do it.

Permalink Reply by Chris Tietjen on November 26, 2011 at 1:33pm

Probably not useful...

Chris

Permalink Reply by TheChosenOne on November 27, 2011 at 11:24pm

I like it. An interesting solution.

Permalink Reply by Yoann Mescam (Systemiq) on November 27, 2011 at 2:34am

Voronoi can also be used for useful things:

Still a slider to move to get expected results though, some Kangaroo would be needed for hardest curve or perfect result.

Permalink Reply by Yoann Mescam (Systemiq) on November 27, 2011 at 2:54am

The setting of the slider is about (length of curve/(number of division points-1))/2

Or is there a way to find a circle inscribed in a convex polyline and tangent to at least a given side?

Permalink Reply by Yoann Mescam (Systemiq) on November 27, 2011 at 3:19am

A bit better but still needs adjusting (Kangaroo or Hoopsnake)

Attachments:

CircleTang2.gh, 8 KB

Permalink Reply by RWNB on November 27, 2011 at 4:53am

impressively!

Permalink Reply by Pieter Segeren on November 27, 2011 at 10:49am

hi everyone here, I found this a very interesting topic so I tried something too, with incircles, but got stuck for now...
then I tried to follow what you did Systemiq, and if I follow correctly I think maybe you meant to voronoi the found Crv CP's instead of the original division points, or? And can you teach me about the calculation of the offset amount please?

Permalink Reply by Chris Tietjen on November 27, 2011 at 12:44pm

Permalink Reply by Yoann Mescam (Systemiq) on November 27, 2011 at 1:39pm

The offseted curve is just an heuristic to find centers of circles:

as we are looking to distribute N circles on a curve of length L, circles have an average radius of about (N/L)/2, so their centers are near the curve offseted by (N/L)/2.

I wrote N-1 because I ignored the circles on the start/end, but this looks actually wrong.

About the Voronoi, it should not need the points on the offseted curve and should be sufficient to find correct circles: what we need is to find the circle inscribed in the V. cell cut by the curve, and touching the surrounding circles. I dont quite know if this is always possible.