algorithmic modeling for Rhino
I thought this group sounded like a fun idea, so I thought I would suggest one based on something I was looking at earlier in the week.
The challenge:
To find the medial axis of a 2d polygon in 15 native components or less without scripting.
http://en.wikipedia.org/wiki/Medial_axis
http://w3.impa.br/~paesleme/MedialAxis/MedialAxis.html
Good luck!
Tags:
http://stackoverflow.com/questions/1069523/find-medial-axis-of-a-po...
I've looked at this before, but I do not think it's actually the medial axis, but an approximation. I think Daniel has done some work with these.
My entry, though again, I do not think it is exactly the medial axis.
Ok, and one more, to deal with 'islands' within the boundary curve. Inspired by this post on codequotidien.
Hi Luis,
I created this geometry via tspline tweaks on Rhino.
In order to have more control over the generative form, I was looking up ways to work with tsplines in grasshopper and found threads on voronoi medial axes.
I ran your definition and wondering how best to apply tsplines to the resulting voronoi curves? Or is this even the best way?
Many thanks again - your definition was very helpful.
RP
As far as I know, this is not medial axis - cant remind where I read about this ;/
But the paper Adam linked seems to tell something else - so really dont know now :)
Yes, like I said, I think it's an approximation, but perhaps not the real deal....
I bet this is how GCode for V carving is made. Do you know about any papers that show how to make exact medial axis ? Wikipedia says that curves of medial axis are parabolic, so should be possible to do that.
Back to GCode : distance to closest point on curve = Z axis movement.
5. The poster judges the answer. They should offer a sample solution as well when they declare the winner.
I am looking forward to the sample solution from Adam...
Well, the solution I got was the same as you Luis (using voronoi), although you did it in less components than me:
It seems though that you have proved that it isn't exactly the medial axis that we are getting, so I guess no one has really succeeded...
I did think though that maybe there is another simple way of doing it, based on the article I posted, by generating circles from sets of 3 points on the curve that have normal vectors at obtuse angles to each other. I am looking into figuring this out now.
Why is it more accurate? Again, take a look at where those points go when you use a CurveCP component. Using the distance as a radius for a circle, it still does not meet the bounding curve at more than one location...
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