Make Surfaces from Contour Points - UPDATED with internalised data

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Permalink Reply by Laurent DELRIEU on June 14, 2016 at 1:18pm

Hello I ooked at your problem, I am sure there are others smarters solutions. Here is one using this script 

http://www.grasshopper3d.com/group/milkbox/forum/topics/alpha-shape...

hope it helps a bit. Have you looked at components to make the kind of stuff you want ? 

Perphas it is best to extract pt in Rhino and finish the work by hand ?

Attachments:

• QLD2.gh, 37 KB

Permalink Reply by Alessio Erioli on June 15, 2016 at 8:56am

Hi!

Sadly, you incurred in a known problem that has neither an easy nor a unique solution: finding a non-convex contour given an array of points. It means that there is no unique mathematical solution to finding a concave contour polyline (which is in general what you need). In your case each contour section contains a series of points of which you do not know the order and you need to sort them so that by connecting them you find the contour. This is fairly easy to do when the contour is convex (basically you find the average point then calculate the vectors from the average to the points and sort the vectors by angle - sorting the points by the same angle gives you the right order for the contour), but generally impossible to find uniquely when the contour is concave (PS: convex means that, for ANY 2 points inside the figure, a straight line connecting them doesn't intersect with the border curve - i.e. circles, ellipses, rectangles, triangles - concave shapes are a star, a crescent moon, an arrow, a boomerang, etc.).

The problem goes like this: given a generic list of points:

Each of these configurations for a perimeter equally fits the above:

Laurent already went for another possible solution, the stochastic approach (by subdividing the connecting lines), I slightly adjusted a few things over his solution:

namely, I added a rounding option to adjust for some weird tolerance issues (some points that should be at Y=80 were at Y=79.99998 or something) and a more straightforward solution to group them by section plane using sets logic. This, coupled with alpha shape, gives a quite good approach, still very coarse in terms of results but that depends on the sampling resolution of the field (i.e. number of height sections in which you calculate the metaballs) and sampling length of the connecting lines.

Definition attached.

Attachments:

• sectioning metaball curves AE.gh, 267 KB