How does Grasshopper evaluates a curve/srf centroid?

I wa wondering if anyone could explain the mathematical method Grasshopper applies for calculating the centroid of a surface/curve, I'm aware that the Polygon Center component uses the average of the vertices and or the average of the edges to calculate the center of a polygonal curve, but I'd like to understand the method it uses to calculate the centroid of an irregular planar curve/srf in the Area Component.

Thank a lot.

Replies to This Discussion

Permalink Reply by peter fotiadis on September 20, 2015 at 1:30am

I had several centroid (not to mention ...er...umbrella sticks[don't ask] stuff) related examples just for fun (polys, curves, cats, dogs, whatever comes first) ... but a recent major crash (in 2 workstations simultaneously: Karma, what else?) caused "some" MIA stuff, he he.

Until I'll fix(?) things(???) get this polygon related thingy that explains the approach (obviously you should "read" the code).

PS: test polys are internalized (I do hope that GH ... blah, blah).

best, Peter

Attachments:

poly_centroid_V1.gh, 126 KB

Permalink Reply by David Rutten on September 20, 2015 at 3:32am

It uses the Rhino SDK methods, and I'm afraid I don't know the methodology they took, though you can try asking on our discourse forum where the Rhino programmers hang out.

Curves are converted to single face breps for area calculations, but the polygon centroid component (which is way faster) calculates three kinds of centroid:

Average of all the vertices (excluding the last vertex which is coincident with the first one for closed polylines).
Weighted average of all the edge centres, where the edge length counts as the weight.
Actual area centroid from edge triangles. This one only works if the polygon is planar though.

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