Center of quadrangular

Question

Having 4 points A (ax, ay), B (bx, by), C (cx, cy) and D (dx, dy) that describe any quadrangular in 2D, with x and y in range [-100, 100] I would like to calculate point E (ex, ey), which would be a center of this quadrangular.

What algorithm can be used for such calculation and why?

score 9 · Accepted Answer · answered Jun 30 '12 at 14:30

9

The formula for a polygon's centroid is easily expressed in Mathematica:

PolygonCentroid[pts_?MatrixQ] := With[{dif = Map[Det, Partition[pts, 2, 1, {1, 1}]]},
                       ListConvolve[{{1, 1}}, Transpose[pts], {-1, -1}].dif/(3 Total[dif])]

This works for any Polygon[], not just quadrilaterals.

answered Jun 30 '12 at 14:30

J. M.'s missing motivation

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I'll note that I used this routine previously to help with coloring the proposed mathematica.SE logo... – J. M.'s missing motivation Jun 30 '12 at 14:32
Thank you for prompt answer. Where can I find a algorithm/formula in simple math that can be used for coding in programming language such as C, Perl, etc.? – Jun 30 '12 at 14:33
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@Ωmega: I linked to the formula already; you should not have any trouble translating the formula to your computing environment of choice. If you do have trouble, then this site is not the place to ask questions not related to Mathematica. – J. M.'s missing motivation Jun 30 '12 at 14:35
I have notice the link now. Thanks. – Jun 30 '12 at 14:36
@J.M. I wonder if the OP wants the centroid, or another center definition ... – Dr. belisarius Jun 30 '12 at 14:54
@bel: good point. At least, all those possibilities coalesce in the square case... – J. M.'s missing motivation Jun 30 '12 at 14:59
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@J.M. Ahhh! The infamous pointlike massless cow ... – Dr. belisarius Jun 30 '12 at 15:05
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@belisarius I immediately thought of spherical horses in vacuum when I read J.M.'s comment. – Heike Jun 30 '12 at 16:56
In the convex case you can just average the vertex coordinates. I think that gives the usual centroid. Well, it gives something plausible. – Daniel Lichtblau Jul 01 '12 at 16:06

Center of quadrangular

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