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| Guilhem |
 Posted: Sat Feb 12, 2005 2:22 am |
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Hello everyone,
I would like to know if there is an explicit formula to calculate the
centroid (center of masses) of a polygon with holes in it.
Thank you.
guilhem |
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| David Kastrup |
| Posted: Sat Feb 12, 2005 6:02 am |
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guilhem@borntobechicken.com (Guilhem) writes:
[quote:f3dcadddc7]Hello everyone,
I would like to know if there is an explicit formula to calculate the
centroid (center of masses) of a polygon with holes in it.
Thank you.
[/quote:f3dcadddc7]
Well, the centroid is the integral of the coordinates over coordinates
of all interior points, divided by the integral of 1 of all interior
points.
So you can obviously just add the signed triangle areas formed around
some arbitrary point and subtract the integrals for the holes.
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum |
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| Dezekana |
| Posted: Sat Feb 12, 2005 1:03 pm |
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It would be the centroid of the holes,
as a polygon is the center.
just locate the holes, find centroid of them
"David Kastrup" <dak@gnu.org> wrote in message
news:x54qgi11od.fsf@lola.goethe.zz...
[quote:078c7becf1]guilhem@borntobechicken.com (Guilhem) writes:
Hello everyone,
I would like to know if there is an explicit formula to calculate the
centroid (center of masses) of a polygon with holes in it.
Thank you.
Well, the centroid is the integral of the coordinates over coordinates
of all interior points, divided by the integral of 1 of all interior
points.
So you can obviously just add the signed triangle areas formed around
some arbitrary point and subtract the integrals for the holes.
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum[/quote:078c7becf1] |
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| David Kastrup |
| Posted: Sat Feb 12, 2005 1:26 pm |
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Please don't top post it is complete illegible.
"Dezekana" <invalid@invalid.com> writes:
[quote:73e0a0edc6]It would be the centroid of the holes,
as a polygon is the center.
just locate the holes, find centroid of them
[/quote:73e0a0edc6]
Wrong. Polygons need not be symmetric, and of _course_ the rest of
the polygon's area _does_ matter.
I can't punch a pinhole into one corner of a large square and expect
the centroid of the punched figure to now be in the pinhole.
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum |
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