Revisions to Compute the Centroid of a 3D Planar Polygon

replaced http://upload.wikimedia.org/ with https://upload.wikimedia.org/

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edited Mar 10, 2017 at 9:42

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Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so on), how to calculate the centroid of the surface?

More specifically, I am looking for a natural extension of the following 2D centroid algorithm in 3 or more dimension:

alt text http://upload.wikimedia.org/math/e/e/1/ee14cbb2b170c4bb435f1d84e78f6d66.png $alt text$ alt text http://upload.wikimedia.org/math/a/4/c/a4cee81a1d18e4d067f66d4d40a8a1fe.png $alt text$

alt text http://upload.wikimedia.org/math/0/2/a/02aecb75f67f8c7b2fc11fdcbcb6ea80.png $alt text$

Any idea?

P/S: All the points are coplanar, this is the assumption.

Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so on), how to calculate the centroid of the surface?

More specifically, I am looking for a natural extension of the following 2D centroid algorithm in 3 or more dimension:

alt text http://upload.wikimedia.org/math/e/e/1/ee14cbb2b170c4bb435f1d84e78f6d66.png alt text http://upload.wikimedia.org/math/a/4/c/a4cee81a1d18e4d067f66d4d40a8a1fe.png

alt text http://upload.wikimedia.org/math/0/2/a/02aecb75f67f8c7b2fc11fdcbcb6ea80.png

Any idea?

P/S: All the points are coplanar, this is the assumption.

Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so on), how to calculate the centroid of the surface?

More specifically, I am looking for a natural extension of the following 2D centroid algorithm in 3 or more dimension:

$alt text$ $alt text$

$alt text$

Any idea?

P/S: All the points are coplanar, this is the assumption.

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edited Nov 21, 2014 at 12:34

user9072

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edited Mar 4, 2010 at 3:47

Graviton

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Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so on), how to calculate the centroid of the surface?

More specifically, I am looking for a natural extension of the following 2D centroid algorithm in 3 or more dimension:

alt text http://upload.wikimedia.org/math/e/e/1/ee14cbb2b170c4bb435f1d84e78f6d66.png alt text http://upload.wikimedia.org/math/a/4/c/a4cee81a1d18e4d067f66d4d40a8a1fe.png

alt text http://upload.wikimedia.org/math/0/2/a/02aecb75f67f8c7b2fc11fdcbcb6ea80.png

Any idea?

P/S: All the points are coplanar, this is the assumption.P/S: All the points are coplanar, this is the assumption.

Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so on), how to calculate the centroid of the surface?

More specifically, I am looking for a natural extension of the following 2D centroid algorithm in 3 or more dimension:

alt text http://upload.wikimedia.org/math/e/e/1/ee14cbb2b170c4bb435f1d84e78f6d66.png alt text http://upload.wikimedia.org/math/a/4/c/a4cee81a1d18e4d067f66d4d40a8a1fe.png

alt text http://upload.wikimedia.org/math/0/2/a/02aecb75f67f8c7b2fc11fdcbcb6ea80.png

Any idea?

P/S: All the points are coplanar, this is the assumption.

Given a list of 3D coordinates that define the surface( Point3D1, Point3D2, Point3D3, and so on), how to calculate the centroid of the surface?

More specifically, I am looking for a natural extension of the following 2D centroid algorithm in 3 or more dimension:

alt text http://upload.wikimedia.org/math/e/e/1/ee14cbb2b170c4bb435f1d84e78f6d66.png alt text http://upload.wikimedia.org/math/a/4/c/a4cee81a1d18e4d067f66d4d40a8a1fe.png

alt text http://upload.wikimedia.org/math/0/2/a/02aecb75f67f8c7b2fc11fdcbcb6ea80.png

Any idea?

P/S: All the points are coplanar, this is the assumption.

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edited Mar 4, 2010 at 3:33

Graviton

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asked Mar 4, 2010 at 3:07

Graviton

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