The (signed) area of a planar non-self-intersecting polygon with vertices , ..., is
where denotes a determinant. This can be written
where the signs can be found from the diagram above.
Note that the area of a convex polygon is defined to be positive if the points are arranged in a counterclockwise order, and negative if they are in clockwise order (Beyer 1987).
SEE ALSO: Area, Convex Polygon, Polygon, Triangle Area
Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 123-124, 1987.
Weisstein, Eric W. "Polygon Area." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolygonArea.html
posted on 2009-03-09 09:14 zmj 閱讀(890) 評論(0) 編輯 收藏 引用
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