Signed 2D Triangle Area from the Cross Product of Edge Vectors

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The signed area of a triangle in the - plane with vertices , , is given by half the component of the cross product of the edge vectors and .

Contributed by: Jim Arlow (April 2014)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The edge vectors are

,

.

The cross product of the edge vectors is .

The signed triangle area is half the component of the cross product: ,

which is equivalent to half the determinant of the matrix formed by the coordinates of when it is embedded in 3D space at : .

Reference

[1] J. O'Rourke, Computational Geometry in C (Cambridge Tracts in Theoretical Computer Science), 2nd ed., Cambridge: Cambridge University Press, 1998.



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