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I have three dimensional coordinates of a face, how do I calculate surface area?

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  • $\begingroup$ What kind of face do you mean? $\endgroup$ – Matthias Sep 22 '14 at 15:07
  • $\begingroup$ It can be any shape, but in the simpler case I can assume it to be a rectangle face. $\endgroup$ – user10550 Sep 22 '14 at 15:09
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    $\begingroup$ Likely you have faces of a polyhedron in mind (it's worth stating this explicitly). One difficulty is that if the coordinates are not represented exactly, a face with more than three vertices may fail to lie exactly in a plane, due to rounding errors. $\endgroup$ – hardmath Sep 22 '14 at 15:26
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In general for a parametized face $\vec F(u,v)$ the area is the integral $$A=\int \left|\frac{\text d\vec F(u,v)}{\text du}\times\frac{\text d\vec F(u,v)}{\text dv}\right|\text du \text dv$$

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