How do I go about defining this area without using a piecewise function?
I think it has something to do with Bilinear Surfaces but I'm not sure how to get started.
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$\begingroup$ What kind of properties are you after for that surface? $\endgroup$– joojaaSep 13, 2015 at 12:35
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1 Answer
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One solution is bilinear mapping, which works for every convex quadrilateral.
Let $A, B, C, D$ be the vertices of a quadrilateral $Q$ in the plane, in this order.
Then $f(u,v)=(1-u)(1-v)A + u(1-v)B + uvC + (1-u)vD$ maps the square $[0,1] \times [0,1]$ to $Q$.
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$\begingroup$ Yep, looks like it's not working yet :(. Would you mind just using plain code formatting for time being, so all those symbols won't distract from the formulas? $\endgroup$– glampertSep 13, 2015 at 18:09
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$\begingroup$ I've added this question to the list of examples on meta to add to the case for adding MathJax to our site. $\endgroup$ Sep 14, 2015 at 13:37
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$\begingroup$ "which works for every quadrilateral." Unless I've messed up my "back of the envelope sketch", I think you need to amend that to "every convex quadrilateral". $\endgroup$– Simon FSep 14, 2015 at 13:45
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