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How do I define this without using piecewise function?

I think it has something to do with Bilinear Surface but not sure how to get started.

enter image description here

$x_1=-1, x_2=1, x_3=0, x_4=1$

$y_1=0, y_2=1, y_3=1, y_4=0$

$ x(u,v)=x_1+u·(x_2-x_1)+v·(x_3-x_1+u·(x_4-x_3-x_2+x_1))$

$y(u,v)=y_1+u·(y_2-y_1)+v·(y_3-y_1+u·(y_4-y_3-y_2+y_1))$

I don't understand what is this $u & v$ we have here.

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I don't know exactly what you mean by "without using piecewise function", but the description

$$\{(x,y)| y\in[0,1] \land x\in[-1, 1-y]\}$$

has no piecewise functions...

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  • $\begingroup$ As in define the shape with $x = x(t), y=y(t)$ $\endgroup$ – Gavin Sep 13 '15 at 12:19
  • $\begingroup$ @MaTaKazer That would define a curve, not an area. $\endgroup$ – 5xum Sep 13 '15 at 13:07

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