Parametric representation of a solid trapezoid

Question

Question: Define a parametrical representation of a solid trapezoid as shown in the following figure:

I came up with a solution by combining representations of the left rectangle and the right triangle $x=u$

$y=\frac{v}{-2}(\frac{|u|}{u}-1)+\frac{v}{2}(\frac{|u|}{u}+1)(1-u)(1-v)$

$-1 \leq u \leq 1 $

$0 \leq v \leq 1 $

Is there any simpler representation?

Answer 1

Your representation focused on $x$ (made its equation completely simple). Let us instead focus on $y$:

$$x=u(2-v)-1$$ $$y=v$$ $$0\le u\le 1,\ 0\le v\le 1$$