= Ratio-of-uniforms method
{title2=$X=V/U,\quad0<U\le\sqrt{h(V/U)}$}
For a nonnegative integrable function $h$ with integral $Z$, its ratio-of-uniforms region has area $Z/2$. A uniform point in the region transforms under $v=ux$ with <Jacobian determinant> $u$; integrating $2u/Z$ over $0<u\le\sqrt{h(x)}$ gives density $h(x)/Z$. A rectangle containing the region gives a practical <rejection sampling> algorithm using only uniform random variables, with acceptance $Z/(2\operatorname{area}(B))$.
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