曲线 C: $\left\{\begin{array}{c}x=\mathit{cos}\theta -1.\\ y=\mathit{sin}\theta +1\end{array}\right.$ ( $\theta$ 为参数)的普通方程为（ ）

A．	${\left(x-1\right)}^2+{\left(y+1\right)}^2=1$	B．	${\left(x+1\right)}^2+{\left(y+1\right)}^2=1$
C．	${\left(x+1\right)}^2+{\left(y-1\right)}^2=1$	D．	${\left(x-1\right)}^2+{\left(y-1\right)}^2=1$