已知旋转曲面 \(X(u,v)=\begin{array}{c@{}cc} \left[\begin{array}{ccccc} & cos(v) & -sin(v) & 0 & \\ & sin(v) & cos(v) & 0 &\\ & 0 & 0 & 1 & \\ \end{array}\right] \end{array}\begin{array}{c@{}cc} \left[\begin{array}{cc} x(u)\\0\\ z(u)\\ \end{array}\right] \end{array},\) 取$(x(u),z(u)) = (r cos(u)+a, r sin(u)), a >0, r > 0$.

1. 在$[0, 2\pi]\times[0, 2\pi]$范围内展示曲面X.
2. 计算Gauss曲率和平均曲率，并在曲面上用颜色展示正(red)负(blue)零(green)曲率值.