防止 3D tikz 图片中部分圆的末端连接

Question

我想画一个三维抛物线（即绘制 $z=x^2 + y^2$），最大值为 z=1，然后标记抛物线中 $x^2 + y^2 =1$、$x\leq 0$ 和 $y \leq 0$ 的部分，这是圆的一部分。我有以下代码

\begin{figure}
    \centering
    \begin{tikzpicture}[radius=1]
        \begin{axis}[
            xlabel=$l_1$, ylabel=$l_2$, zlabel=$u$, 
            xmin=-1, xmax=1,
            ymin=-1, ymax=1,
            zmin=-0.1, zmax=1.05,
            %x={(-0.125cm,-0.05cm)}, y={(0.125cm,-0.05cm)}, z={(0cm,0.05cm)},
            axis lines=middle,
            every axis x label/.style={  at={(ticklabel* cs:1.05)},  },
            every axis y label/.style={  at={(ticklabel* cs:1.05)},  },
            every axis z label/.style={  at={(ticklabel* cs:1.05)},  },
            colormap/blackwhite,]
            % Paraboloid
            \addplot3[surf,
            samples=50,
            shader=interp, draw=lightgray, ultra thin, 
            opacity=0.5, fill opacity=0.5,
            data cs=polar, domain=0:360, 
            y domain=0:1,
            restrict z to domain=0:1, 
            ](x, y, y^2);
            % Part of parabola
            \addplot3[surf,
            samples=50,
            shader=interp, draw=lightgray, fill=green, ultra thin,
            left color=green, right color=green, middle color=green!25,  
            data cs=polar, domain=180:270, 
            y domain=0:1,
            restrict z to domain=0:1, 
            ](x, y, y^2);
            %partial circle
            \addplot3[
            domain=180:270,
            samples=20,
            variable=\t,
            color=red,
            ultra thin,
            ] ({cos(\t)}, {sin(\t)}, {1});
        \end{axis}
\end{tikzpicture} 
\end{figure}

我不想连接部分圆的端点。如何防止这种情况发生？