Costa minimal surface

May i ask that when i plot the surface of Costa minimal surface follow costa minimal surface in wikipedia website, the end of top and bottom part of the Costa do not look smooth like a circle. If want to make the top and bottom part of the Costa look smooth is't just cut through the cross section so will look smooth? May i know where or how to decide an accurately boundary condition of the minimal surface? Mean need to take at which point of the Costa ended on the top and bottom part? May i know that what is the minimal surface of the moebius strip? thank you.