The purpose of thes paper is to show regularity of (0,1,... r-2,r) and (0,1,... r-2,r)* interpolations on the sets obtained by projecting vertically the zeros of  \((1-x^2)P_n^{(\alpha , \beta)} \ \ \ \ \ \ (-1<\alpha , \beta <= \frac {1}{2})\\ (1-x)P_n^{(\alpha ,...