To make generable a free-form surface with high reliability and excellent operability by calculating a differential vector of second order by using the result obtained by performing differentiation of second order for the curved surface definition expression of a general border Gregory patch.

The general border Gregory patch is defined as a curved surface equation S(u, v)=Sa(u, v)+Sb(u, v)-Sc(u, v) by four border curves and a boundary crossing function (CBD function) at the border. Here, the differentiation of second order of Sa(u, v) is found by the sum of differentiation of second order by (u), differentiation by (v) after differentiation by (u), differentiation by (u) after differentiation by (v), and differentiation of second order by (v). Differentiation of second order of Sb(u, v) is similarly found. Further, differentiation of second order of Sc(u, v) is found by using a function of differentiation of second order of an existent rational Gregory patch or rational Bezier patch. The result obtained by adding the respective results of differentiation of second order is a found differentiation vector of second order.