Geophysical applications such as ray-tracing modeling require surfaces to respect at least G1 continuity (i.e. tangent plane continuity). We present here a method for building a piecewise G1 suface, composed of triangular Gregor patches, from a triangulated surface. The patches of the resulting surface are curvilinear triangles in a one-to-one correspondence with trinagles of the original triangulated surface. Each patch interpolates the three comers of its corresponding trinagle. Moreover, the method can take into account various types of user defined contraints so as to maje, for instance, the surface passing through given points or triangulation vertices belonging to given lines.