| In 1964, S.A.Coons had adopted the definition of Coons surfaces, and had described characters of Coons surfaces. For Coons surfaces, its speciality is that the surface is structured by transfinite interpolation. To connecting Coons surfaces smoothly, Coons had added the tangent vectors to boundary curves. That maight lead to the Coons surfaces is not compatible. In this paper, these results are extended. First, it gives the definition of C~1 continuous line, gives the problem of C~1 transfinite interpolation and the new definition of Coons surfaces. Second, it gives the informational compatibility condition of imitative Coons surfaces, and proves that the necessary and sufficient condition of imitative Coons surfaces. Next, it gives three new kinds of correction, and proves that the corrected Coons surfaces are compatible. At last, it gives the definition of C~n continuous and latticed Coons surfaces, and gives the informational compatibility condition of imitative Coons surfaces, and proves that the necessary and sufficient condition of imitative Coons surfaces. |
