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A method of constructing piecewise G1 continuous spline surface using boundary C-curves is presented. C-curves are developed by the basis (sin t, cos t, t, 1), and it overcomes some shortcomings of the nonuniform rational B-splines (NURBS) model. How to develop C-curve into surface becomes a very important problem. Using the convex combination method proposed by Nielson, a piecewise G1 spline triangular surface is constructed by boundary C-curves.