A new method for interpolating boundary function values and first derivatives of a triangle is presented. This method has a relatively simple construction and involves no compatibility constraints. The polynomial precision set of the interpolation function constructed includes all the cubic polynomial and less. The testing results show that the surface produced by the proposed method is better than the ones by weighted combination schemes in both of the fairness and preciseness.

A C1 interpolation scheme for constructing surface patch on n-sided region (n5, 6) is presented. The constructed surface patch matches the given boundary curves and cross-boundary slopes on the sides of the n-sided region (n5, 6). This scheme has relatively simple construction, and offers one degree of freedom for adjusting interior shape of the constructed interpolation surface. The polynomial precision set of the scheme includes all the polynomials of degree three or less. The experiments for comparing the proposed scheme with two schemes proposed by Gregory and Varady respectively and also shown.

A method is described for constructing an interpolant to a set of arbitrary data points (xi, yi), i1, 2, , n. The constructed interpolant is a piecewise parametric cubic polynomial and satisfies C1 continuity, and it reproduces all parametric polynomials of degree two or less exactly. The experiments to compare the new method with Bessel method and spline method are also shown.

A new global method for constructing a C2 piecewise quartic polynomial curve is presented. The coefficient matrix of equations which must be solved to construct the curve is tridiagonal. The joining points of adjacent curve segments are the given data points. The constructed curve reproduces exactly a polynomial of degree four or less. The results of experiments to test the efficiency of the new method are also shown.