A C1-rational spline in range restricted interpolation of scattered data

A range restricted C1 interpolation local scheme to scattered data is developed. CμCμ-rational spline function classes over triangles and quadrilaterals have been investigated by the first author. In this paper we concentrate on the C1-rational spline over triangles and represent it as piecewise a convex combination of three cubic Bézier triangular patches. Further, with such an equivalent form of C1 rational spline, the construction of a range restricted C1 interpolant subject to polynomial constraint surface of degree up to three is considered. In the end of this paper some numerical examples are illustrated.