Range Restricted Interpolation Using Cubic Bezier Triangles

A range restricted C interpolation local scheme to scattered data is derived. Each macro triangle of the triangulated domain is split into three mini triangles and the interpolating surface on each mini triangle is a cubic Bézier triangle. Sufficient conditions derived for the non-negativity of these cubic Bézier triangles are expressed as lower bounds to the Bézier ordinates. The non-negativity preserving interpolation scheme extends to the construction of a range restricted interpolating surface with lower or upper constraints which are polynomial surfaces of degree up to three. The scheme is illustrated with graphical examples.