Range Restricted Interpolation Using Cubic Bezier Triangles

A range restricted C 1 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 Bezier triangle. Sufficient conditions derived for the non-negativity of these cubic Bezier triangles are expressed as lower bounds to the Bezier 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.

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