V.P. Kong, B.H. Ong, K.H. Saw
Universiti Sains Malaysia
School of Mathematical Sciences
11800 Penang
Malaysia
e-mail: kongvp@hotmail.com, bhong@cs.usm.my, Khsaw939@hotmail.com
http://www.mat.usm.my/math/ |
Abstract
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 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.