C1 Non-Negativity Preserving Interpolation Using Clough-Tocher Triangulation - Yeong, Yee Yon (2019)
Nowadays, scientific visualization is an important branch in computer graphics to graphically visualize the scientific data from three dimensional phenomena. The construction of a surface usually involves generating a set of surface patches that smoothly connected together and the surface should inherit certain shape property of the data like non-negativity. The construction of non-negativity preserving 1C interpolation surface to scattered data is considered. The given data is triangulated using Delaunay triangulation. The interpolating surface to scattered data is piecewise with Bézier triangular patches. The surfaces are produced using the method of Clough-Tocher split. Sufficient non-negativity conditions on the Bézier ordinates are derived to ensure the non-negativity of a cubic Bézier triangular patch. New set of lower bounds is proposed to the Bézier ordinates. The initial values of the Bézier ordinates are determined by the given data and the estimated gradients at the data sites. The Bézier ordinates are adjusted if necessary by modifying the gradients at the data sites so that the Bézier ordinates fulfill the non-negativity conditions. The scheme for constructing the non-negativity preserving surface is local. It constructs 1C interpolating surface to scattered data subject to constraint plane. Some graphical examples are presented.