VISUALIZATION OF SURFACE DATA TO PRESERVE POSITIVITY AND OTHER SIMPLECONSTRAINTS

The presentation of 2-D data in the form of a contour map or surface v iew is a common operation in scientific visualization. It involves bui lding some empirical model from the data (by means of interpolation), and then ''picturing'' that model. If there are inherent constraints, such as positivity for example, it is vital that these are incorporate d into the model. This paper therefore addresses the problem of interp olation subject to simple linear constraints. Specifically, it looks a t the problem of constructing a piecewise bicubic function u(x, y) fro m data on a rectangular mesh, such that u(x, y) is nonnegative (positi ve). Sufficient conditions for positivity are derived in terms of the first partial derivatives and mixed partial derivatives at the grid po ints. These conditions form the basis of a positive interpolation algo rithm. The problem of positivity is generalized to the case of linearl y constrained interpolation, where it is required that u(x, y) lie bet ween bounds which are linear functions of x and y.