VISUALIZATION OF SURFACE DATA TO PRESERVE POSITIVITY AND OTHER SIMPLE CONSTRAINTS

The presentation of 2-D data in the form of a contour map or surface view is a common operation in scientific visualization. It involves building 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 incorporated into the model. This paper therefore addresses the problem of interpolation subject to simple linear constraints. Specifically, it looks at the problem of constructing a piecewise bicubic function u(x, y) from data on a rectangular mesh, such that u(x, y) is nonnegative (positive). Sufficient conditions for positivity are derived in terms of the first partial derivatives and mixed partial derivatives at the grid points. These conditions form the basis of a positive interpolation algorithm. The problem of positivity is generalized to the case of linearly constrained interpolation, where it is required that u(x, y) lie between bounds which are linear functions of x and y.