Discretisation and Interpolation

Abstract

One of the fundamental requirements for numerical modelling is a description of the problem, its boundaries, boundary conditions and material properties, in a mathematical way. The exact definition of the shape of a complicated boundary would require the specification of the location (relative to the origin of a set of axes) of a large number of points on the surface (indeed an exact definition will take an infinite number). In order to be able to model such problems with a reasonable amount of input data, only a limited number of points may be defined and the shape between the points approximated by functions. This is known as solid modelling ¹. Solid modelling is being used, for example, to describe the shape of car bodies in mechanical engineering and ore bodies in mining, for the purpose of generating displays on computer graphics terminals. Thus, a new form of car body can be visualised, in perspective, from various angles, even before a scale model is built and the location and grade of ore bodies can be displayed for optimising excavation strategies in mine planning.