In this thesis we introduce and develop a new method for the automatic contouring of smooth surfaces, which produces high quality results at relatively low cost. We begin (Chapter 1) by reviewing the contouring methods in the literature; serious limitations are revealed which appear to justify a search for a new and better method. In Chapter 2 a seamed quadratic finite element is introduced which is suitable for approximating smooth functions whose values and gradients may be evaluated at the nodes of a rectangular grid. We suggest using an efficient published subroutine due to Marlow and Powell (1976) or some suitable alternative to plot the contours of the approximant surface; the resulting method produces accurate and visually smooth contours at relatively little expense. Chapter 3 is an explanation of CONICON, the Fortran subroutine package which implements this contouring method. In Chapter 4 CONICON is used to contour surfaces arising from a variety of applications. Chapter 5 describes an error analysis of the seamed quadratic element which enables us to obtain bounds for the error involved in using the element to approximate a function. In Chapter 6 we implement an extension of our contouring method which uses local subdivision of elements in order to reduce local variations in the error involved in contouring a function. Various possible criteria for splitting are suggested, some of which are tested on known functions. Finally (Chapter 7) we conduct a (fairly superficial) comparison of a number of contouring packages which are currently available. We discuss the features which each package offers and attempt to assess their quality, simply on the evidence available from user documentation and advertising literature.
|Date of Award||1984|