Computer representation of graphical information with applications

Abstract

The research work contained in this thesls lies mainly in the field of computer graphics. The initial chapters are concerned with methods of representing three dimensional solids in two dimensions. Chapter 2 describes a method by which points in three dimensions can be projected onto a two dimensional plane of This is an essential requirement in the projection. This is an essential requirement in the representation of three dimensional solids. Chapter 3 describes a method by which convex polyhedra can be represented by computer. Both the hidden polyhedra and visible face of the polyhedron can be represented by computer. Having tackled this problem, the

more difficult problem of representing the non convex polyhedron has been attempted and the results of this work are presented in Chapter 4. Line drawings of the various polyhedra, produced on a graph plotter, are given as examples at the end of Chapters 2, 3 and 4. The problem of how to connect a given line drawing such that the distance travelled by the pen of some computer display is kept to a minimum is discussed in Chapter 5 and various definitions of the concepts involved are given. Theory associated with this 'Pen-Up Problem' has been developed and is explained in detail in the early part of Chapter 6. A method of obtaining an optimal solution to the problem is presented in the latter part of this chapter in addition to various enumerative schemes which have been developed to obtain good feasible solutions to the pen up problems under various conditions Extensive C.P.U. timing experiments have been carried out in Chapter 7 on the various enumerative schemes in Chapter 6 and it has introduced been possible to reach conclusions on the applicability of the various methods. Several topics of interest which have arisen during the main research work are presented as appendices. The programs which have been coded during the period of research are also inc1udeu as appendices.