AN APPROACH TO GEOMETRIC MODELING OF SOLID OBJECTS

Abstract

Recent years have seen growing interest in the modeling (representation, manipulation and display) of solid objects with a computer. Three dimensional object modeling is essential for computer graphics, CAD/CAM systems, image understanding systems, and other applications. The search for better modeling techniques have been and continue to be one of the major problems in solid modeling. This thesis presents a 'Hex-tree representational technique' for geometric modeling of solid objects. This is a tree oriented, recursive type new constructional technique for representation and display of any 3-D object. A single cubical cell is used as primitive in this approach. In the Hex-tree data structure, the full identity of a node (i.e. cubical cell) is represented in six Bits of a word, indicating the life entities in all direc tions which represent the six faces. In order to get a realistic display of the Hex-tree based solid models, two Hidden-line algorithms are developed for simple and complex objects. These algorithms are suitable for Linedrawings display devices. A complete hidden lines removed pers pective picture of solid models, viewed from various distances and/or positions in space could be perceived. Provisions are also incorporated to visualise the object models, without remov ing hidden lines. Same algorithm can be used for both plana:1 and curve surfaced objects.

Necessary methods have been developed to calculate some of the integral properties of the Hex-tree based solid models. The volume, weight, center of gravity and moment of inertia of an unsymmetrical model have been computed and shown. The merits of providing 'Screen-layout' by creating multiple screen areas, for a better user-interface are also shown. Using this approach, it is possible to define, modify and display any planar and curve surfaced three dimensional object. The implementation of the geometric modeling system has been done in the FORTRAN language on VAX-ll/780 computer system using Tektronix-4027 graphics terminal.