Chapter 3 - Computer Representations of Shapes

Abstract

This chapter outlines model representations available for the solution of engineering problems. Entities such as elements of engineering object representations in models of mechanical systems in present industrial practice are explained. The characteristics of curves and surfaces for the description of engineering shapes are discussed in the chapter. All curved and planar surfaces as well as curves and lines must be described by using the same class of mathematical functions. Surfaces must have closed contours or curves in their inner and outer boundaries. At the connection of surfaces, a specified continuity must be kept. The chapter focuses on the principles, methods, and practice of industrially applied shape modeling in computer-aided design (CAD)/computer aided manufacturing (CAM) systems. The chapter focuses on model characteristics for the application of geometry in problem solving for industrial engineering practice. Industrial practice of shape modeling applies only a small number of representations for curves. Polynomials are the preferred class of mathematical functions for the description of curves and surfaces. Basis functions are often called blending functions because they affect the shape of the entire curve or only several of its segments. They are connected to control vertices or interpolation points.