Chapter 1 - Elements of Descriptive Geometry

Abstract

The traditional, graphic description of the ship hull is a specialized application of descriptive geometry. This chapter is an elementary introduction to this branch of geometry. It begins by showing that the human eye, like photographic or TV cameras, sees the world in central projection, but drawing or measuring in this projection requires special techniques. To simplify the work, in engineering drawing it is first assumed that the projection rays are parallel, and finally that they are perpendicular to the projection plane. The results are orthographic projections. The basic fact is that a point in 3D space can be completely defined by its projections on two planes that are perpendicular one to the other. Straight lines are projected as straight lines, in special cases as points. Planes can be conveniently defined by their traces, that is by their intersections with the projection planes. The method is exemplified on a cube, a helix, a cylinder, and on right, circular cones. Cutting the surfaces of such cones by planes generates the conic sections, i.e. circles, ellipses, parabolas and hyperbolas. It is shown how to draw them by graphical means. The definitions of conical sections as geometrical loci are given, as well as their canonic equations.