Lines, Planes and Polyhedra

In advanced CAD, its software has to process information on the models of 3D objects as though a person treats real ones. In construction and processing of the models, their information must be sufficient and have no contradiction, and their processing methods must be robust, efficient and flexible, because the result is directly connected to real processes of physical objects. From this point of view, a polyhedron is a fundamental object to be modelled in the computer. Its information structure and processing methods are clear, and numerical approximation enters least compared with those of other 3D objects. Polygons and polyhedra or wire-frames are also useful in describing objects with free-form surfaces, because free-form curves and surfaces are defined by their control points (refer to Chap. 9). So we explain in this chapter their basic equations as well as their geometric and topological properties and their interference.