Implementation of a Solid Modelling System with Quadric Surfaces

摘要

Quadric surfaces, or quadrics, are sets of points in space that satisfy a seconddegree equation F(x, y, z) = 0. These surfaces, which include planes, spheres, cones, cylinders, ellipsoids, paraboloids and hyperboloids, were studied thoroughly in the 19th century. The so-called natural quadrics are a subset of the general quadrics, and include planes, cones, spheres and cylinders. Natural quadrics appear frequently in the design of mechanical parts as stock material (plane), circular holes (cylinder), pockets (cylinder and plane) and simple blends (cylinder, cone, and sphere). In computer graphics, quadrics are used to visualize phenomena such as molecular structures, human body parts and natural scenes. In the last decade quite a lot was published about the theoretical backgrounds of solid modeling and graphics systems with quadrics, but very little was written about how to implement such systems. An overview of the functions and the global structure of an implemented model is given. The basic data structures and the routines to manipulate them are discussed. Some algorithms, including an algorithm for calculating the silhouette of a quadric, and the algebraic p rinciples of homogeneous second degree equations on which these algorithms rely, are discussed.