Finding Intersection Points of Curves and Surfaces for Solid Modeling in Curved-Surface Environment

摘要

Intersecting is an important factor which influences the efficiency and robustness of Boolean algorithms in solid modeling based on surved-surfaces, and intersecting algorithms are closely related to geometric representations of curved-surfaces. Although surfaces can be commonly represented with NURBS, unnecessary complexities are caused in the intersecting of quadric surfaces. Quadrics are frequently used to describe geometric features of shafts, holes and grooves etc. in mechanical part designing, therefore, their intersection algorithms are required to have higher accuracy, higher efficiency and higher robustness. For this reason, a practical representation of quadric surfaces is studied in detail, and on the basis of that, algorithms of intersecting points are developed between quadric suraces and their boundaies, i.e., conics, quartic nonplanar space curves.