Reconstructing boundary representations from extended bintrees

摘要

In this paper, a new algorithm method forreconstructing boundary representation (Brep) from extendedbintree (EB) is presented. The EB is a general method of binarycellular models based on a regular cellular bisection of theuniverse. It allows face, edge and vertex node types as well as theclassical black, white and grey nodes, so that the data of geometricelements can be stored in the tree nodes. Using Brep, a body isdefined by faces, a face by at least three edges, an edge by twovertices and a vertex by three coordinates. Consequently, ahierarchy of elements, which are connected in a network form, in adata structure come into being. After the geometric hierarchy ofbody-face-edge-vertex, the hierarchical affiliation of elements andthe topology are described by forward pointer: element of a highlevel in the hierarchy consists of elements of the next lower level.Therefore, an algorithm for the reconversion from EB to Brep hasto be provided in accordance with the geometric hierarchy frombottom to top: vertex-edge-face-body. The reconversion starts withvertices of an EB, an edge is determined by two vertices, a face byseveral edges or a polygon, a body by faces. The Brep can begenerated from EB without loss of geometric information. Bothplanes and round faces have been considered in the process.