Reconstruction of curved solids from engineering drawings

Abstract

This paper presents a new approach for reconstructing solids with planar, quadric and toroidal surfaces from three-view engineering drawings. By applying geometric theory to 3-D reconstruction, our method is able to remove restrictions placed on the axes of curved surfaces by existing methods. The main feature of our algorithm is that it combines the geometric properties of conics with af®ne properties to recover a wider range of 3-D edges. First, the algorithm determines the type of each 3-D candidate conic edge based on its projections in three orthographic views, and then generates that candidate edge using the conjugate diameter method. This step produces a wire-frame model that contains all candidate vertices and candidate edges. Next, a maximum turning angle method is developed to ®nd all the candidate faces in the wire-frame model. Finally, a general and ef®cient searching technique is proposed for ®nding valid solids from the candidate faces; the technique greatly reduces the searching space and the backtracking incidents. Several examples are given to demonstrate the ef®ciency and capability of the proposed algorithm. q

Constructing Regularity Feature Trees for Solid Models

“…Construction of regularity features from recoverable edges requires similar steps to converting wire-frame models into solid models [1,5,11,13]. Given a wireframe model linking vertices and edges, these methods produce a corresponding volumetric description by deciding which edge loops are covered by faces.…”

“…A general approach for polyhedra is based on ordering edges around each vertex and faces around each edge to create all possible solutions [13]. More general work to reconstruct curved solids from engineering drawings uses a maximal turning angle method to detect all possible faces in a wire-frame with straight and conic edges [11]. Graph theory has been applied to resolve the conversion problem for 0-, 2-and 3-connected wire-frames [1,5].…”

“…These are the cells determined by original faces F together with the recoverable faces F R . As the input solid S already has proper loops and face normals, generating these cells is much simpler than the general problem of converting wire-frame models to solid models [1,5,11,13]. To ensure that the resulting solids are manifold and closed, the Möbius rule is applied: each edge belongs to two faces and the orientation of the edge is opposite on each face [9].…”

Handling sectional views in volume-based approach to automatically construct 3D solid from 2D views

“…The approaches reported thus far can be classified into two broad categories [10] -the bottom-up or wireframe based approach and the top-down or volume-based approach. In the wireframe approach [5,6,13,14], 3D vertices are first generated from the input 2D views. These vertices are connected by 3D edges in accordance to the input views, resulting in a wireframe.…”

“…Loop {1, 2,3,11,12,6,7,8,9,10,1} in view 2 is a nonfundamental loop. The fundamental loops in a view can be determined by the leftmost search described in Yan et al [14].…”