Reconstruction of 3D interacting solids of revolution from 2D orthographic views
Introduction
Two-dimensional engineering drawings have been a staple of the design process since the late 18th century, when the principles of orthographic projection and descriptive geometry were first developed and applied to engineering problems. 2D drawings still play an important role in engineering practice, and in many cases serve as the definitive design documentation that guides manufacture, fabrication, and assembly of products. However, 2D drawings have critical limitations that unnecessarily extend design cycle time, compromise product quality, and increase engineering and manufacturing costs. These weaknesses primarily arise from the aspects that it is difficult to inspect 2D design data intuitively and to verify it without physical prototyping and to use it directly in downstream processes.
It is necessary to convert existing 2D drawings into 3D solid models, because 3D solid models can overcome the limitations of 2D drawings. There have been two general approaches for solid reconstruction according to the solid representation schemes used: B-rep based approach and CSG based approach [6], [7]. The B-rep based approach has a relatively wider domain of objects that can be reconstructed than the CSG based approach. However, it cannot reconstruct complex objects efficiently due to exhaustive search and computation, and ambiguity may occur. The CSG based approach is relatively more efficient and often provides a unique solution, because it generally employs Boolean operations that ensure the validity of geometric models, thus avoiding the creation of nonsense objects. However, it has a limited domain of objects because it typically uses either pre-defined 2.5D primitives or identifies only entities that can be extruded.
The purpose of this paper is to extend the capabilities of the CSG based approach by proposing a procedure to reconstruct solids of revolution from orthographic views. A hint-based method is proposed to recognize interacting solids of revolution as well as isolated ones using minimal conditions. This approach is restricted to recognizing axis-aligned solids of revolution (axis of revolution is normal to one of the planes of projection).
Section snippets
B-rep based approach
Most of the work done on constructing solid models from orthographic views has been based on the B-rep based approach. Fig. 1 shows the typical procedure of the B-rep based approach. The B-rep based approach assembles candidate vertices, edges, and faces. The B-rep based approach was first proposed by Idesawa [1]. The most comprehensive work based on this approach has been done by Markowsky and Wesley [2], [3], who introduced the concept of constructing an intermediate wireframe. Sakurai et al.
Terminology
Common coordinate axis. The coordinate axis that is common between a pair of views. In Fig. 4, the x-axis is the common coordinate axis between view 1 and view 2.
Loop. A simple closed cycle of edges in a view is defined as a loop. An endpoint of each edge can be connected by two and only two edges.
Extreme points. Points on a circle with the maximum or minimum coordinate values along the common coordinate axis are called as the extreme points of the circle. If the point p on the circle C has the
The patterns for solids of revolution in orthographic views
If a solid that is generated by rotating a profile 360° along an axis is projected to 2D planes, as Fig. 5(a) shows, there should be circles on the view that is perpendicular to the axis of rotation, and entities that are symmetric with each other along the axis of rotation on the view that is parallel to the axis of rotation. Using these patterns for solids of revolution, the existing approach can handle isolated solids of revolution that have no interaction with other volumes.
However, if some
Hint-based method for recognizing solids of revolution
Input drawings are in DXF (drawing interchange format) file format. By parsing the input drawings according to the group codes and group values of DXF, 2D geometric entities such as LINE, ARC, and CIRCLE are identified. These entities are converted as a graph which consists of a set of vertices, edges, and incidence relations [13].
Implementation and experiments
A hint-based reconstruction system for a rotational part has been implemented using Visual Basic 6.0 and Solidworks 2004 API. Several sample drawings are tested to verify the proposed method.
Fig. 14 shows the result of reconstructing a switch from orthographic views. Fig. 14(a) is the input drawing. Fig. 14(b) shows the solid of revolution that is generated by the method proposed in this paper, and Fig. 14(c) show the solids that are generated by extrusion and intersection proposed in the
Conclusions
The CSG based approaches have several advantages over B-rep based approaches in that a valid solid model that is consistent with the input views is always available at any point in the solution process and there is no need for an intermediate wireframe. On the other hand, the major limitation of CSG based approaches proposed has been the limited domain of objects, because they use either pre-defined primitives or identify only entities that can be extruded. To solve this problem, an approach
Hanmin Lee received his MS degree (2000) and BS degree (1998) from Korea Advanced Institute of Science and Technology, Korea. His research interests include STEP, solid model reconstruction, knowledge-based design system.
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Hanmin Lee received his MS degree (2000) and BS degree (1998) from Korea Advanced Institute of Science and Technology, Korea. His research interests include STEP, solid model reconstruction, knowledge-based design system.
Soonhung Han is an Associate Professor in the Department of Mechanical Engineering at Korea Advanced Institute of Science and Technology (KAIST). He is leading the Intelligent CAD Laboratory (http://icad.kaist.ac.kr) at the KAIST and the STEP center of Korea (http://www.kstep.or.kr). He is the editor of the new web-based journal IJCC (http://www.ijcc.org). His research interests include STEP, geometric modeling kernel, VR application in design, and knowledge-based design system. He has a BS and an MS from the Seoul National University, Korea, and a PhD from the University of Michigan, USA.