Solid reconstruction from orthographic views using 2-stage extrusion
Introduction
The reconstruction of a three-dimensional (3-D) solid computer model from two-dimensional (2-D) multiple orthographic projection line drawings of a physical solid object has been studied for more than two decades. There are two main approaches to this reconstruction problem: single-view and multiple-view. The former includes Labeling Scheme, Gradient Space method, Linear Programming, Perceptual algorithm, and Primitive Identification method. Huffman [1] and Clowes [2] were the first to propose a systematic method to interpret polyhedral line drawings based on vertex and edge configurations in a single view. They also introduced a labeling scheme for line drawing. Falk [3] studied the interpretation of imperfect line drawings for which one is allowed to miss a few lines, but is not allowed to include extra lines. Turner [4] interpreted line drawings from polyhedra and objects with quadratic surfaces such as ellipsoids and cones. Waltz [5] extended the work of Huffman and Clowes to include line drawings with shadows and cracks. He also proposed the sequential labeling method for interpreting line drawings. Kanade [6] introduced line drawings of paper-folded objects to the Origami world interpretation. Sugihara [7] improved the labeling method with hidden lines.
On the other hand, the multiple-view approach uses either the Boundary Representation (BRep) method or the Constructive Solid Geometry (CSG) method. Research using the BRep method has been done by Idesawa [8] who was also the first to reconstruct solid models from multiple orthographic projection views of a 3-D polyhedron. Lafue [9] and Preiss [10] focused on heuristic approaches to find a probable solution. The relaxation of constraints would, however, generate multiple solutions to a given problem. Markowsky and Wesley [11], [12] conducted certain tests to eliminate all false elements and to ensure that all correct solutions are obtained. Haralick and Queeney [13], Gujar [14], You [15], Tanaka [16], and Shin [17] extended Wesley and Markowsky's work and have developed more efficient, precise and robust algorithms with a wider input geometric domain.
On the CSG side, Aldefeld [18] viewed a complex part as being composed of several elementary objects (CSG primitives), and he makes use of attributes and relationships (CSG tree) of the elementary object in the reconstruction process. However, objects of only uniform thickness can be reconstructed. Bin [19] used a similar approach, but his program requires less user interaction, and treats a wider class of engineering objects, such as incomplete views, incomplete projections or cross sections. Chen [20] proposed a reconstruction process consisting of three phases: decomposition, reconstruction and composition. This user-interactive method can handle polyhedral objects with non-uniform thickness.
In summary, the single-view approach, which is basically a syntactic and structural method, cannot give a complete solution to the reconstruction problem. The multiple-view approach can, however, provide better results. In the multiple-view approach, the BRep/wire-frame algorithm cannot handle complex objects efficiently and ambiguity may occur. The CSG algorithm is in comparison more efficient and often provides a unique solution, because CSG algorithm usually employs boolean operations which ensure the validity of geometric models, thus avoiding the creation of nonsense objects. However, very few CSG algorithms have been reported for the reconstruction problem. A new CSG algorithm viz. 2-stage extrusion in multiple-view approach is proposed in this paper to reconstruct 3-D solids from 2-D line drawings which are preprocessed from multiple orthogonal images of translucent objects by either visible light or X-ray (see Fig. 1).
Section snippets
Proposed method
The method involves two extrusion stages. In each stage, the geometric entities of only three orthogonal views are used. However, the entities contain both solid and dashed lines. Solid line information is simply captured by a digital camera whereas dashed line information captured by X-rays in preprocessing. Here, the 1st stage is to extract exterior solid boundary to build up a basic-solid, while the 2nd stage makes use of any non-redundant interior solid and dashed lines to generate an
Background of 2-stage extrusion
An object can be projected in six orthogonal views as shown in Fig. 2 according to the ISO system [21]. However, if hidden detail in the form of dashed lines is included, three orthogonal views, (viz. top, front and right-side) in third angle projection (or first angle projection) [22] as shown in Fig. 3 are usually sufficient to provide all details of an object. BS308:1972 states that the first and the third angle projections ‘are regarded as being of equal status’. However, third angle
Background theory
There are three types of entities in the projection of line drawings: exterior solid boundaries, interior solid lines, and interior dashed lines. For images captured by digital camera using visible light with proper illumination, each view comprises both exterior and interior solid lines. There is no dashed line at all, since visible light is unable to capture any hidden or obscured boundary of an object. Although most materials are opaque to light, they are moderately transparent to X-rays,
Case study
The 2-D input drawing is shown in Fig. 18. Firstly, contour areas are extracted from line drawings. The basic-solid (see Fig. 19) is formed in the 1st stage by sweeping three contour areas along their normal vectors and intersecting them. Next, interior lines are also extracted (see Fig. 20) for filtering. All interior lines are projected along their line directions to match for any associate vertex/vertices on the boundaries in adjacent views.
In Fig. 20(a), the associate vertices of line L1 in
Discussion
There are objects that cannot be recovered by the proposed methods. For example in Fig. 25(a), the linear sweeping/extrusion method is unable to generate the inside sphere. An interior cube can, however, be generated by extrusion, and thus the object in Fig. 25(b) can be recovered. Symmetrical parts such as shafts, multiple regular patterns or 2-view parts (see example in Fig. 26) are possible to be generated but it requires more intelligence to handle. In fact, CSG primitive solids such as
Conclusion
Solid reconstruction from multiple views has been studied over two decades. Many literatures were reported in extending Idesawa's and Markowsky's Brep approaches in which 3-D vertices, edges and faces were used, and all possibilities for the reconstruction were explored. However, the computation effort is very large if there are many redundant entities. The proposed 2-stage method employs a CSG extrusion approach. The extrusion result from boolean operations is unique. In addition, the method
Acknowledgements
The work described in this paper was supported by a grant from the Hong Kong Polytechnic University (Project no. G-V124).
Dr Simon S.P. Shum received his MSc in Production Engineering from the University of Strathclyde in 1988. He obtained his PhD from the Hong Kong Polytechnic University, Department of Manufacturing Engineering in 1999. He worked in the mould making industry from 1988 to 1995. He is very experienced in CAD modeling and reverse engineering. He is currently a lecturer at the Hong Kong Institute of Vocational Education (Tsing Yi). His research interests include solid reconstruction, CAD modeling,
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Dr Simon S.P. Shum received his MSc in Production Engineering from the University of Strathclyde in 1988. He obtained his PhD from the Hong Kong Polytechnic University, Department of Manufacturing Engineering in 1999. He worked in the mould making industry from 1988 to 1995. He is very experienced in CAD modeling and reverse engineering. He is currently a lecturer at the Hong Kong Institute of Vocational Education (Tsing Yi). His research interests include solid reconstruction, CAD modeling, reverse engineering and mould design.
Prof. W.S. Lau is Principal of the Hong Kong Institute of Vocational Education (Chai Wan). He received his MSc and PhD degrees in Mechanical Engineering from the University of Manchester Institute of Science and Technology, UK, in 1967 and 1970, respectively. He is currently Honorary Professors of the Hong Kong Polytechnic University and University of Warwick, UK. He is also an active member of CIRP.
Dr M.M.F. Yuen has extensive research experience in design and manufacturing automation. He spent four years in UK industry before taking up a teaching position in Hong Kong in 1979 and received the 1987 Edwin Walker Prize from the Institution of Mechanical Engineers, UK. He is currently an Associate Professor of the Department of Mechanical Engineering at the Hong Kong University of Science and Technology. He has provided consultancies in design and manufacturing automation, and vibration control. His research interests include intelligent CAD/CAM systems, soft object modeling, electronic packaging, rapid prototyping, vibration control and polymer processing.
Dr Kai-Ming Yu received his BSc (Eng) in Mechanical Engineering from the University of Hong Kong in 1985. He obtained his PhD from the University of Hong Kong, Department of Mechanical Engineering in 1991. He worked in the Research Centre and Mechanical Engineering Department of the Hong Kong University of Science & Technology until 1993. He is currently an Assistant Professor in the Hong Kong Polytechnic University Manufacturing Engineering Department. His research interests include CAD/CAM, CAE, PDM, reverse engineering and rapid prototyping technologies. He is also a Senior Member of the Society of Manufacturing Engineers.