Computer-Aided Design 36 (2004) 723–734
www.elsevier.com/locate/cad

A single solution method for converting 2D assembly drawings
to 3D part drawings
Masaji Tanakaa,*, Laurence Anthonyb,1, Toshiaki Kaneedaa,2, Junji Hirookac,3baDepartment of Mechanical Systems Engineering, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan
Department of Information and Computer Engineering, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japanc
Sanyo Engineering and Design Co., Ltd, 3-1-9 Tama, Tamano 706-0012, Japan

Received 5 May 2003; received in revised form 18 August 2003; accepted 26 August 2003

Abstract
Although solid models play a central role in modern CAD systems, 2D CAD systems are still commonly used for designing products
without complex curved faces. Therefore, an important task is to convert 2D drawings to solid models, and this is usually carried out
manually even in present CAD systems. Many methods have been proposed to automatically convert orthographic part drawings of solid
objects to solid models. Unfortunately, products are usually drawn as 2D assembly drawings, and therefore, these methods cannot be applied.
A further problem is the difficult and time-consuming task of decomposing 2D assembly drawings into 2D part drawings. In previous work,
the authors proposed a method to automatically decompose 2D assembly drawings into 3D part drawings, from which 2D part drawings canbe easily generated. However, one problem with the proposed method was that the number of solutions could easily explode if the 2D
assembly drawings became complex. Building on this work, here we describe a new method to automatically convert 2D assembly drawings
to 3D part drawings, generating a unique solution for designers regardless of the complexity of the original 2D assembly drawings. The only
requirement for the approach is that the assembly drawings consist of standard parts such as bars and plates. In 2D assembly drawings, thedimensions, part numbers and parts lists are usually drawn, and the proposed method utilizes these to obtain a unique solution.
q 2003 Elsevier Ltd. All rights reserved.
Keywords: Assembly drawing; Part drawing; Orthographic view; Solid model

1. Introduction
In recent years, solid modelers have become popularmechanical CAD systems. On the other hand, 2D CAD
systems are usually used in the design of products that do
not need complex curved faces. If products consist of a great
many parts, 2D drawings are often more effective than solid
models, because it is difficult and time consuming to create
the solid models of the products. Despite this, solid models
are still required for catalogs, manuals, etc. and so it isnecessary to convert 2D drawings to solid models. In
present CAD systems, this conversion is usually carried out* Corresponding author. Tel./fax: þ 81-86-256-9594.
E-mail addresses: tanaka@mech.ous.ac.jp (M. Tanaka); anthony@ice.
ous.ac.jp (L. Anthony); kaneeda@mech.ous.ac.jp (T. Kaneeda); jhirooka@
mail.tamano.or.jp (J. Hirooka).
1
Tel./fax: þ81-86-256-9593.
2
Tel./fax: þ81-86-256-9538.
3
Tel.: þ81-863-21-3996; fax: þ 81-863-32-0627.
0010-4485/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cad.2003.08.003

manually, which can be troublesome when the 2D drawings
become complex.
Though several automatic conversion systems have beendeveloped, they cannot be applied in many situations
because they can only deal with a single solid. Many actual
products, on the other hand, are drawn as 2D assembly
drawings consisting of several parts. In previous work, we
attempted to solve this problem by proposing a method toautomatically decompose 2D assembly drawings into 3Dpart drawings [1], from which 2D part drawings could be
easily generated. However, one drawback to the method wasthat the number of solutions could easily explode when the
2D assembly drawings became complex.
In this paper, we propose a new method to automaticallyconvert 2D assembly drawings to 3D part drawings, which
overcomes the limitations of our previous method. To
achieve this, the only requirement is that the original
assembly drawing consists of standard parts such as bars andplates.

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When standard parts are used in 2D assembly drawings,
the dimensions, part numbers and parts lists are usuallylisted. Utilizing this information, the method here is able togenerate a unique solution, regardless of the complexity ofthe original 2D assembly drawing. This method has been
partially implemented to verify the algorithm.

2. Related works
Many researchers have investigated ways to automatically convert orthographic views to solid models [2 – 7]. An
early example is that of Idesawa [8], who proposed amethod to automatically generate wireframe models andsurface models from orthographic views. The wireframe
models were generated by projecting orthographic views
onto a 3D environment, and then a closed loop of wires wasrecognized as a face. In these models, a number of false
wires and faces could be generated. Therefore, it wasnecessary to search for true wires and faces before the solid
model solutions could be obtained. Idesawa proposed a
search process to obtain the solutions from the surface
models. However, it was found that the search process
would become increasingly complex and the number ofsolutions would increase in proportion to the complexity oforthographic views. When the number of faces is n in thesurface model, there are 2n decisions to make concerning
the existence of the faces before solutions can be found.
Therefore, a more efficient search procedure has beenrequired to obtain the solutions easily and quickly.
Wesley and Markowsky [9] proposed a method thatobtained the solutions by blocks. Each of the blocks wasrecognized as a closed region of faces in the surface model.
There could be some false blocks, and so true blocks weresearched to obtain solid models as the solutions. Since thenumber of blocks is much fewer than the number of faces ineach orthographic view, blocks are more effective than faces
in the search process to obtain the solutions. However,Wesley and Markowsky did not indicate an efficientalgorithm to obtain solutions from blocks. Therefore,
when the number of blocks made from an orthographic
view was n; their method searched 2n combinations of theblocks to obtain the solutions. As a result, it was difficult toapply their method to complex orthographic views.
In Wesley and Markowsky’s method [9], the faces ofblocks were limited to planes. Sakurai and Gossard [10], on
the other hand, applied cylindrical, conical, spherical andtoroidal faces to the blocks, and Dutta and Srinivas [11]proposed a method to convert two polygonal orthographic
views to solid models. In previous work, we proposed amethod that effectively reduced the search process for true
blocks [12,13] and extended this method to 2D assembly
drawings [1]. However, there was still an issue that the
number of solutions easily exploded when the 2D assembly
drawings became complex. In this paper, we propose amethod that solves this problem for 2D assembly drawings.

In Section 3, we review the authors’ previous method
to convert 2D assembly drawings to 3D part drawings. In
Section 4, we show how this approach can be modified
to generate unique solutions even for complex 2D
assembly drawings. In Section 5, we offer a number ofexamples that demonstrate the effectiveness of the
proposed method. In Section 6, we discuss some of thelimitations of the method, and in Section 7, we make ourconclusions.

3. Overview of original method
3.1. 2D vertices and edges
When 2D assembly drawings are input into a CAD
system, the outlines are divided into straight and curvedlines. These lines are called 2D edges. The end points of the
2D edges are called 2D vertices. 2D edges and vertices
correspond to edges and vertices of 3D assemblies, althoughsome 2D vertices and edges appear as silhouettes if the 3D
assemblies include curved faces. Since these silhouettes areneeded to make the wireframe models of the 3D assemblies,
all 2D vertices and edges that can exist as silhouettes are
drawn in the 2D drawings. These are called silhouette 2D
vertices and edges.
Fig. 1 illustrates a product (Example 1) that consists of
two parts. The coordinate systems on the front view and top
view of Example 1 are x 2 z and x 2 y; respectively. The 2D
vertices and edges of Example 1 are recognized as in Fig. 2.
In this figure, a dash-dot 2D edge on the front view is asilhouette 2D edge.

Fig. 1. Example 1.

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Fig. 4. Each face of Example 1.

Fig. 2. The 2D vertices and 2D edges of Example 1.

with the exception of silhouette 2D edges. 2D faces are used
to find false blocks. Fig. 6 illustrates each 2D face and partnumber for Example 1.

3.2. 3D vertices and edges
The combinations of 2D vertices of front views and top
views can be used to make vertices of solid models ofassemblies. Each 3D edge that can correspond to 2Dvertices and/or 2D edges are drawn between two 3Dvertices. If two or more edges cross each other at a point
other than one of the 3D vertices, these edges are erased inthis method because they can easily generate redundantsolutions [11]. Fig. 3 illustrates all the 3D vertices and edges
that form the wireframe model of Example 1.
3.3. 3D faces, blocks and 2D faces
A face is recognized as a closed loop of edges. Fig. 4
illustrates each face of Example 1, which combine to form
the surface model of Example 1. Note that the method canalso use curved faces as in Sakurai and Gossard’s method[10]. A block is recognized as a closed region of faces. For
Example 1, three blocks (B1; B2; B3) are recognized as inFig. 5. A 2D face is recognized as a closed loop of 2D edges,

Fig. 3. The wireframe model of Example 1.

3.4. Search for solutions
The solutions are obtained by combining true blocks foreach part. Fig. 7 illustrates the relationships between 2D
faces and blocks for Example 1. In this figure, suppose bothB1 and B2 belong to the same part. Then, four 2D edges
forming a circle on the top view of Example 1 would be
erased. This contradicts with the actual 2D assembly
drawing of Example 1, and therefore, it is found that neither
B1 nor B2 belong to the same part. Similarly, suppose B2 isfalse. Then, four 2D edges would be erased on the top view,which contradicts with the actual Example 1. Therefore, it isfound that B2 is true, and belongs to part 2, because its partnumber points to a 2D face of B2. In the same way, it isfound that B3 belongs to part 1, and B1 is false or belongs topart 1. Therefore, two solutions are obtained as in Fig. 8.

Fig. 5. Each block of Example 1.

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M. Tanaka et al. / Computer-Aided Design 36 (2004) 723–734

Fig. 8. Two solutions for Example 1.

that consists of only bars and plates, the strange solutions
such as those in Fig. 12 will never be output.

4. A novel method to convert 2D assembly drawings
to 3D part drawings

Fig. 6. Each 2D face of Example 1.

3.5. Complex drawings

Standard parts, such as bars and plates, are often used todesign products, and the dimensions, part numbers and parts
list are usually indicated in the 2D assembly drawing.

Since Example 1 is a simple 2D assembly drawing, only
two solutions are obtained. However, when 2D assembly
drawings become complex, the number of solutions
increases rapidly. Fig. 9 shows a complex drawing of atable consisting of six parts (Example 2), and Fig. 10
illustrates the wireframe model of Example 2. Fifteen
blocks are made from the model as in Fig. 11. To obtainsolutions for Example 2, 215 combinations of the blocks are
possible. Using our original method, 107 solutions weregenerated, two of which are illustrated in Fig. 12. In Section
4, we show that if Example 2 is recognized as an assembly

Fig. 7. The 2D faces and blocks of Example 1.

Fig. 9. Example 2.

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Fig. 10. The wireframe model of Example 2.

Fig. 12. Two examples of the solutions for Example 2.

The proposed method utilizes the dimensions and parts list
to convert 2D drawings to solid models. If the dimensions
and parts list are added to the assembly drawing for
Example 2, the resulting drawing is that given in Fig. 13(Example 3). This figure will be used as a test 2D assembly
drawing for the method proposed here.
The basic algorithm to convert the 2D assembly drawing
to a 3D assembly model is as follows

1. Input 2D assembly drawing.
2. Separate 2D assembly drawing into virtual 2D partdrawings.
3. Recognize blocks from virtual 2D part drawings.
4. Search for true blocks for each part.
5. Output 3D assembly drawing.
Each step of the algorithm will now be explained indetail.
4.1. Virtual 2D part drawings
When a 2D assembly drawing is input, the 2D vertices,
2D edges, 2D faces, part numbers and parts list are first

Fig. 11. The blocks of Example 2.

Fig. 13. Example 3.

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Fig. 14. An example to make virtual 2D part drawings.

Fig. 15. The solid models of parts defined in the parts list of Example 3.

recognized. The experimental system for the proposed
method uses Drawing Interchange File (DXF) files as CAD
files. Using DXF files enables lines, texts and dimensions to
be distinguished as different entities from each other. For
example, each dimension is expressed as a block of text andlines in DXF files. The parts list is recognized as a tableconsisting of straight lines and characters. Each part number
can be recognized as a circle containing a number and aleader line attached to the circle. If a part forms a cylinder,
its size is expressed as fa £ b in the parts list, and if a partforms a cuboid, its size is expressed as a £ b £ c in the parts

list. When the size of a cylinder or cuboid is recognizedfrom the parts list of the 2D drawing, a rectangular or
circular region corresponding to this part is recognized in
the 2D drawing and separated from the drawing as a whole.
We refer to these separated regions as virtual 2D partdrawings.
Fig. 14 illustrates an example to make virtual 2D partdrawings. Fig. 14(a) is an example 2D drawing. There is apart X with size a £ b in this figure. Fig. 14(b) illustrates
each 2D face (f 1; f 2; …; f 7) recognized from Fig. 14(a). It is
recognized that part number X points to f 3: Each virtual 2D
part drawing must consist of 2D faces recognized from its
original 2D assembly drawing and must form one closed
region in each view. Therefore, 2D faces are not cut whenvirtual 2D part drawings are made from their original
drawings. Also, 2D edges that do not form any 2D faces are
excluded from virtual 2D part drawings in this process. The
separation of virtual 2D part drawings from their original
drawings is performed by extending the leader lines ofdimensions automatically. If some dimensions lack leaderlines, the required leader lines are added to the dimensions.
As a result, the virtual 2D part drawing of part X consists off 1, f 2; f 3; f 6 as in Fig. 14(c). In this figure, since part X
consists of two separated regions, it is found that Fig. 14(a)is not a correct drawing.
In the parts list for Example 3 (Fig. 13), it is recognizedthat there is one part 1 with a size of 25 £ 300 £ 300, onepart 2 with a size of 25 £ 300 £ 300, and four part 3, with asize of 50 £ 50 £ 275. Dimensions that correspond to thesix parts in the list are searched in the 2D assembly drawing.
Fig. 15 shows an overview of the solid model solutions of allparts of Example 3. Fig. 15 is different to the wireframe
model in Fig. 10, as it includes both the part numbers anddimensions obtained from the dimensions, part numbers andparts list in Fig. 13. Fig. 16 illustrates three virtual 2D partdrawings for Example 3, where the four part 3 arerepresented by the same front and top drawings. The virtual

Fig. 16. Three virtual 2D part drawing for Example 3.

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Fig. 17. The blocks recognized from Fig. 14.

2D part drawings in Fig. 16 contain the information needed
to generate exact solid models of each part as the solution.
4.2. Four conditions to determine existence of blocks
In the proposed method, blocks are recognized in each
virtual 2D part drawing by constructing wireframe models
and surface models as described in our earlier paper [1]. The
existence of each block is decided for each part to obtain thesolutions. If the truth of a block cannot be decided, it iscalled an undecided block. Fig. 17 illustrates the blocks
recognized from Fig. 16. Since there are four part 3, there
are four blocks called B7-1; 2; 3; 4; four blocks called
B8-1; 2; 3; 4 and four blocks called B9-1; 2; 3; 4 recognized
for the parts as shown in Fig. 17. Fig. 18 illustrates theoverview of the 3D relationships among the blocks in
Fig. 17. In this figure, it is found that B2, B3, B5, B6 are thesame blocks as B8-1; 2; 3; 4: To obtain the solution, theseoverlaps of blocks must be excluded.
When true blocks are searched for in each part, thefollowing four conditions are applied. Let us consider a part
A in the 2D assembly drawing, and a block B that isrecognized from the virtual 2D drawing of part A:

4.2.3. 2D edge_condition
If the types of 2D edge projected from block B change ordisappear for block B to be true for part A; block B must be
false for part A: For example, for B5 and B6 to be true in part2, all of the dotted 2D edges must be changed into solid 2Dedges on the top view in Example 3. Therefore, B5 and B6
are false in part 2.
4.2.4. Identity_condition
Suppose that there are two part A called part A1 and partA2: When the existence of all blocks in part A1 are decided andthe existence is undecided for blocks in part A2; the undecided
blocks can be decided as the shape of part A1 is the same aspart A2: For example, if B7-1 is false, B7-2; 3; 4 become false,
or if B7-1 is true, B7-2; 3; 4 become true in Example 3.
4.3. Search for solutions
The existence of almost all blocks can be determined by
the Existence_condition and Overlap_condition.
Subsequently, the 2D edge_condition and Identity_condition

4.2.1. Existence_conditionIf, without block B; the dimensions and/or part number inthe virtual 2D part drawing cannot be generated when thesolid of part A is projected, or part A does not form a solid,
block B must be a portion of part A: For example, thecandidates of blocks consisting of part 3 are B7-1; 2; 3; 4;
B8-1; 2; 3; 4 and B9-1; 2; 3; 4 in Example 3 and if one ofthem is false, one of part 3 cannot be projected to its virtual
2D part drawing or it does not form a solid. Therefore, all of
the blocks must be true.
4.2.2. Overlap_condition
If block B overlaps part A and one or more other parts(part A; 0 part A00 ; …), block B is true in only one part and isfalse in the other parts. For example, since B7-1; 2; 3; 4;
B8-1; 2; 3; 4 and B9-1; 2; 3; 4 are true in part 3 because of the
Existence_condition described above, B2; B3; B5; B6
become false in part 2.

Fig. 18. The 3D relationships among blocks in Fig. 17.

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the Existence_condition. (2) B2; B3; B5; and B6 are shown tobe false in part 2 by the Overlap_condition. As a result, only
one solution is obtained as in Fig. 19. Fig. 20 illustrates the
3D assembly model obtained from the solution in Example 3.
In the same way, if Example 1 consists of two plates and thedimensions, and so on, are drawn in Fig. 1, only one solution
is obtained by the proposed method, corresponding to thedrawing given in Fig. 8(a).

5. Examples

Fig. 19. The solution for Example 3.

Fig. 20. The 3D assembly model of Example 3.

can be used to perform a detailed search for solutions. For
Example 3, the existence of each block is decided in thefollowing steps. (1) B1 in part 1, B4 in part 2 and B7-1; 2; 3; 4;
B8-1; 2; 3; 4; and B9-1; 2; 3; 4 in part 3 are shown to be true by

Fig. 21 shows a 2D assembly drawing of a book shelf(Example 4). Example 4 consists of eight parts that areclassified into three types as given in the parts list.
Fig. 22 illustrates each virtual 2D part drawing for
Example 4. In the dimensions of part 2, three circularregions whose diameter is 30 are recognized bysearching for a leader line with ‘3-f30’ written nearby.
Fig. 23 illustrates the blocks recognized from Fig. 22.
The existence of the blocks is determined as in thefollowing steps. (1) B1 in part 1, B8 , B12 in part 2 andB13 , B17 in part 3 are true according to the
Existence_condition. (2) B2; B3; B4; B6; and B7 inpart 1 are false by the Overlap_condition. As a result, B5
in part 1 is undecided. When the 2D Edge_condition isapplied to B5; it is found that B5 is false and only one
solution is obtained as in Fig. 24. Fig. 25 illustrates the
3D assembly model obtained from the solution for
Example 4. In contrast, using our original method
without applying the parts list, dimensions, etc. Example
4 would generate approximately 70,000 solutions.
Fig. 26 shows a 2D assembly drawing of small
container (Example 5). Example 5 consists of seven parts
that are classified into four types as given in the parts
list. Fig. 27 illustrates the wireframe model of Example
5. Our original method recognizes 17 blocks from thewireframe model as shown in Fig. 28, and generates
approximately 6 £ 106 solutions. Using the proposed
method, virtual 2D part drawings are recognized for
Example 5 using the 2D assembly drawing as in Fig. 26.
Fig. 29 illustrates the virtual 2D part drawings of parts 1

Fig. 21. Example 4.

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Fig. 22. Each virtual 2D part drawing for Example 4.

Fig. 23. The blocks recognized from Fig.19.

and 4 for Example 5. In this figure, since each part
generates only one block, the two generated blocks
become parts 1 and 4. For parts 2 and 3, four possible
virtual 2D part drawings are recognized as in Fig. 30. In
this figure, it is obvious that (a) and (b) correspond toparts 2 and 3 because of their part numbers. Fig. 31
illustrates the blocks recognized from Fig. 30.
Since B3 and B6 overlap with B9 and B10; not all of themcan be true. It is obvious that B1 is part 2. Suppose that (c)corresponds to part 2 and (d) corresponds to part 3. Then, B12
becomes part 3. However, all of the overlapping blocks must
become true by the Identity_condition. Therefore, it is foundthat (c) corresponds to part 3 and (d) corresponds to part 2.
When the 2D Edge_condition is applied to the blocks of (b)and (c), it is found that B5; B6; B7; B8; and B11 are true andB10 is false. Then, B9 becomes true and B3 becomes false by
the Existence_condition and Overlap_condition. When the
Identity_condition is applied to B2 and B4; it is found thatthey are true. As a result, only one solution is obtained for

Example 5, as shown in Fig. 32. Fig. 33 illustrates the 3D
assembly model obtained from the solution.

Fig. 24. The solution for Example 4.

Fig. 25. The 3D assembly model of Example 4.

6. Discussion
When 2D assembly drawings become complex, multiple
combinations of dimensions could be recognized for eachpart, as in Example 5. In this case, the following two
conditions are effective to recognize only one virtual 2D
part drawing for each part
1. If some outlines remain in the 2D assembly drawing after
all virtual 2D part drawings have been separated, weknow that the separation is not correct.

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M. Tanaka et al. / Computer-Aided Design 36 (2004) 723–734

Fig. 26. Example 5.

2. Blocks made from virtual 2D part drawings do notintersect each other at their edges and/or faces.
Moreover, if some dimensions are lacking in the 2D
assembly drawing, the distances between 2D vertices can besearched instead of the dimensions. In this case, many
combinations of distances could be recognized as dimensions in the 2D drawings, and the two conditions describedabove become more effective.
Using the proposed method, it is shown that undecided
blocks seldom exist after all the search conditions havebeen applied. However, in some cases there are blocks that
ignore all of the conditions, and this results in more than

one solution for the 2D assembly drawing. On the other
hand, false blocks generally result in solutions withremoved regions in the bars and plates. It is difficult tothink that removed regions are knowingly designed in thebars and plates because of the strength loss and cost ofmachining. Therefore, undecided blocks can usually beconsidered to be true, and so the number of solutions
always becomes one.
In addition to bars and plates, this method can be applied
to the other standard parts such as bolts, nuts, bearings and soon by recognizing their standardized expressions in 2D
drawings. If unspecified parts that are not standard parts areincluded in the 2D assembly drawings, this method can besynthesized with our original method [1] to generate 3D
assembly models. In this case, the numbers of solutions
would be increased in proportion to the shapes of theunspecified parts. However, the numbers of unspecified parts

Fig. 29. The virtual 2D part drawings of parts 1 and 4 for Example 5.

Fig. 27. The wireframe model of Example 5.

Fig. 30. Four possible virtual 2D part drawings of parts 2 and 3 for Example 5.

Fig. 28. The blocks generated from Fig. 24.

Fig. 31. The blocks recognized from Fig. 25.

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Also, when the simplified expressions described above areapplied to them, no solutions can be generated.

7. Conclusion

Fig. 32. The solution for Example 5.

A method was proposed that automatically converted
2D assembly drawings consisting of bars and plates to 3Dpart models. Although with previous approaches thenumber of solutions could easily explode when thedrawings became complex, this method can usually obtain
only one solution that is required by designers regardlessof the complexity of the drawings. Five examples were
given in this paper, and the proposed method could obtain
only one solution for each of them. The possibility ofmultiple solutions, and ways to prevent them werediscussed.

Acknowledgements
The authors would like to express their thanks to
Shigeyuki Okabe at NICS Inc., for supporting this research,and Kenzo Iwama at Engicom corporation for his commentson this paper.
Fig. 33. The 3D assembly model of Example 5.

are much fewer than standard parts in almost all mechanicalproducts. Therefore, the search process to obtain correct
solutions would not become overly difficult.
In general, 2D assembly drawings must be drawn
correctly for this method to be successful. However, typical2D drawings often incorporate many simplified expressions
such as partial views, local views and sectional views. In
these cases, the overview of the solid models as solutions
can be obtained by using the dimensions and parts lists, andthen the exact solid models as the solutions can be obtainedby adding or erasing some lines in the virtual 2D partdrawings. This may introduce many solutions, and so new
conditions to reduce the solutions would be needed. Also,
the application to hierarchical 2D assembly drawings
consisting of a great many parts is an important issue forthis method.
Practical conversion systems of 2D drawings and 3Dmodels have been developed for low and mid-range
commercial CAD systems. For example, SOLIDWORKS
is a major mid-range CAD system and it can be used togenerate 3D models from 2D drawings arranged in a 3D
environment. However, the conversion is largely a manual
process. Although a few automatic conversion systems
have been developed, such as CADPAC FUSION producedby DESIGN AUTOMATION, and new methods proposedin the literature [7], their objects have comprised of only
one part and they have also only dealt with geometricelements in 2D drawings. Therefore, these systems andmethods cannot be applied to most 2D assembly drawings.

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M. Tanaka et al. / Computer-Aided Design 36 (2004) 723–734
Masaji Tanaka is a Lecturer in the Department of Mechanical Systems Engineering at
Okayama University of Science, Japan. He
received his undergraduate degree from Saga
University, Japan, and his Doctor of Engineering from Ritsumeikan University, Japan.
His current research interests include geometric modeling and processing, and softwaredevelopment in CAD, CAPP, CAM andvarious automation systems.

Toshiaki Kaneeda is a Professor of Mechanical Systems Engineering and the Dean of
the Graduate School of Engineering at
Okayama University of Science, Japan. He
received his Doctor of Engineering from
Osaka University, Japan. His current
research interests are ultraprecision machining, precision cutting, biotribology andmanufacturing.

Laurence Anthony is a Lecturer in the
Department of Information and Computer
Engineering at Okayama University of
Science, Japan. He received a BSc degree inmathematical physics from the University ofManchester Institute of Science and Technology (UMIST), UK, and a PhD in applied
linguistics from the University of Birmingham, UK. His current research interests are in
corpus linguistics, data mining and natural language processing. He also
serves as a technical writer and advisor in various joint projects in the fieldsof mechanical engineering, applied chemistry and computer science.

Junji Hirooka retired from Mitsui Engineering and Shipbuilding Co., Ltd in 1998, and is
now President of Sanyo Engineering Co., Ltd
in Tamano City, Okayama Pref., Japan. The
company has traditionally designed piping andfittings for various industrial apparatus, ship
and plants. Recently, these machinery designs
have been extended to the fields of mechatronics, welfare equipment and IT.