3d drawing and 2d orthographics

Open up access peer-reviewed chapter

3D Solid Reconstruction from 2d Orthographic Views

Submitted: Nov 4th, 2019 Reviewed: March 3rd, 2020 Published: June 16th, 2020

DOI: 10.5772/intechopen.91977

IntechOpen Downloads

549

Total Chapter Downloads on intechopen.com

Abstruse

Three-dimensional computer-aided design (CAD) models are widely used by designers because of their useful applications in the areas of CAD/CAM/CAE/CAQ. A desirous trend to create this model, which has long been studied by scientists around the world, is a 3D model reconstruction from 2D orthographic views. With this method, information technology is piece of cake to enter geometric information as well as use 2D drawings that have already existed. Nearly of the previous works used three views, just many of the mechanical parts needed only two views. An avant-garde 3D solid reconstruction organization using only two orthographic views is the subject of this affiliate. The proposed method has been implemented and verified reliability by an ObjectARX program plugged into AutoCAD 2018. The 3D models have been checked for their compatibility with 3D CAD/CAM systems. This chapter presents principles, algorithms, databases, programming for the advanced reconstruction system, and some of its technical applications.

Keywords

• 2D
• 3D
• reconstruction
• orthographic views
• drawing

• Long Hoang*

  • Ha Noi University of Science and Technology, Vietnam

*Address all correspondence to: long.hoang@mail.hust.edu.vn

1. Introduction

Currently, in the industry, there are 2 main types of geometric blueprint: 2D designing shown in a multi-view drawing, which is a popular and traditional technical document, and 3D designing, which exists in the computer-aided design (CAD) and CAM systems such every bit Inventor, Catia, and Solidwork.

The 3D designing has many advanced applications, such as dynamic and static simulation, digital machining, visual ascertainment, etc., and is required when nosotros operate a CAM/CAE system. This approach has been hugely successful, initially appearing from 1990 with AutoCAD R12 and getting better and near perfect at present. Withal, besides its advantages, designers should accept the skills to read and empathize technical drawings as well as proficiently utilize the 3D CAD systems, which is inconvenient for long-time engineers who are familiar with the traditional design only. Also, these 3D solid files have poor compatibility betwixt 3D CAD software fifty-fifty with the aforementioned software but different versions (due to commerciality). As well, modifying a 3D CAD file is much more complicated than editing a 2D CAD File. Additionally, the training for erstwhile engineers to go used to using 3D CAD systems instead of using 2D drawing consumes a long time. Fifty-fifty after having a xxx-hour preparation course, they feel that creating two views is easier and faster than creating a 3D model, which normally uses auxiliary objects such every bit piece of work plane, work axis, piece of work signal (e.one thousand., in Inventor), etc.

With 2d designing, the designer but needs to create 2d technical drawings, which are comfortable and very familiar to the engineers. Compatibility between 2D CAD versions is besides perfect (the higher version volition read the file of the lower version and can convert files of the newer version to the older version form). Besides, almost of the electric current products have been being produced and stored by technical drawings.

Both types of pattern mentioned in a higher place need the CAD system can convert from one to another automatically. From 3D to 2D, the conversion process is very unproblematic, but the reverse procedure (i.e., 2nd to 3D that is also called reconstruction) is then complex that up to at present, there is still not any software that can do information technology every bit thoroughly as we take been expecting. That is why the reconstruction problem has been studied since the first 1970s, and a big number of works can be found in the scientific literature. These tin be classified into two significant categories: B-rep-oriented approach [ane, 2, 3, iv, 5, 6, 7, 8, 9, ten, 11, 12, 13, 14] and CSG-oriented approach [15, 16, 17, 18].

The survey of these works allows for the following assessments: recently, the B-rep-based reconstruction arroyo is more appreciated than the CSG-based approach. That is mainly considering CSG-based methods are less suitable for complex shapes and structures (especially when basic blocks collaborate, which will be difficult to identify them) and oftentimes crave more user interaction than the B-rep-based method. However, there are notwithstanding some limitations that exist in the B-rep-based approach equally follows:

Some methods are simply appropriate and proposed for polyhedral subjects. In dissimilarity, the other authors have expanded the polyhedral approach for the objects formed by curved faces but accept non yet dealt with complex intersections and interactive structures of basic blocks containing curved surfaces. Most of the reconstruction methods require the input of three views, while the technical drawings usually use simply two views to draw the common machine parts. The emptying of all the invalid candidate objects is oftentimes incomplete and has not used line-type data on the views, leading to the need for more views to remove these invalid objects. At that place has not been a single work that has accomplished all three main advantages: reconstructing a 3D solid object formed by revolving surfaces, from two views, and giving plenty solutions of the 3D solid compatible with CAD/CAM systems.

This chapter presents in particular our 3D solid reconstruction system without the limitations above; that ways the following accept been applied:

• Using only two given views.

• Employing B-rep approach instead of the CGS.

• Extending the object domain into the solids formed by planes, cylinders, and cones.

• Outputting all solutions of the 3D solid while reducing the consumed fourth dimension.

• Creating the 3D solid compatible with CAD/CAM/CAE systems.

Advertisement

ii. Elaborating an avant-garde 3D solid reconstruction system

2.one Approach

2.1.1 Typical traditional B-rep-based arroyo

The following constructed reconstruction method [half dozen] combines and develops polyhedron reconstruction methods of Wesley and Yan with Sakurai's reconstruction method of objects with curved faces. Let f exist a mapping function from an object O to its view Ps, set Ps  = f ( O ). The 3D model reconstruction is to find a reverse mapping f⁻¹ such that O * = f ⁻¹( Ps ), where O * is the 3D solid object model of object O . f ⁻¹ tin be analyzed in the following five main functions:

f − i Ps = fSL fBL fFA fED fVR Ps

E1

where fVR is the mapping function from 2d vertices in Ps to 3D vertices, fED is the mapping function from 3D vertices to 3D edges, fFA is the mapping office from 3D edges to faces, fBL is the mapping office from the faces to the candidate blocks, and fSL is the mapping function from blocks to a solid model.

In each mapping function, rules, forth with some constraints, are applied to low-level objects to create higher-level objects and eliminate "ghost" elements.

Figure one shows the steps of a typical B-rep-based 3D model automatic reconstruction method. The method consists of eight steps. The master steps are candidate vertex formation, candidate edge formation, candidate face cosmos, candidate block creation, and conclusion-making. These steps correspond to the mapping functions in Eq. (1). When two edges intersect, they are divided into iv edges in the edge sectionalization step. If the two faces intersect, they are also divided into four faces in the cutting edge insertion stride.

Figure ane.

Block diagram of a typical B-rep-based 3D model reconstruction method.

2.1.2 The author's avant-garde approach

* The following are the definitions in 2D view (see Figure 2).

• Lines are divided into line segments by intersecting points.

• A node is an endpoint of a line segment.

• A curved line containing extreme points should be divided into 2 segments (eastward.one thousand., a circumvolve should be divided into 2 arcs).

• A view is a set of nodes and line segments.

Effigy 2.

Definitions in 2D view and 3D object [xiv].

* Definitions in 3D object (see Figure 2).

• A solid is a body occupying a range in the three-dimensional infinite enclosed by several surfaces.

• A face is a segment of surface which constitutes a boundary between the solid and the exterior space.

• An edge line is an intersection of 2 different faces. If we desire to distinguish the line added for the identity of a curved surface from the others, the added line is chosen an auxiliary edge line.

• A vertex is an intersecting indicate of more than three edge lines.

The reconstruction problem (see Effigy iii) is that from the front end view and top view to observe out the solid object O considered every bit a set {{ Five }; { E }; { F }} satisfying the two groups of conditions below.

• The projection conditions:

Figure iii.

Cake diagram of the reconstruction system.

• Topology conditions of a solid:

An edge forms boundary of to precisely ii faces

E4

Two faces do not intersect at any border except their boundary border

E5

A range is inside of projection boundaries of an fifty-fifty number of faces

E6

Where: {V} is the gear up of vertices; {Eastward} is the set of edges; {F} is the set of faces; O₁ is the projection of the object onto the front airplane; O₂ is the projection of the object onto the top plane; front view and top view are given on the 2D engineering drawing.

A general way to solve the trouble consists of two main phases:

• From front view and meridian view, to find out a set of candidate objects (vertices, edges, faces—these objects satisfy but the condition of projection).

• To find out a subset in the ready of candidate objects to encounter 2 groups of conditions in a higher place, which means some faux candidate objects must be removed.

The growing bug are:

• The algorithm to create the candidate objects should be in general for many types of surfaces such as plane, cylinder, cone, and sphere.

• The algorithm for removing faux candidate elements can exist against the increase in the number of the candidate. And so, nosotros need to use an efficient strategy for browsing the combination of assumed values by using the rule for the propagation of attributes (true and false) of elements, satisfying the projection and topology conditions, avoiding the combination of all.

2.ii Database and algorithms of the advanced arroyo

2.2.one Specify candidate vertices

From the original database of 2 given views in AutoCAD that follows the DXF code, create the database as follows:

Node1[] and Node2[] are two matrices of the type ADS-POINT (used for ObjectARX programming in Microsoft Visual Studio 2015).

From database Node1[] and Node2[] above, find out whatsoever pair i , j satisfying the condition as:

where ﻉ is the small value depending on the user's input.

The pair i , j specifies a candidate vertex k . The algorithm for recognition of all candidate vertices is shown in Figure 4.

Figure 4.

The algorithm for recognition of all candidate vertices.

It is not difficult to specify X, Y, and Z coordinates of the 3D vertex thou from its two views, which belong to the descriptive geometry every bit follows:

Set up Y0  = min {Node1[][ Y ]}, which means we choose the everyman point on the given forepart view as the projection of the origin point of the coordinate system; so create the database Ver3D [] that is a matrix of ADS_3D POINT:

2.2.2 Specify candidate edges

From the original database of the front end view, create the database every bit follows:

• Matrix lineseg1 [100, two]: lineseg1[ k ] [i] and lineseg1[ yard ] [2] bear witness 2 endpoints of line segment k.

• Matrix line1[100][twenty]: line1[ one thousand ][] contains endpoints of line segments that belong to a unique line.

It is similar to create lineseg2[][] and line2[][] from the top view.

From the database above, find out any pair of vertices k , m satisfying the atmospheric condition as follows:

There is a member of line1 that includes ver k 1 and ver thousand 1

E11

There is a fellow member of line2 that includes ver grand ii and ver 1000 2

E12

The pair k, m specifies 2 endpoints (vertex) of a candidate edge. The set of the establish edges should be stored in the matrix Ed [100, iv] (100 and four are dimensions of the matrix).

Ed[] [ane] and Ed[] [2] testify two vertices k and m.

Ed[] [3] and Ed[] [4] show the members of line1[][] and line2[][] (i.e., Ed[] [3] and Ed[] [4] show front view and top view of the edge).

The weather condition (11) and (12) are used for recognition of any regular edge.

If ver[ one thousand ] [i] = ver[grand] [one] and they satisfy status (12), then the pair m, chiliad specifies 2 vertices of a frontal projecting border (the edge is perpendicular to the frontal plane of projection).

If ver[k] [ii] = ver[ one thousand ] [2] and they satisfy condition (11), then the pair k, m specifies two vertices of a horizontal projecting edge (the edge is perpendicular to the horizontal airplane of projection).

Note: for each edge, check for the possible existence of intermediate vertices. If an intermediate vertex is establish, the vertex causes the cosmos of two new edges (unless one of them already exists).

ii.two.3 Specify candidate faces

1. i. Projecting face (the face is perpendicular to the plane of projection)

2. For each fellow member j of the matrix line1[][], find out all of the edges i as follows:

fronted = ed . i three ; brainstorm = ed . i one ; end = ed . i two ; frontbegin = ver brainstorm 1 ;

If frontbegin is equal to frontend and they vest to line1 j , and then the edge i is a frontal projecting edge that belongs to the surface j that has front end view as the line corresponding to line1 j .

E13

If frontbegin is not equal to frontend only fronted is equal to j , and so edge i belongs to the surface j

E14

1. From the set of edges on the frontal projecting surface j, detect out all minimal closed loops of edges, they specify a new candidate face. The algorithm for recognition of frontal projecting faces is shown in Figure 5. Information technology is similar to recognizing horizontal projecting faces. The candidate faces should exist stored in the database as follows:

2. Faceed[100][xxx]: faceed[ k ][0] shows the number of edges that belong to the face thousand; faceed[ k ][ i ] shows edge i of face up yard , faceed[ k ][29] equal to j mentioned above that specify geometry data of the face k (100 and 30 are dimensions of the matrix).

3. 2. Cylinder. The cylinders mentioned here are projecting cylinders then that in any view, ane projection of the cylinder becomes a circle. The circumvolve should exist divided into 2 arcs. The cylinder is divided into two half projecting cylinders; the algorithm for recognition of these half cylinders is the same as the algorithm above.

4. iii. Cone. The axis of the cone mentioned hither is perpendicular to the plane of projections so that in any view, ane project of the cone becomes 2 circles (1 of them may be a indicate). The two circles were divided into four arcs, which mean the cone is divided into ii one-half cones.

Figure v.

Algorithm for recognition of projecting faces.

2.2.4 Removing false elements

A searching tree removes false candidate elements by checking conditions (5), (half dozen), and (seven). The purpose of this traversal process is to eliminate false assumptions due to dissatisfaction with topological atmospheric condition. To counteract the increase in browsing time on assumption binary tree, the duration of this process is exponentially increased: ii^north, where due north is the number of assumed faces. Status direction and browse planning aim at selecting the face for the next step with the highest priority (the priority is assessed by its corporeality of information, for example, the face contains many edges, and the face will see a high level of priority). Conflicts are found during the browsing procedure. If it meets any disharmonize, the side by side step will be backtracked.

2.2.5 Solid creation

Based on the status (5), the algorithm to create the solid is described equally follows: for each range, the faces are numbered in height gild; the primitive solid is generated from first to second, third to quaternary, etc. The outcome solid is a union of all such primitive solids (run across Figure 7b).

two.3 Implementation and verification results

The proposed reconstruction method has verified reliability by a program written in Visual Studio (run across Figure half-dozen). The program was compiled and then built an Objectarx file to run in AutoCAD. After downloading the Objectarx file, AutoCAD has an extended command to rebuild the 3D solid model from its two views (run across Figure seven). The 3D solid model has been exported as the Saturday file that PTC Creo Parametric 3.0 (CAM software parcel) can use. The tool paths generated in PTC Creo (see Effigy 7c) have been compiled into the specific codes needed for the HS Super MC500 CNC motorcar to mill the surfaces. The machined part was then 3D scanned. The 3D comparison result generated by Geomagic software is shown in Figure vii(d). The machining accurateness in Figure seven(d) indicates that the 3D solid model reconstructed from its ii views is compatible and usable for CAD/CAM/CAQ/CNC systems. The proposed method is express to perfect input drawings that contain only lines, circles, and arcs. However, an engineering drawing is frequently a mixture of geometric representations and annotations, and information technology's challenging to ensure that engineering drawings are absolutely accurate. Therefore, techniques to reconstruct the 3D solid model from existent drawings should consider these imperfections [six].

Figure 6.

Extracting of ObjectARX program in Microsoft visual studio 2015.

Effigy vii.

(a) Two given views; (b) solid creating automatically; (c) tool path generation; (d) 3D comparing between the CAD model and the function machined by CNC.

Advertisement

3. Conclusions

The 3D solid models are extremely useful in techniques. An splendid way to create the 3D solid is an automated reconstruction from its views. The 3D solid automatic reconstruction system presented in this chapter has advanced features as follows:

• Using only 2 given views.

• Outputting all solutions of the 3D solid while reducing the consumed fourth dimension.

• Creating the 3D solid uniform with CAD/CAM/CAE systems.

References

1. 1. Idesawa M. A system to generate a solid figure from three view. Bulletin of JSME. 1973;xvi(92):216-225
2. 2. Wesley MA, Markowsky G. Fleshing out projections. IBM Journal of Inquiry and Evolution. 1981;25(6):229-258
3. iii. Sakurai H, Gossard DC. Solid model input through orthographic views. ACM SIGGRAPH Computer Graphics. 1983;17(3):243-252
4. 4. Dutta D, Srinivas YL. Reconstructing curved solids from 2 polygonal orthographic views. Estimator-Aided Design. 1992;24(3):149-159
5. 5. You CF, Yang SS. Automatic characteristic recognition from engineering drawings. The International Periodical of Advanced Manufacturing Engineering science. 1998;fourteen(seven):495-507
6. 6. Watanabe T. Revision of inconsistent orthographic views. Journal for Geometry and Graphics. 1998;2(i):45-53
7. seven. Shin BS, Shin YG. Fast 3D solid model reconstruction from orthographic views. Figurer-Aided Design. 1998;30(1):63-76
8. 8. Liu SX et al. Reconstruction of curved solids from engineering drawings. Estimator-Aided Design. 2001;33(xiv):1059-1072
9. 9. Furferi R, Governi L, Palai M, Volpe. 3D model retrieval from mechanical drawings analysis. International Journal of Mechanics. 2011:91-99
10. 10. Long H, Long BT. Automatic creating 3D pseudo-wireframe from 2nd orthographic views. Journal of Science and Engineering science of Ha Noi University of Science and Engineering. 2015;106:46-49
11. eleven. Long H, Long BT, Van Hieu P. Conical solid model reconstruction of 3D pseudo-wireframe model found from 2D orthographic views. Journal of Science and Engineering science of Ha Noi Academy of Science and Technology. 2015;108:68-72
12. 12. Long H, Long BT. Automatic 3D model reconstruction from a multi-views engineering drawing file containing even curves and hidden lines for CAD/CAM systems. In: Proceedings RCMME. 2014. pp. 20-23. ISBN: 978–604–911-942-2
13. 13. Long H. Expanding a 3D solid reconstruction system using two views to the system using three views. Journal of Science and Technology of Ha Noi University of scientific discipline and engineering. 2018;125:twoscore-45
14. 14. Hoang Fifty, Tien LB. A flexible solid 3D model reconstruction system for mechanical CAD/CAM systems. Journal of the Korean Society for Precision Engineering science. 2019;36(viii):753-759
15. 15. Aldefeld B. On automatic recognition of 3-D structures from 2-D representations. Computer-Aided Design. 1983;15:59-64
16. 16. Geng W, Wang J, Zhang Y. Embedding visual cognition in 3D reconstruction from multi-view technology drawings. Reckoner-Aided Design. 2002;34(4):321-336
17. 17. Lee H, Han S. Reconstruction of 3D interacting solids of revolution from 2D orthographic views. Figurer-Aided Design. 2005;37(13):1388-1398
18. 18. Wang Z, Latif K. Reconstruction of 3D solid models using fuzzy logic recognition. Proceedings of the World Congress on Engineering science. 2007;ane:37-42

Submitted: November 4th, 2019 Reviewed: March 3rd, 2020 Published: June 16th, 2020

© 2022 The Author(southward). Licensee IntechOpen. This chapter is distributed nether the terms of the Creative Commons Attribution iii.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

meeksbeerbeen.blogspot.com

Source: https://www.intechopen.com/chapters/72385

Share this post