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1、BRITISH STANDARD BS ISO 5456-4:1996 Technical drawings Projection methods Part 4: Central projection ICS 01.100.01 NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS ISO
2、5456-4:1996 This British Standard, having been prepared under the direction of the Consumer Products and Services Sector Committee, was published under the authority of the Standards Committee and comes into effect on 15 September 2001 BSI 07-2001 ISBN 0 580 38242 7 National foreword This British St
3、andard reproduces verbatim ISO 5456-4:1996 and implements it as the UK national standard. The UK participation in its preparation was entrusted by Technical Committee TDW/4, Engineering drawing, metrology, precision measurement and all related documents, to Subcommittee TDW/4/-/1, General drawing pr
4、inciples, conventions and related documents, which has the responsibility to: A list of organizations represented on this committee can be obtained on request to its secretary. Cross-references The British Standards which implement international or European publications referred to in this document
5、may be found in the BSI Standards Catalogue under the section entitled “International Standards Correspondence Index”, or by using the “Find” facility of the BSI Standards Electronic Catalogue. A British Standard does not purport to include all the necessary provisions of a contract. Users of Britis
6、h Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. aid enquirers to understand the text; present to the responsible international/European committee any enquiries on the interpretation, or proposals
7、 for change, and keep the UK interests informed; monitor related international and European developments and promulgate them in the UK. Summary of pages This document comprises a front cover, an inside front cover, the ISO title page, pages ii and iii, a blank page, pages 1 to 33 and a back cover. T
8、he BSI copyright date displayed in this document indicates when the document was last issued. Amendments issued since publication Amd. No. DateComments Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI A Reference number ISO 5456-4:1996(E) INT
9、ERNATIONAL STANDARD ISO 5456-4 First edition 1996-06-15 Corrected and reprinted 1998-08-01 Technical drawings Projection methods Part 4: Central projection Dessins techniques Mthodes de projection Partie 4: Projection centrale Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00
10、 2006, Uncontrolled Copy, (c) BSI ISO 5456-4:1996(E) ii Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees
11、. Each member body interested in a subject for which a technical committee has been established has the right to be rep- resented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the Inte
12、rnational Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member
13、bodies casting a vote. International Standard ISO 5456-4 was prepared by Technical Committee ISO/TC 10, Technical drawings, product definition and related documen- tation, Subcommittee SC 1, Basic conventions. ISO 5456 consists of the following parts, under the general title Technical drawings Proje
14、ction methods: Part 1: Synopsis Part 2: Orthographic representations Part 3: Axonometric representations Part 4: Central projection Annexes A and B of this part of ISO 5456 are for information only. Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c
15、) BSI OSIISO 5456-4:1996(E) iii Introduction Central projection (perspective) is a realistic pictorial representation ob- tained by projecting the object to be represented from a point at finite distance (projection centre) on a single projection plane (normally the drawing surface). Central project
16、ion provides excellent visual appearance of the object (monocular vision) and is often used in architectural draw- ings. Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:0
17、0 2006, Uncontrolled Copy, (c) BSI INTERNATIONAL STANDARD OSIISO 5456-4:1996(E) 1 Technical drawings Projection methods Part 4: Central projection 1 Scope This part of ISO 5456 specifies basic rules for the development and application of central projection in technical drawings. 2 Normative referenc
18、e The following standard contains provisions which, through reference in this text, constitute provisions of this part of ISO 5456. At the time of publication, the edition indicated was valid. All standards are subject to revision, and parties to agreements based on this part of ISO 5456 are encoura
19、ged to investigate the possibility of applying the most recent edition of the standard indicated below. Members of IEC and ISO maintain registers of currently valid International Standards. ISO 10209-2:1993, Technical product documentation Vocabulary Part 2: Terms relating to projection methods. 3 D
20、efinitions For the purposes of this part of ISO 5456, the defi- nitions given in ISO 10209-2 and the following defi- nitions apply. 3.1 alignment line: Line parallel to a given line passing through the projection centre. Its intersection with the projection plane gives the vanishing point of all lin
21、es parallel to the given line. 3.2 height of projection: Vertical distance of the projection centre from the basic plane. 3.3 horizontal distance: Distance between the projection centre and the projection plane. 3.4 projection angle: Angle formed by the projec- tion plane and the horizon plane. 3.5
22、scale point: Vanishing point of the horizontal direction orthogonal to that bisecting the angle formed by the horizon line and the alignment line of the given horizontal line, and allowing the true length of the projection of the given line to be determined. 3.6 station of observation: Orthogonal pr
23、ojection of the projection centre onto the basic plane. Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 5456-4:1996(E) ISO 2 4 Symbols Letter symbols for terms used in central projection are given in table 1 and illustrated in figures 1
24、and 2, as well as in the figures mentioned in table 1. Table 1 Letter symbols No.TermLetter symbolFigure 1) 1) 1) 3.4 1) 1) 3.1 1) 1) 1) 1) 3.2 3.3 1) 1) 1) 1) 1) 3.5 3.6 Projection plane Basic plane Basic line Projection angle Horizon plane Horizon line Alignment line Main point Vanishing point Mai
25、n projector Projection centre Height of projection Horizontal distance Vision cone Circle of vision Vision angle Projector Distance point Scale point Station of observation T G X b HT h Vl C V pL O H d K Ks a Pl DP MP Sp 1 1 1 5 1 1 4 1 4 1 1 1 1 2 3 2 3 13 14 1 1) Terms already defined in ISO 10209
26、-2. 5 Central projection methods The mode of the central projection depends on the position of the object to be represented with respect to the projection plane. For possible positions and applicable projection methods, see 5.1 to 5.4. 5.1 One-point method A one-point projection method is a central
27、projection of an object having its principal face parallel to the projection plane (special position). All parallel outlines and edges of the object which are parallel to the projection plane retain their direction in this represen- tation (horizontal lines remain horizontal and vertical lines remai
28、n vertical). All lines perpendicular to the projection plane converge at the vanishing point, V, coinciding with the main point, C, (see figure 3 and 7.2.1 and 7.3). 5.2 Two-point method A two-point projection method is a central projection of an object having its vertical outlines and edges paralle
29、l to the projection plane (particular position). All horizontal lines of a representation converge at multi- ple vanishing points V1, V2, V3, ., on the horizon line (see figure 4 and 7.2.2 and 7.4). 5.3 Three-point method A three-point projection method is a central projection of an object having no
30、 outlines or edges parallel to the projection plane (any position). If the projection plane is inclined towards the projection centre, i.e. b 90, the vanishing point for vertical lines is situated below the horizon line (see figure 5 and 7.5.1 and 7.5.2). 5.4 Coordinate method Representation by the
31、coordinate method is based on simple proportions. The coordinates, related to the main projector of all relevant points of the object to be represented, are taken by the graphic method from the basic plane and elevation. From these point coordinates, the image coordinates are obtained by a calculati
32、on method and entered to scale. The image points are connected to each other to provide a clear representation of the object (see figure 6). 6 Principle 6.1 Location and position of the projection plane The image size of an object can be varied by parallel shifting of the projection plane. If the ob
33、ject is placed in front of the projection plane, the representation will be enlarged. The object behind the projection plane will result in a smaller image. Figure 7 shows the change in image size depending on the position of the object with respect to the projection plane. Figure 8 shows the change
34、 in image size depending on the method of representation with vertical or inclined projection planes. b is the included angle between the projection plane and the basic plane near the projection centre. Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy
35、, (c) BSI OSIISO 5456-4:1996(E) 3 Figure 1 Projection model of the central projection Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 5456-4:1996(E) ISO 4 Figure 2 Vision cone and vision angle in the projection model of the central proje
36、ction Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI OSIISO 5456-4:1996(E) 5 Figure 3 Projection model with vertical projection plane and an object in a special position with respect to the projection plane Figure 4 Projection model with ve
37、rtical projection plane and an object in a particular position with respect to the projection plane Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 5456-4:1996(E) OSI 6 Figure 5 Projection model with inclined projection plane and an obje
38、ct in any position with respect to the projection plane (b 90) Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI OSIISO 5456-4:1996(E) 7 Figure 6 Projection model with vertical projection plane and an object in special position, showing the le
39、ngths used in the mathematical formula for calculation of the perspective image Figure 7 Location of projection planes b = 90, b1 90; b2 90 Due to the inclination away from the projection cen- tre, the vanishing point for vertical lines of the object to be depicted moves below the horizon line from
40、infinite to finite, so that tilting projected vertical lines provide an optical distortion suggesting a tapering form (see figure 16). Figure 16 Object, framed in a cube (indicated by a double-dashed line), in front of a projection plane inclined away from the projection centre Licensed Copy: sheffi
41、eldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI ISO 5456-4:1996(E) OSI 16 7.6 Coordinate piercing method The coordinate piercing method is based on simple proportions, in which each piercing point of the pro- jectors in the projection plane is not established by
42、 drawing, but by calculation. This method is based on dividing the space in four quadrants by two reference planes, one horizontal and one vertical, each perpen- dicular to the projection plane, their common line being the main projector. The common lines of the horizontal and vertical reference pla
43、nes and the pro- jection plane are the X and Y axes of a rectangular Cartesian coordinate system situated in the projection plane, the origin of which is the main point. The projector OP of point P pierces the projection plane at point P (X, Y). The coordinates X and Y of the point P can be deter- m
44、ined from the distances PA1 = B C 1 1 and PB1 = A C 1 1 of the point P from the reference planes, from the object distance D =OC1 and the distance d =OC : X = B C 1 1d D / and Y = A C 1 1d D / The values calculated for X and Y for all points of the object to be represented are transferred into the c
45、oordinate system to obtain the representation of the object. The dimensions needed for the calculation of B C 1 1, A C 1 1 and D are taken from the basic plane, elevation, side view, etc. of the object, whereby these planes may be drawn in various scales. The represen- tation may be reduced or enlar
46、ged in a similar mode by multiplying the coordinates X and Y by the scale factor (see figure 17). NOTE 1 BC 1 1 is positive (negative) when B1 is on the right (left) side of the main projector; AC 1 1 is positive (negative) when A1 is above (below) the main projector. 8 Development of a central proj
47、ection By turning the basic plane into the projection plane (see figure 1), it is possible to present the represen- tation of the basic plane on the drawing surface and subsequently to create the complete representation of the dimensions taken from the elevation. There are two different ways to turn
48、 the basic plane: Figure 17 Coordinate piercing method Licensed Copy: sheffieldun sheffieldun, na, Sat Nov 25 12:48:58 GMT+00:00 2006, Uncontrolled Copy, (c) BSI OSIISO 5456-4:1996(E) 17 8.1 Turning the basic plane downwards The station of observation, (Sp), is placed at the distance d from C, below
49、 the basic line (X). The representation is above, and the basic plane is below the basic line; they do not cover each other. This arrangement is called regular arrangement and gives the best survey, but requires considerable space on the drawing surface (see figure 18). 8.2 Turning the projection plane downwards The basic line becomes the axis of symmetry. This frequently-used arrangement saves space on the drawing surface and is called economy arrangement (see figure 19). Figure 18 Re