ISO 5456-4:1996
(Main)Technical drawings — Projection methods — Part 4: Central projection
Technical drawings — Projection methods — Part 4: Central projection
Dessins techniques — Méthodes de projection — Partie 4: Projection centrale
La présente partie de l'ISO 5456 prescrit des règles de base pour le développement et l'application de la projection centrale dans les dessins techniques.
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INTERNATIONAL
STANDARD
First edition
1996-06-15
Technical drawings - Projection methods -
Part 4:
Central projection
Dessins techniques - Mkthodes de projection -
Partie 4: Projection ten trale
Reference number
IS0 5456-4:1996(E)
IS0 5456-4: 1996(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work of
preparing International Standards is normally carried out through IS0
technical committees. 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. IS0
collaborates closely with the International 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 bodies casting
a vote.
International Standard IS0 5456-4 was prepared by Technical Committee
lSO,K 10, Technical drawings, product definition and related documen-
tation, Subcommittee SC 1, Basic conventions.
IS0 5456 consists of the following parts, under the general title Technical
drawings - Projection methods:
- Part I: Synopsis
Part 2: Orthographic representations
- Part 3: Axonometric representations
Part 4: Central projection
Annexes A and B of this part of IS0 5456 are for information only.
0 IS0 1996
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 l CH-121 1 Geneve 20 l Switzerland
Printed in Switzerland
II
@ IS0 IS0 5456-4: 1996(E)
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 projection provides excellent visual appearance
of the object (monocular vision) and is often used in architectural drawings.
This page intentionally left blank
IS0 5456-4: 1996(E)
INTERNATIONAL STANDARD @ IS0
Projection methods -
Technical drawings -
art 4:
Central projection
3.1 alignment line: Line parallel to a given line
1 Scope
passing through the projection centre. Its intersection
with the projection plane gives the vanishing point of
This part of IS0 5456 specifies basic rules for the
all lines parallel to the given line.
development and application of central projection in
technical drawings.
3.2 height of projection: Vertical distance of the
2 Normative referermce
projection centre from the basic plane.
The following standard contains provisions which,
through reference in this text, constitute provisions of
3.3 horizontal distance: Distance between the
this part of IS0 5456. At the time of publication, the
projection centre and the projection plane.
edition indicated was valid. All standards are subject
to revision, and parties to agreements based on this
part of IS0 5456 are encouraged to investigate the
possibility of applying the most recent edition of the
3.4 projection angle: Angle formed by the projec-
standard indicated below. Members of IEC and IS0
tion plane and the horizon plane.
maintain registers of currently valid International
Standards.
IS0 10209-2: 1993, Technical product documentation 3.5 scale point: Vanishing point of the horizontal
- Vocabulary - Part 2: Terms relating to projection
direction orthogonal to that bisecting the angle formed
methods. 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 Qefinitions
For the purposes of this part of IS0 5456, the defi-
nitions given in IS0 10209-2 and the following defi-
3.6 station of observation: Orthogonal projection
nitions apply. of the projection centre onto the basic plane.
@ IS0
IS0 5456-4: 1996(E)
plane retain their direction in this representation
4 Symbols
(horizontal lines remain horizontal and vertical lines
remain vertical). All lines perpendicular to the projec-
Letter symbols for terms used in central projection
tion plane converge at the vanishing point, V, coincid-
are given in table 1 and illustrated in figures 1 and 2,
ing with the main point, C, (see figure 3 and 7.2.1
as well as in the figures mentioned in table 1.
and 7.3).
Table 1 - Letter symbols
5.2 Two-point perspective
No. Term Letter symbol Figure
A two-point perspective is a central projection of an
1)
Projection plane T 1
object having its vertical outlines and edges parallel to
1)
Basic plane G 1 the projection plane (particular position). All horizontal
lines of a representation converge at the relative
1) 1
Basic line X
vanishing point on the horizon line (see figure 4 and
P 5
3.4 Projection angle
7.2.2 and 7.4).
1)
Horizon plane HT 1
1)
Horizon line h
5.3 Three-point perspective
3.1 Alignment line VI 4
1)
Main point C 1
A three-point perspective is a central projection of an
object having no outlines or edges parallel to the
1)
V 4
Vanishing point
projection plane (any position). If the projection plane
1)
Main projector 1
PL
is inclined towards the projection centre, i.e. p > 90°,
the vanishing point for vertical lines is situated below
0 1
1) Projection centre
the horizon line (see figure 5 and 7.5.1 and 7.5.2).
3.2 Height of projection H 1
3.3 Horizontal distance d
1)
Vision cone K 2
5.4 Coordinate method
1)
Circle of vision KS 3
Representation by the coordinate method is based on
1)
Vision angle a 2
simple proportions.
1)
Projector PI 3
The coordinates, related to the main projector of all
1)
Distance point DP 15
relevant points of the object to be represented, are
3.5 Scale point MP 16
taken by the graphic method from the basic plane and
elevation. From these point coordinates, the image
3.6 Station of observation SP
coordinates are obtained by a calculation method and
1) Terms already defined in IS0 10209-2.
entered to scale. The image points are connected to
each other to provide a clear representation of the
object (see figure 6).
5 Central projection methods
6 Principle
The mode of the central projection depends on the
position of the object to be represented with respect
to the projection plane.
6.1 Location and position of the projection
plane
5.1 One-point perspective
The image size of an object can be varied by parallel
A one-point perspective is a central projection of an shifting of the projection plane. If the object is placed
in front of the projection plane, the representation will
object having its principal face parallel to the projec-
tion plane (special position). All parallel outlines and be enlarged. The object behind the projection plane
will result in a smaller image. Figure 7 shows the
edges of the object which are parallel to the projection
IS0 5456-4: 1996(E)
0 IS0
change in image size depending on the position of the 6.2 Two-point projection method
object with respect to the projection plane.
The two-point projection method is a central projec-
tion of an object having its vertical outlines and edges
Figure 8 shows the change in image size depending
parallel to the projection plane. All horizontal lines of a
on the method of representation with vertical or
representation converge at the relative vanishing point
inclined projection planes.
on the horizon line (see figure 9).
Figure l- Projection model of the central projection
IS0 5456-4: 1996(E)
Figure 2 - Vision cone and vision angle in the projection model of the central projection
@ IS0 IS0 5456-4: 1996(E)
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 vertical projection plane and an object in a particular position
with respect to the projection plane
Figure 5 - Projection model with inclined projection plane and an object in any position with respect
to the projection plane (p > 90°)
@ IS0 IS0 5456-4: 1996(E)
Figure 6 - Projection model with vertical projection plane and an object in
special position, showing the
lengths used in the mathematical formula for calculation of the perspective image
IS0 5456=4:1996(E)
Figure 7 -
Location of projection planes
Figure 8 -
Position of projection planes
Figure 9 - . .
ProJectton model with vertical projection plane and an object in any position with respect to the
projection plane
IS0 5456-4: 1996(E)
@ IS0
Heavy peripheral distortions occur on images outside
6.3 Circle of vision and vision cone
the circle of vision; the image does not appear fully
To obtain a fully instructive image of an object without instructive since length, width and height do not
peripheral distortions on the projection plane, the
match the object’s inherent proportions (see fig-
object must be positioned within a vision cone having ure 10).
an aperture angle not greater than 60°.
Figure IO - Object, framed in a cube, within and outside the circle of vision
IS0 5456-4: 1996(E)
@ IS0
6.4 Three-point projection method 6.5 Distance
The three-point projection method is a central projec- Relative distances influence the image size and its
tion of an object having no outlines or edges parallel appearance. When the distance object-projection
to the projection plane (any position). If the projection plane is fixed and the projection centre and the object
lie on opposite sides of the projection plane, increas-
plane is inclined towards the projection centre, i.e.
p > 90°, the vanishing point for vertical lines is situ- ing the distance (d) between the projection centre and
the projection plane gives enlarged and flattened
ated below the horizon line (see figure 11).
representations. When the distance (d) is fixed and
the object and the projection centre lie on opposite
An object can be depicted nearly undistorted if the
sides of the projection plane, increasing the distance
projectors result in a bundle of rays inclined not more
object-projection plane gives reduced and flattened
than 30° with respect to the main projector. At this
representations.
aperture angle the vision cone provides only a small
distortion on the projection plane.
The main projector should hit the object to be de-
picted in a part which is visually important, so that the
object is contained within the minimum vision cone.
Figure II- Projection model with inclined projection plane and an object in any position with respect to the
projection plane (fl> 90°)
@ IS0 IS0 5456-4: 1996(E)
basic plane and elevation, and may be determined
7 Principles and methods of depiction
either by drawing or by calculation (see figure 12).
7.1 Piercing, method
The piercing method allows even complex objects
(round shapes, helicoids, etc.) to be easily repre-
Using the piercing method, the piercing points of
projectors with the projection plane are shown by sented in central projection.
-h
/’
KS
A
tl
I
Figure I2 - Projection model turned into the drawing surface with side view
IS0 5456-4: 1996(E) @ IS0
projection plane is situated at infinity and the vanish-
7.2 Trace point - vanishing point m’ethods
ing point for those edges perpendicular to the projec-
tion plane is the main point (see figure 13).
With the trace point - vanishing point methods, the
outlines and edges of the object to be depicted are
7.2.2 Trace point - vanishing point method B
imaged from basic plane and elevation.
(particular position of the object)
7.2.1 Trace point - vanishing point method A
In method B, horizontal faces of the object are per-
(special position of the object)
pendicular to the vertical projection plane (particular
In method A, one vertical face of the object is parallel
position of the object with respect to the projection
to the vertical projection plane (special position of the plane) so that the lines are represented by their trace
object with respect to the projection plane), so that
on the projection plane and by their vanishing point
the vanishing point for those edges parallel to the
(see figure 14).
Figure 13 - Object, framed in a cube, in special position with respect to the projection plane
according to method A
@ IS0 IS0 5456-4: 1996(E)
Figure 14 - Object, framed in a cube, in particular position with respect to the projection plane
according to method B
@ IS0
IS0 5456-4: 1996(E)
position). The distance point has the same distance
7.3 Distance point method
from the main point as the projection centre from the
(special position of the object)
projection plane. All horizontal lines inclined at 45’
The distance point method gives the central projection with respect to the projection plane align to the dis-
of an object without its basic plane, by setting up a tance point. The vanishing point of the depth lines of
perspective screen. The outlines and edges are paral- the screen is the main point (see figure 15).
lel or perpendicular to the projection plane (special
Figure 15 - Object, framed in a cube, on a horizontal screen, in special position with respect to
the projection plane
@ IS0 IS0 5456-4: 1996(E)
of the object to be depicted may be transferred from
7.4 Scale point method
the basic line in the projection plane on depth lines
(particular position of the object)
(see figure 16). By means of the basic plane, a definite
For any
...
INTERNATIONAL ISO
STANDARD 5456-4
First edition
1996-06-15
Corrected and reprinted
1998-08-01
Technical drawings — Projection
methods —
Part 4:
Central projection
Dessins techniques — Méthodes de projection —
Partie 4: Projection centrale
A
Reference number
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. 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 International 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 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 — Projection 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.
© ISO 1996
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet iso@iso.ch
Printed in Switzerland
ii
©
ISO ISO 5456-4:1996(E)
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 projection provides excellent visual appearance
of the object (monocular vision) and is often used in architectural draw-
ings.
iii
©
INTERNATIONAL STANDARD ISO ISO 5456-4:1996(E)
Technical drawings — Projection methods —
Part 4:
Central projection
3.1 alignment line: Line parallel to a given line
1 Scope
passing through the projection centre. Its intersection
with the projection plane gives the vanishing point of
This part of ISO 5456 specifies basic rules for the
all lines parallel to the given line.
development and application of central projection in
technical drawings.
3.2 height of projection: Vertical distance of the
2 Normative reference
projection centre from the basic plane.
The following standard contains provisions which,
through reference in this text, constitute provisions of
3.3 horizontal distance: Distance between the
this part of ISO 5456. At the time of publication, the
projection centre and the projection plane.
edition indicated was valid. All standards are subject
to revision, and parties to agreements based on this
part of ISO 5456 are encouraged to investigate the
possibility of applying the most recent edition of the
3.4 projection angle: Angle formed by the projec-
standard indicated below. Members of IEC and ISO
tion plane and the horizon plane.
maintain registers of currently valid International
Standards.
3.5 scale point: Vanishing point of the horizontal
ISO 10209-2:1993, Technical product documentation
— Vocabulary — Part 2: Terms relating to projection direction orthogonal to that bisecting the angle formed
by the horizon line and the alignment line of the given
methods.
horizontal line, and allowing the true length of the
projection of the given line to be determined.
3 Definitions
For the purposes of this part of ISO 5456, the defi-
nitions given in ISO 10209-2 and the following defi- 3.6 station of observation: Orthogonal projection
of the projection centre onto the basic plane.
nitions apply.
©
tation (horizontal lines remain horizontal and vertical
4 Symbols
lines remain vertical). All lines perpendicular to the
projection plane converge at the vanishing point, V,
Letter symbols for terms used in central projection
coinciding with the main point, C, (see figure 3 and
are given in table 1 and illustrated in figures 1 and 2,
7.2.1 and 7.3).
as well as in the figures mentioned in table 1.
5.2 Two-point method
Table 1 — Letter symbols
A two-point projection method is a central projection
No. Term Letter symbol Figure
of an object having its vertical outlines and edges
1)
Projection plane T 1 parallel to the projection plane (particular position). All
horizontal lines of a representation converge at multi-
1)
Basic plane G 1
ple vanishing points V , V , V , ., on the horizon line
1 2 3
1)
Basic line X 1 (see figure 4 and 7.2.2 and 7.4).
3.4 Projection angle b 5
1) 5.3 Three-point method
Horizon plane HT 1
1)
Horizon line h 1
A three-point projection method is a central projection
3.1 Alignment line Vl 4 of an object having no outlines or edges parallel to the
projection plane (any position). If the projection plane
1)
Main point C 1
is inclined towards the projection centre, i.e. b > 90°,
1)
Vanishing point V 4
the vanishing point for vertical lines is situated below
the horizon line (see figure 5 and 7.5.1 and 7.5.2).
1)
Main projector pL 1
1)
Projection centre O 1
5.4 Coordinate method
3.2 Height of projection H 1
3.3 Horizontal distance d 1
Representation by the coordinate method is based on
simple proportions.
1)
Vision cone K 2
1)
Circle of vision Ks 3
The coordinates, related to the main projector of all
1)
relevant points of the object to be represented, are
Vision angle a 2
taken by the graphic method from the basic plane and
1)
Projector Pl 3
elevation. From these point coordinates, the image
1)
Distance point DP 13
coordinates are obtained by a calculation method and
entered to scale. The image points are connected to
3.5 Scale point MP 14
each other to provide a clear representation of the
3.6 Station of observation Sp 1
object (see figure 6).
1) Terms already defined in ISO 10209-2.
6 Principle
5 Central projection methods
6.1 Location and position of the projection
plane
The mode of the central projection depends on the
position of the object to be represented with respect
The image size of an object can be varied by parallel
to the projection plane.
shifting of the projection plane. If the object is placed
in front of the projection plane, the representation will
For possible positions and applicable projection
be enlarged. The object behind the projection plane
methods, see 5.1 to 5.4.
will result in a smaller image. Figure 7 shows the
change in image size depending on the position of the
5.1 One-point method
object with respect to the projection plane.
A one-point projection method is a central projection
Figure 8 shows the change in image size depending
of an object having its principal face parallel to the
on the method of representation with vertical or
projection plane (special position). All parallel outlines
inclined projection planes. b is the included angle
and edges of the object which are parallel to the
between the projection plane and the basic plane near
projection plane retain their direction in this represen- the projection centre.
©
ISO ISO 5456-4:1996(E)
Figure 1 — Projection model of the central projection
©
Figure 2 — Vision cone and vision angle in the projection model of the central projection
©
ISO ISO 5456-4:1996(E)
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 vertical projection plane and an object in a particular position
with respect to the projection plane
©
Figure 5 — Projection model with inclined projection plane and an object in any position with respect
to the projection plane (b > 90°)
©
ISO ISO 5456-4:1996(E)
Figure 6 — Projection model with vertical projection plane and an object in special position, showing the
lengths used in the mathematical formula for calculation of the perspective image
b = 90°, b > 90°; b < 90°
1 2
Figure 7 — Location of projection planes Figure 8 — Position of projection planes
©
6.2 Circle of vision and vision cone instructive since length, width and height do not
match the object’s inherent proportions (see figure 9).
To obtain a fully instructive image of an object without
peripheral distortions on the projection plane, the
An object can be depicted nearly undistorted if the
object must be positioned within a vision cone having
projectors result in a bundle of rays inclined not more
an aperture angle not greater than 60°.
than 30° with respect to the main projector. At this
aperture angle the vision cone provides only a small
Heavy peripheral distortions occur on images outside
distortion on the projection plane.
the circle of vision; the image does not appear fully
Figure 9 — Object, framed in a cube, within and outside the circle of vision
©
ISO ISO 5456-4:1996(E)
The main projector should hit the object to be de- between the object and the projection plane gives re-
picted in a part which is visually important, so that the duced and flattened representations.
object is contained within the minimum vision cone.
7 Principles and methods of depiction
6.3 Distance
7.1 Piercing method
Different relative distances influence the image size and
its appearance. When the distance between the object
Using the piercing method, the piercing points of
and the projection plane is fixed and the projection centre
projectors with the projection plane are shown by
and the object lie on opposite sides of the projection
basic plane and elevation, and may be determined
plane, increasing the distance (d) between the projection
either by drawing or by calculation (see figure 10).
centre and the projection plane gives enlarged and
flattened representations. When the distance (d) is fixed The piercing method allows even complex objects
and the object and the projection centre lie on opposite (round shapes, helicoids, etc.) to be easily repre-
sides of the projection plane, increasing the distance sented in central projection.
Figure 10 — Projection model turned into the drawing surface with side view
©
7.2 Trace point — vanishing point methods projection plane is situated at infinity and the vanish-
ing point for those edges perpendicular to the projec-
tion plane is the main point (see figure 11).
With the trace point — vanishing point methods, the
outlines and edges of the object to be depicted are
imaged from basic plane and elevation.
7.2.2 Trace point — vanishing point method B
(particular position of the object)
7.2.1 Trace point — vanishing point method A
In method B, horizontal faces of the object are per-
(special position of the object)
pendicular to the vertical projection plane (particular
In method A, one vertical face of the object is parallel
position of the object with respect to the projection
to the vertical projection plane (special position of the
plane) so that the lines are represented by their trace
object with respect to the projection plane), so that
on the projection plane and by their vanishing point
the vanishing point for those edges parallel to the
(see figure 12).
Figure 11 — Object, framed in a cube (indicated by a double-dashed line), in special position
with respect to the projection plane according to method A
©
ISO ISO 5456-4:1996(E)
Figure 12 — Object, framed in a cube (indicated by a double-dashed line), in particular position
with respect to the projection plane according to method B
©
7.3 Distance point method tion). The distance point has the same distance from
the main point as the projection centre from the
(special position of the object)
projection plane. All horizontal lines inclined at 45°
The distance point method gives the central projection with respect to the projection plane align to the dis-
of an object without its basic plane, by setting up a
tance point. The vanishing point of the depth lines of
perspective grid. The outlines and edges are parallel the grid is the main point (see figure 13).
or perpendicular to the projection plane (special posi-
Figure 13 — Object, framed in a cube (indicated by a double-dashed line), in special position
with respect to the projection plane
©
ISO ISO 5456-4:1996(E)
of the object to be depicted may be transferred from
7.4 Scale point method
the basic line in the projection plane on depth lines
(particular position of the object)
(see figure 14). By means of the basic plane, a definite
For any vanishing point there is a corresponding scale
relation between the perspective representation of
point. With the aid of scale points, certain dimensions the object and the object itself may be established.
Figure 14 — Object, framed in a cube (indicated by a double-dashed line), in particular position
with respect to the projection plane
©
7.5 Trace point method with inclined the vertical lines of the object to be depicted moves
from infinite to finite. The angle b, i.e. the angle of
projection plane
inclination of the projection plane with respect to the
horizon plane, defines the position of the vanishing
7.5.1 Inclined projection plane b < 90°
point above the horizon. Vertical object lines are
represented as tilting lines, which gives an optical dis-
Due to the inclination of the projection plane with
tortion suggesting a tapering form (see figure 15).
res
...
INTERNATIONAL
STANDARD
First edition
1996-06-15
Technical drawings - Projection methods -
Part 4:
Central projection
Dessins techniques - Mkthodes de projection -
Partie 4: Projection ten trale
Reference number
IS0 5456-4:1996(E)
IS0 5456-4: 1996(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work of
preparing International Standards is normally carried out through IS0
technical committees. 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. IS0
collaborates closely with the International 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 bodies casting
a vote.
International Standard IS0 5456-4 was prepared by Technical Committee
lSO,K 10, Technical drawings, product definition and related documen-
tation, Subcommittee SC 1, Basic conventions.
IS0 5456 consists of the following parts, under the general title Technical
drawings - Projection methods:
- Part I: Synopsis
Part 2: Orthographic representations
- Part 3: Axonometric representations
Part 4: Central projection
Annexes A and B of this part of IS0 5456 are for information only.
0 IS0 1996
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 l CH-121 1 Geneve 20 l Switzerland
Printed in Switzerland
II
@ IS0 IS0 5456-4: 1996(E)
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 projection provides excellent visual appearance
of the object (monocular vision) and is often used in architectural drawings.
This page intentionally left blank
IS0 5456-4: 1996(E)
INTERNATIONAL STANDARD @ IS0
Projection methods -
Technical drawings -
art 4:
Central projection
3.1 alignment line: Line parallel to a given line
1 Scope
passing through the projection centre. Its intersection
with the projection plane gives the vanishing point of
This part of IS0 5456 specifies basic rules for the
all lines parallel to the given line.
development and application of central projection in
technical drawings.
3.2 height of projection: Vertical distance of the
2 Normative referermce
projection centre from the basic plane.
The following standard contains provisions which,
through reference in this text, constitute provisions of
3.3 horizontal distance: Distance between the
this part of IS0 5456. At the time of publication, the
projection centre and the projection plane.
edition indicated was valid. All standards are subject
to revision, and parties to agreements based on this
part of IS0 5456 are encouraged to investigate the
possibility of applying the most recent edition of the
3.4 projection angle: Angle formed by the projec-
standard indicated below. Members of IEC and IS0
tion plane and the horizon plane.
maintain registers of currently valid International
Standards.
IS0 10209-2: 1993, Technical product documentation 3.5 scale point: Vanishing point of the horizontal
- Vocabulary - Part 2: Terms relating to projection
direction orthogonal to that bisecting the angle formed
methods. 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 Qefinitions
For the purposes of this part of IS0 5456, the defi-
nitions given in IS0 10209-2 and the following defi-
3.6 station of observation: Orthogonal projection
nitions apply. of the projection centre onto the basic plane.
@ IS0
IS0 5456-4: 1996(E)
plane retain their direction in this representation
4 Symbols
(horizontal lines remain horizontal and vertical lines
remain vertical). All lines perpendicular to the projec-
Letter symbols for terms used in central projection
tion plane converge at the vanishing point, V, coincid-
are given in table 1 and illustrated in figures 1 and 2,
ing with the main point, C, (see figure 3 and 7.2.1
as well as in the figures mentioned in table 1.
and 7.3).
Table 1 - Letter symbols
5.2 Two-point perspective
No. Term Letter symbol Figure
A two-point perspective is a central projection of an
1)
Projection plane T 1
object having its vertical outlines and edges parallel to
1)
Basic plane G 1 the projection plane (particular position). All horizontal
lines of a representation converge at the relative
1) 1
Basic line X
vanishing point on the horizon line (see figure 4 and
P 5
3.4 Projection angle
7.2.2 and 7.4).
1)
Horizon plane HT 1
1)
Horizon line h
5.3 Three-point perspective
3.1 Alignment line VI 4
1)
Main point C 1
A three-point perspective is a central projection of an
object having no outlines or edges parallel to the
1)
V 4
Vanishing point
projection plane (any position). If the projection plane
1)
Main projector 1
PL
is inclined towards the projection centre, i.e. p > 90°,
the vanishing point for vertical lines is situated below
0 1
1) Projection centre
the horizon line (see figure 5 and 7.5.1 and 7.5.2).
3.2 Height of projection H 1
3.3 Horizontal distance d
1)
Vision cone K 2
5.4 Coordinate method
1)
Circle of vision KS 3
Representation by the coordinate method is based on
1)
Vision angle a 2
simple proportions.
1)
Projector PI 3
The coordinates, related to the main projector of all
1)
Distance point DP 15
relevant points of the object to be represented, are
3.5 Scale point MP 16
taken by the graphic method from the basic plane and
elevation. From these point coordinates, the image
3.6 Station of observation SP
coordinates are obtained by a calculation method and
1) Terms already defined in IS0 10209-2.
entered to scale. The image points are connected to
each other to provide a clear representation of the
object (see figure 6).
5 Central projection methods
6 Principle
The mode of the central projection depends on the
position of the object to be represented with respect
to the projection plane.
6.1 Location and position of the projection
plane
5.1 One-point perspective
The image size of an object can be varied by parallel
A one-point perspective is a central projection of an shifting of the projection plane. If the object is placed
in front of the projection plane, the representation will
object having its principal face parallel to the projec-
tion plane (special position). All parallel outlines and be enlarged. The object behind the projection plane
will result in a smaller image. Figure 7 shows the
edges of the object which are parallel to the projection
IS0 5456-4: 1996(E)
0 IS0
change in image size depending on the position of the 6.2 Two-point projection method
object with respect to the projection plane.
The two-point projection method is a central projec-
tion of an object having its vertical outlines and edges
Figure 8 shows the change in image size depending
parallel to the projection plane. All horizontal lines of a
on the method of representation with vertical or
representation converge at the relative vanishing point
inclined projection planes.
on the horizon line (see figure 9).
Figure l- Projection model of the central projection
IS0 5456-4: 1996(E)
Figure 2 - Vision cone and vision angle in the projection model of the central projection
@ IS0 IS0 5456-4: 1996(E)
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 vertical projection plane and an object in a particular position
with respect to the projection plane
Figure 5 - Projection model with inclined projection plane and an object in any position with respect
to the projection plane (p > 90°)
@ IS0 IS0 5456-4: 1996(E)
Figure 6 - Projection model with vertical projection plane and an object in
special position, showing the
lengths used in the mathematical formula for calculation of the perspective image
IS0 5456=4:1996(E)
Figure 7 -
Location of projection planes
Figure 8 -
Position of projection planes
Figure 9 - . .
ProJectton model with vertical projection plane and an object in any position with respect to the
projection plane
IS0 5456-4: 1996(E)
@ IS0
Heavy peripheral distortions occur on images outside
6.3 Circle of vision and vision cone
the circle of vision; the image does not appear fully
To obtain a fully instructive image of an object without instructive since length, width and height do not
peripheral distortions on the projection plane, the
match the object’s inherent proportions (see fig-
object must be positioned within a vision cone having ure 10).
an aperture angle not greater than 60°.
Figure IO - Object, framed in a cube, within and outside the circle of vision
IS0 5456-4: 1996(E)
@ IS0
6.4 Three-point projection method 6.5 Distance
The three-point projection method is a central projec- Relative distances influence the image size and its
tion of an object having no outlines or edges parallel appearance. When the distance object-projection
to the projection plane (any position). If the projection plane is fixed and the projection centre and the object
lie on opposite sides of the projection plane, increas-
plane is inclined towards the projection centre, i.e.
p > 90°, the vanishing point for vertical lines is situ- ing the distance (d) between the projection centre and
the projection plane gives enlarged and flattened
ated below the horizon line (see figure 11).
representations. When the distance (d) is fixed and
the object and the projection centre lie on opposite
An object can be depicted nearly undistorted if the
sides of the projection plane, increasing the distance
projectors result in a bundle of rays inclined not more
object-projection plane gives reduced and flattened
than 30° with respect to the main projector. At this
representations.
aperture angle the vision cone provides only a small
distortion on the projection plane.
The main projector should hit the object to be de-
picted in a part which is visually important, so that the
object is contained within the minimum vision cone.
Figure II- Projection model with inclined projection plane and an object in any position with respect to the
projection plane (fl> 90°)
@ IS0 IS0 5456-4: 1996(E)
basic plane and elevation, and may be determined
7 Principles and methods of depiction
either by drawing or by calculation (see figure 12).
7.1 Piercing, method
The piercing method allows even complex objects
(round shapes, helicoids, etc.) to be easily repre-
Using the piercing method, the piercing points of
projectors with the projection plane are shown by sented in central projection.
-h
/’
KS
A
tl
I
Figure I2 - Projection model turned into the drawing surface with side view
IS0 5456-4: 1996(E) @ IS0
projection plane is situated at infinity and the vanish-
7.2 Trace point - vanishing point m’ethods
ing point for those edges perpendicular to the projec-
tion plane is the main point (see figure 13).
With the trace point - vanishing point methods, the
outlines and edges of the object to be depicted are
7.2.2 Trace point - vanishing point method B
imaged from basic plane and elevation.
(particular position of the object)
7.2.1 Trace point - vanishing point method A
In method B, horizontal faces of the object are per-
(special position of the object)
pendicular to the vertical projection plane (particular
In method A, one vertical face of the object is parallel
position of the object with respect to the projection
to the vertical projection plane (special position of the plane) so that the lines are represented by their trace
object with respect to the projection plane), so that
on the projection plane and by their vanishing point
the vanishing point for those edges parallel to the
(see figure 14).
Figure 13 - Object, framed in a cube, in special position with respect to the projection plane
according to method A
@ IS0 IS0 5456-4: 1996(E)
Figure 14 - Object, framed in a cube, in particular position with respect to the projection plane
according to method B
@ IS0
IS0 5456-4: 1996(E)
position). The distance point has the same distance
7.3 Distance point method
from the main point as the projection centre from the
(special position of the object)
projection plane. All horizontal lines inclined at 45’
The distance point method gives the central projection with respect to the projection plane align to the dis-
of an object without its basic plane, by setting up a tance point. The vanishing point of the depth lines of
perspective screen. The outlines and edges are paral- the screen is the main point (see figure 15).
lel or perpendicular to the projection plane (special
Figure 15 - Object, framed in a cube, on a horizontal screen, in special position with respect to
the projection plane
@ IS0 IS0 5456-4: 1996(E)
of the object to be depicted may be transferred from
7.4 Scale point method
the basic line in the projection plane on depth lines
(particular position of the object)
(see figure 16). By means of the basic plane, a definite
For any
...
INTERNATIONAL ISO
STANDARD 5456-4
First edition
1996-06-15
Corrected and reprinted
1998-08-01
Technical drawings — Projection
methods —
Part 4:
Central projection
Dessins techniques — Méthodes de projection —
Partie 4: Projection centrale
A
Reference number
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. 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 International 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 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 — Projection 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.
© ISO 1996
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet iso@iso.ch
Printed in Switzerland
ii
©
ISO ISO 5456-4:1996(E)
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 projection provides excellent visual appearance
of the object (monocular vision) and is often used in architectural draw-
ings.
iii
©
INTERNATIONAL STANDARD ISO ISO 5456-4:1996(E)
Technical drawings — Projection methods —
Part 4:
Central projection
3.1 alignment line: Line parallel to a given line
1 Scope
passing through the projection centre. Its intersection
with the projection plane gives the vanishing point of
This part of ISO 5456 specifies basic rules for the
all lines parallel to the given line.
development and application of central projection in
technical drawings.
3.2 height of projection: Vertical distance of the
2 Normative reference
projection centre from the basic plane.
The following standard contains provisions which,
through reference in this text, constitute provisions of
3.3 horizontal distance: Distance between the
this part of ISO 5456. At the time of publication, the
projection centre and the projection plane.
edition indicated was valid. All standards are subject
to revision, and parties to agreements based on this
part of ISO 5456 are encouraged to investigate the
possibility of applying the most recent edition of the
3.4 projection angle: Angle formed by the projec-
standard indicated below. Members of IEC and ISO
tion plane and the horizon plane.
maintain registers of currently valid International
Standards.
3.5 scale point: Vanishing point of the horizontal
ISO 10209-2:1993, Technical product documentation
— Vocabulary — Part 2: Terms relating to projection direction orthogonal to that bisecting the angle formed
by the horizon line and the alignment line of the given
methods.
horizontal line, and allowing the true length of the
projection of the given line to be determined.
3 Definitions
For the purposes of this part of ISO 5456, the defi-
nitions given in ISO 10209-2 and the following defi- 3.6 station of observation: Orthogonal projection
of the projection centre onto the basic plane.
nitions apply.
©
tation (horizontal lines remain horizontal and vertical
4 Symbols
lines remain vertical). All lines perpendicular to the
projection plane converge at the vanishing point, V,
Letter symbols for terms used in central projection
coinciding with the main point, C, (see figure 3 and
are given in table 1 and illustrated in figures 1 and 2,
7.2.1 and 7.3).
as well as in the figures mentioned in table 1.
5.2 Two-point method
Table 1 — Letter symbols
A two-point projection method is a central projection
No. Term Letter symbol Figure
of an object having its vertical outlines and edges
1)
Projection plane T 1 parallel to the projection plane (particular position). All
horizontal lines of a representation converge at multi-
1)
Basic plane G 1
ple vanishing points V , V , V , ., on the horizon line
1 2 3
1)
Basic line X 1 (see figure 4 and 7.2.2 and 7.4).
3.4 Projection angle b 5
1) 5.3 Three-point method
Horizon plane HT 1
1)
Horizon line h 1
A three-point projection method is a central projection
3.1 Alignment line Vl 4 of an object having no outlines or edges parallel to the
projection plane (any position). If the projection plane
1)
Main point C 1
is inclined towards the projection centre, i.e. b > 90°,
1)
Vanishing point V 4
the vanishing point for vertical lines is situated below
the horizon line (see figure 5 and 7.5.1 and 7.5.2).
1)
Main projector pL 1
1)
Projection centre O 1
5.4 Coordinate method
3.2 Height of projection H 1
3.3 Horizontal distance d 1
Representation by the coordinate method is based on
simple proportions.
1)
Vision cone K 2
1)
Circle of vision Ks 3
The coordinates, related to the main projector of all
1)
relevant points of the object to be represented, are
Vision angle a 2
taken by the graphic method from the basic plane and
1)
Projector Pl 3
elevation. From these point coordinates, the image
1)
Distance point DP 13
coordinates are obtained by a calculation method and
entered to scale. The image points are connected to
3.5 Scale point MP 14
each other to provide a clear representation of the
3.6 Station of observation Sp 1
object (see figure 6).
1) Terms already defined in ISO 10209-2.
6 Principle
5 Central projection methods
6.1 Location and position of the projection
plane
The mode of the central projection depends on the
position of the object to be represented with respect
The image size of an object can be varied by parallel
to the projection plane.
shifting of the projection plane. If the object is placed
in front of the projection plane, the representation will
For possible positions and applicable projection
be enlarged. The object behind the projection plane
methods, see 5.1 to 5.4.
will result in a smaller image. Figure 7 shows the
change in image size depending on the position of the
5.1 One-point method
object with respect to the projection plane.
A one-point projection method is a central projection
Figure 8 shows the change in image size depending
of an object having its principal face parallel to the
on the method of representation with vertical or
projection plane (special position). All parallel outlines
inclined projection planes. b is the included angle
and edges of the object which are parallel to the
between the projection plane and the basic plane near
projection plane retain their direction in this represen- the projection centre.
©
ISO ISO 5456-4:1996(E)
Figure 1 — Projection model of the central projection
©
Figure 2 — Vision cone and vision angle in the projection model of the central projection
©
ISO ISO 5456-4:1996(E)
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 vertical projection plane and an object in a particular position
with respect to the projection plane
©
Figure 5 — Projection model with inclined projection plane and an object in any position with respect
to the projection plane (b > 90°)
©
ISO ISO 5456-4:1996(E)
Figure 6 — Projection model with vertical projection plane and an object in special position, showing the
lengths used in the mathematical formula for calculation of the perspective image
b = 90°, b > 90°; b < 90°
1 2
Figure 7 — Location of projection planes Figure 8 — Position of projection planes
©
6.2 Circle of vision and vision cone instructive since length, width and height do not
match the object’s inherent proportions (see figure 9).
To obtain a fully instructive image of an object without
peripheral distortions on the projection plane, the
An object can be depicted nearly undistorted if the
object must be positioned within a vision cone having
projectors result in a bundle of rays inclined not more
an aperture angle not greater than 60°.
than 30° with respect to the main projector. At this
aperture angle the vision cone provides only a small
Heavy peripheral distortions occur on images outside
distortion on the projection plane.
the circle of vision; the image does not appear fully
Figure 9 — Object, framed in a cube, within and outside the circle of vision
©
ISO ISO 5456-4:1996(E)
The main projector should hit the object to be de- between the object and the projection plane gives re-
picted in a part which is visually important, so that the duced and flattened representations.
object is contained within the minimum vision cone.
7 Principles and methods of depiction
6.3 Distance
7.1 Piercing method
Different relative distances influence the image size and
its appearance. When the distance between the object
Using the piercing method, the piercing points of
and the projection plane is fixed and the projection centre
projectors with the projection plane are shown by
and the object lie on opposite sides of the projection
basic plane and elevation, and may be determined
plane, increasing the distance (d) between the projection
either by drawing or by calculation (see figure 10).
centre and the projection plane gives enlarged and
flattened representations. When the distance (d) is fixed The piercing method allows even complex objects
and the object and the projection centre lie on opposite (round shapes, helicoids, etc.) to be easily repre-
sides of the projection plane, increasing the distance sented in central projection.
Figure 10 — Projection model turned into the drawing surface with side view
©
7.2 Trace point — vanishing point methods projection plane is situated at infinity and the vanish-
ing point for those edges perpendicular to the projec-
tion plane is the main point (see figure 11).
With the trace point — vanishing point methods, the
outlines and edges of the object to be depicted are
imaged from basic plane and elevation.
7.2.2 Trace point — vanishing point method B
(particular position of the object)
7.2.1 Trace point — vanishing point method A
In method B, horizontal faces of the object are per-
(special position of the object)
pendicular to the vertical projection plane (particular
In method A, one vertical face of the object is parallel
position of the object with respect to the projection
to the vertical projection plane (special position of the
plane) so that the lines are represented by their trace
object with respect to the projection plane), so that
on the projection plane and by their vanishing point
the vanishing point for those edges parallel to the
(see figure 12).
Figure 11 — Object, framed in a cube (indicated by a double-dashed line), in special position
with respect to the projection plane according to method A
©
ISO ISO 5456-4:1996(E)
Figure 12 — Object, framed in a cube (indicated by a double-dashed line), in particular position
with respect to the projection plane according to method B
©
7.3 Distance point method tion). The distance point has the same distance from
the main point as the projection centre from the
(special position of the object)
projection plane. All horizontal lines inclined at 45°
The distance point method gives the central projection with respect to the projection plane align to the dis-
of an object without its basic plane, by setting up a
tance point. The vanishing point of the depth lines of
perspective grid. The outlines and edges are parallel the grid is the main point (see figure 13).
or perpendicular to the projection plane (special posi-
Figure 13 — Object, framed in a cube (indicated by a double-dashed line), in special position
with respect to the projection plane
©
ISO ISO 5456-4:1996(E)
of the object to be depicted may be transferred from
7.4 Scale point method
the basic line in the projection plane on depth lines
(particular position of the object)
(see figure 14). By means of the basic plane, a definite
For any vanishing point there is a corresponding scale
relation between the perspective representation of
point. With the aid of scale points, certain dimensions the object and the object itself may be established.
Figure 14 — Object, framed in a cube (indicated by a double-dashed line), in particular position
with respect to the projection plane
©
7.5 Trace point method with inclined the vertical lines of the object to be depicted moves
from infinite to finite. The angle b, i.e. the angle of
projection plane
inclination of the projection plane with respect to the
horizon plane, defines the position of the vanishing
7.5.1 Inclined projection plane b < 90°
point above the horizon. Vertical object lines are
represented as tilting lines, which gives an optical dis-
Due to the inclination of the projection plane with
tortion suggesting a tapering form (see figure 15).
res
...
NORME ISO
INTERNATIONALE 5456-4
Première édition
1996-06-15
Corrigée et réimprimée
1998-08-01
Dessins techniques — Méthodes de
projection —
Partie 4:
Projection centrale
Technical drawings — Projection methods —
Part 4: Central projection
A
Numéro de référence
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération
mondiale d'organismes nationaux de normalisation (comités membres de
l'ISO). L'élaboration des Normes internationales est en général confiée aux
comités techniques de l'ISO. Chaque comité membre intéressé par une
étude a le droit de faire partie du comité technique créé à cet effet. Les
organisations internationales, gouvernementales et non gouvernemen-
tales, en liaison avec l'ISO participent également aux travaux. L'ISO colla-
bore étroitement avec la Commission électrotechnique internationale (CEI)
en ce qui concerne la normalisation électrotechnique.
Les projets de Normes internationales adoptés par les comités techniques
sont soumis aux comités membres pour vote. Leur publication comme
Normes internationales requiert l'approbation de 75 % au moins des
comités membres votants.
La Norme internationale ISO 5456-4 a été élaborée par le comité technique
ISO/TC 10, Dessins techniques, définition de produits et documentation y
relative, sous-comité SC 1, Conventions générales.
L'ISO 5456 comprend les parties suivantes, présentées sous le titre
général Dessins techniques — Méthodes de projection:
— Partie 1: Récapitulatif
— Partie 2: Représentations orthographiques
— Partie 3: Représentations axonométriques
— Partie 4: Projection centrale
Les annexes A et B de la présente partie de l’ISO 5456 sont données
uniquement à titre d’information.
© ISO 1996
Droits de reproduction réservés. Sauf prescription différente, aucune partie de cette publi-
cation ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun pro-
cédé, électronique ou mécanique, y compris la photocopie et les microfilms, sans l'accord
écrit de l'éditeur.
Organisation internationale de normalisation
Case postale 56 • CH-1211 Genève 20 • Suisse
Internet iso@iso.ch
Imprimé en Suisse
ii
©
ISO ISO 5456-4:1996(F)
Introduction
La projection centrale (perspective) est une représentation imagée réaliste
obtenue par projection de l’objet à représenter, à partir d’un point placé à
une distance définie (centre de projection), sur un plan de projection uni-
que (normalement la surface de dessin). Ce type de projection permet
d’obtenir la meilleure visualisation de l’objet (vision monoculaire) et il est
fréquemment utilisé dans les dessins d’architecture.
iii
©
NORME INTERNATIONALE ISO ISO 5456-4:1996(F)
Dessins techniques — Méthodes de projection —
Partie 4:
Projection centrale
3.1 ligne d’alignement: Ligne parallèle à une ligne
1 Domaine d'application
donnée passant par le centre de projection. Son
La présente partie de l’ISO 5456 prescrit des règles
intersection avec le plan de projection donne le point
de base pour le développement et l’application de la de fuite de toutes les lignes parallèles à la ligne don-
projection centrale dans les dessins techniques.
née.
2 Référence normative
3.2 hauteur de projection: Distance verticale du
centre de projection au plan de base.
La norme suivante contient des dispositions qui, par
suite de la référence qui en est faite, constituent des
dispositions valables pour la présente partie de
l'ISO 5456. Au moment de la publication, l'édition indi-
3.3 distance horizontale: Distance entre le centre
quée était en vigueur. Toute norme est sujette à révi-
de projection et le plan de projection.
sion et les parties prenantes des accords fondés sur
la présente partie de l'ISO 5456 sont invitées à re-
chercher la possibilité d'appliquer l'édition la plus
3.4 angle de projection: Angle formé par le plan de
récente de la norme indiquée ci-après. Les membres
projection et le plan d’horizon.
de la CEI et de l'ISO possèdent le registre des Nor-
mes internationales en vigueur à un moment donné.
ISO 10209-2:1993, Documentation technique de pro-
3.5 point d’échelle: Point de fuite de la direction
duit — Vocabulaire — Partie 2: Termes relatifs aux
horizontale orthogonale à celle qui partage l’angle
méthodes de projection.
formé par la ligne d’horizon et la ligne d’alignement de
la ligne horizontale donnée, et permettant de trouver
la vraie longueur de la projection de la ligne donnée.
3 Définitions
Pour les besoins de la présente partie de l’ISO 5456,
3.6 station d’observation: Projection orthogonale
les définitions données dans l’ISO 10209-2 et les
définitions suivantes s'appliquent. du centre de projection sur le plan de base.
©
lèle au plan de projection (position spéciale). Tous les
4 Symboles
contours et arêtes parallèles de l’objet qui sont parallè-
les au plan de projection conservent leur direction
Les symboles utilisés pour les termes définissant la
dans cette représentation (les lignes horizontales
projection centrale sont donnés dans le tableau 1 et
restent horizontales et les lignes verticales restent
illustrés dans les figures 1 et 2, ainsi que dans les
verticales). Toutes les lignes perpendiculaires au plan
figures mentionnées dans ce tableau.
de projection convergent vers le point de fuite, V,
coïncidant avec le point principal, C, (voir figure 3 et
7.2.1 et 7.3).
Tableau 1 — Symboles
o
N Terme Symbole Figure
5.2 Méthode à deux points
1)
Plan de projection T 1
La méthode de projection à deux points est une
1)
Plan de base G 1
projection centrale d’un objet ayant ses contours et
1)
Ligne de base X 1
arêtes verticaux parallèles au plan de projection
(position particulière). Toutes les lignes horizontales
3.4 Angle de projection b 5
d’une représentation convergent vers les multiples
1)
Plan d’horizon HT 1
points de fuite V , V , V , ., sur la ligne d’horizon (voir
1 2 3
1)
figure 4 et 7.2.2 et 7.4).
Ligne d’horizon h 1
3.1 Ligne d’alignement Vl 4
1)
Point principal C 1
5.3 Méthode à trois points
1)
Point de fuite V 4
La méthode de projection à trois points est une pro-
1)
Ligne de projection
jection centrale d’un objet qui n’a aucun contour ou
principale pL 1
arête parallèle au plan de projection (toute position). Si
1)
Centre de projection O 1
le plan de projection est incliné vers le centre de
projection, c’est-à-dire b > 90°, le point de fuite pour
3.2 Hauteur de projection H 1
les lignes verticales est situé au-dessous de la ligne
3.3 Distance horizontale d 1
d’horizon (voir figure 5 et 7.5.1 et 7.5.2).
1)
Cône de vision K 2
1)
Cercle de vision Ks 3
5.4 Méthode par coordonnées
1)
Angle de vision a 2
1)
Ligne de projection Pl 3 La méthode de représentation par coordonnées est
basée sur des proportions simples.
1)
Point de distance DP 13
3.5 Point d’échelle MP 14
Les coordonnées, relatives à la ligne de projection
principale de tous les points essentiels de l’objet à
3.6 Station d’observation Sp 1
représenter, sont relevées par la méthode graphique,
1) Termes définis dans l’ISO 10209-2.
à partir du plan de base et de l’élévation. À partir de
ces points de coordonnées, les coordonnées de
l’image sont obtenues par une méthode de calcul et
entrées à l’échelle. Les points de l’image sont reliés
entre eux pour aboutir à une représentation claire de
5 Méthodes de projection centrale
l’objet à représenter (voir figure 6).
Le mode de projection centrale dépend de la position
de l’objet à représenter par rapport au plan de projec-
tion.
6 Principe
Pour les positions possibles et les méthodes de
projection applicables, voir 5.1 à 5.4.
6.1 Emplacement et position du plan de
projection
5.1 Méthode à un point
La grandeur de l’image d’un objet peut varier par
La méthode de projection à un point est une projec- mouvement parallèle du plan de projection. Si l’objet
est placé devant le plan de projection, la représenta-
tion centrale d’un objet ayant sa face principale paral-
©
ISO ISO 5456-4:1996(F)
tion sera agrandie. L’objet placé derrière le plan de La figure 8 montre le changement de grandeur de
projection aboutira à une image plus petite. La figure 7 l’image en fonction de la méthode de représentation
montre les variations de grandeur de l’image en avec des plans de projection verticaux ou inclinés. b
fonction de la position de l’objet par rapport au plan de est l’angle compris entre le plan de projection et le
projection. plan de base près du centre de projection.
Figure 1 — Modèle de projection de la projection centrale
©
Figure 2 — Cône de vision et angle de vision du modèle de projection de la projection centrale
©
ISO ISO 5456-4:1996(F)
Figure 3 — Modèle de projection avec plan de projection vertical et un objet dans une position spéciale
par rapport au plan de projection
Figure 4 — Modèle de projection avec plan de projection vertical et un objet dans une position particulière
par rapport au plan de projection
©
Figure 5 — Modèle de projection avec plan de projection incliné et un objet dans une position quelconque
par rapport au plan de projection (b > 90°)
©
ISO ISO 5456-4:1996(F)
Figure 6 — Modèle de projection avec plan de projection vertical et un objet dans une position spéciale,
indiquant les longueurs utilisées dans la formule mathématique pour le calcul de la perspective de l’image
b = 90°, b > 90°; b < 90°
1 2
Figure 7 — Emplacement des plans de projection
Figure 8 — Position des plans de projection
©
Un objet peut être représenté en n’étant presque pas
6.2 Cercle de vision et cône de vision
déformé si les lignes de projection mènent à un
Pour obtenir une image pleinement instructive d’un
faisceau de rayons qui n’est pas incliné de plus de 30°
objet sans distorsion périphérique sur le plan de
par rapport à la ligne de projection principale. À cette
projection, l’objet doit être positionné dans un cône de
ouverture d’angle, le cône de vision donne seulement
vision dont l’ouverture ne dépasse pas 60°.
une petite distorsion sur le plan de projection.
Des distorsions périphériques importantes arrivent sur
Il convient que la ligne de projection principale attei-
les images qui se trouvent à l’extérieur du cercle de
gne l’objet à dessiner dans une partie qui est visuel-
vision; l’image n’apparaît pas pleinement instructive,
étant donné que la longueur, l’épaisseur et la hauteur lement importante, de façon que l’objet soit contenu
dans le cône de vision minimal.
ne correspondent pas aux proportions de l’objet (voir
figure 9).
Figure 9 — Objet, contenu dans un cube, à l’intérieur et à l’extérieur du cercle de vision
©
ISO ISO 5456-4:1996(F)
6.3 Distance
7 Principes et méthodes de représentation
Des distances relatives différentes influencent la
7.1 Méthode de percement
grandeur de l’image et son apparence. Si la distance
entre l’objet et le plan de projection est fixe et si le
En utilisant la méthode de percement, les points de
centre de projection et l’objet sont situés de part et
percement de lignes de projection avec le plan de
d’autre du plan de projection, l’accroissement de la
projection sont représentés par plan de base et par
distance (d) entre le centre de projection et le plan de
élévation, et peuvent être déterminés soit par cons-
projection donne des représentations agrandies et
truction, soit par calcul (voir figure 10).
aplaties. Si la distance (d) est fixe et si l’objet et le
centre de projection sont situés de part et d’autre du
plan de projection, l’accroissement de la distance La méthode de percement permet même aux objets
entre l’objet et le plan de projection donne des repré- complexes (formes rondes, hélicoïdes, etc.) d’être
facilement représentés dans la projection centrale.
sentations réduites et aplaties.
Figure 10 — Modèle de projection tourné dans la surface de dessin avec vue de côté
©
parallèles au plan de projection soit situé à l’infini et
7.2 Point de trace — méthodes par point de
que le point de fuite pour les arêtes qui sont perpen-
fuite
diculaires au plan de projection soit le point principal
(voir figure 11).
Avec le point de trace — méthodes par point de fuite,
les contours et les arêtes de l’objet à dessiner sont
7.2.2 Point de trace — méthode par point de fuite B
représentés à partir du plan de base et de l’élévation.
(position particulière de l’objet)
7.2.1 Point de trace — méthode par point de fuite A
Dans la méthode B, les faces horizontales de l’objet
(position spéciale de l’objet)
sont perpendiculaires au plan de projection vertical
(position particulière de l’objet par rapport au plan de
Dans la méthode A, une face verticale de l’objet est
parallèle au plan de projection vertical (position spé- projection), de façon que les lignes soient représen-
ciale de l’objet par rapport au plan de projection), de tées par leur trace sur le plan de projection et par leur
façon que le point de fuite pour les arêtes qui sont point de fuite (voir figure 12).
Figure 11 — Objet, contenu dans un cube (représenté par un trait mixte à deux points et un tiret long),
en position spéciale par rapport au plan de projection conformément à la méthode A
©
ISO ISO 5456-4:1996(F)
Figure 12 — Objet, contenu dans un cube (représenté par un trait mixte à deux points et un tiret long),
en position particulière par rapport au plan de projection conformément à la méthode B
©
tion (position spéciale). Le point de distance est à la
7.3 Méthode par point de distance
même distance du point principal que le centre de
(position spéciale de l’objet)
projection du plan de projection. Toutes lignes hori-
La méthode par point de distance donne la projection
zontales sont inclinées à 45° par rapport au plan de
centrale d’un objet sans plan de base, par placement projection aligné au point de distance. Le point de
d’une grille en perspective. Les contours et arêtes
fuite des lignes de profondeur de la grille est le point
sont parallèles ou perpendiculaires au plan de projec- principal (voir figure 13).
Figure 13 — Objet, contenu dans un cube (représenté par un trait mixte à deux points et un tiret long),
en pos
...
NORME ISO
INTERNATIONALE 5456-4
Première édition
1996-06-15
Corrigée et réimprimée
1998-08-01
Dessins techniques — Méthodes de
projection —
Partie 4:
Projection centrale
Technical drawings — Projection methods —
Part 4: Central projection
A
Numéro de référence
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération
mondiale d'organismes nationaux de normalisation (comités membres de
l'ISO). L'élaboration des Normes internationales est en général confiée aux
comités techniques de l'ISO. Chaque comité membre intéressé par une
étude a le droit de faire partie du comité technique créé à cet effet. Les
organisations internationales, gouvernementales et non gouvernemen-
tales, en liaison avec l'ISO participent également aux travaux. L'ISO colla-
bore étroitement avec la Commission électrotechnique internationale (CEI)
en ce qui concerne la normalisation électrotechnique.
Les projets de Normes internationales adoptés par les comités techniques
sont soumis aux comités membres pour vote. Leur publication comme
Normes internationales requiert l'approbation de 75 % au moins des
comités membres votants.
La Norme internationale ISO 5456-4 a été élaborée par le comité technique
ISO/TC 10, Dessins techniques, définition de produits et documentation y
relative, sous-comité SC 1, Conventions générales.
L'ISO 5456 comprend les parties suivantes, présentées sous le titre
général Dessins techniques — Méthodes de projection:
— Partie 1: Récapitulatif
— Partie 2: Représentations orthographiques
— Partie 3: Représentations axonométriques
— Partie 4: Projection centrale
Les annexes A et B de la présente partie de l’ISO 5456 sont données
uniquement à titre d’information.
© ISO 1996
Droits de reproduction réservés. Sauf prescription différente, aucune partie de cette publi-
cation ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun pro-
cédé, électronique ou mécanique, y compris la photocopie et les microfilms, sans l'accord
écrit de l'éditeur.
Organisation internationale de normalisation
Case postale 56 • CH-1211 Genève 20 • Suisse
Internet iso@iso.ch
Imprimé en Suisse
ii
©
ISO ISO 5456-4:1996(F)
Introduction
La projection centrale (perspective) est une représentation imagée réaliste
obtenue par projection de l’objet à représenter, à partir d’un point placé à
une distance définie (centre de projection), sur un plan de projection uni-
que (normalement la surface de dessin). Ce type de projection permet
d’obtenir la meilleure visualisation de l’objet (vision monoculaire) et il est
fréquemment utilisé dans les dessins d’architecture.
iii
©
NORME INTERNATIONALE ISO ISO 5456-4:1996(F)
Dessins techniques — Méthodes de projection —
Partie 4:
Projection centrale
3.1 ligne d’alignement: Ligne parallèle à une ligne
1 Domaine d'application
donnée passant par le centre de projection. Son
La présente partie de l’ISO 5456 prescrit des règles
intersection avec le plan de projection donne le point
de base pour le développement et l’application de la de fuite de toutes les lignes parallèles à la ligne don-
projection centrale dans les dessins techniques.
née.
2 Référence normative
3.2 hauteur de projection: Distance verticale du
centre de projection au plan de base.
La norme suivante contient des dispositions qui, par
suite de la référence qui en est faite, constituent des
dispositions valables pour la présente partie de
l'ISO 5456. Au moment de la publication, l'édition indi-
3.3 distance horizontale: Distance entre le centre
quée était en vigueur. Toute norme est sujette à révi-
de projection et le plan de projection.
sion et les parties prenantes des accords fondés sur
la présente partie de l'ISO 5456 sont invitées à re-
chercher la possibilité d'appliquer l'édition la plus
3.4 angle de projection: Angle formé par le plan de
récente de la norme indiquée ci-après. Les membres
projection et le plan d’horizon.
de la CEI et de l'ISO possèdent le registre des Nor-
mes internationales en vigueur à un moment donné.
ISO 10209-2:1993, Documentation technique de pro-
3.5 point d’échelle: Point de fuite de la direction
duit — Vocabulaire — Partie 2: Termes relatifs aux
horizontale orthogonale à celle qui partage l’angle
méthodes de projection.
formé par la ligne d’horizon et la ligne d’alignement de
la ligne horizontale donnée, et permettant de trouver
la vraie longueur de la projection de la ligne donnée.
3 Définitions
Pour les besoins de la présente partie de l’ISO 5456,
3.6 station d’observation: Projection orthogonale
les définitions données dans l’ISO 10209-2 et les
définitions suivantes s'appliquent. du centre de projection sur le plan de base.
©
lèle au plan de projection (position spéciale). Tous les
4 Symboles
contours et arêtes parallèles de l’objet qui sont parallè-
les au plan de projection conservent leur direction
Les symboles utilisés pour les termes définissant la
dans cette représentation (les lignes horizontales
projection centrale sont donnés dans le tableau 1 et
restent horizontales et les lignes verticales restent
illustrés dans les figures 1 et 2, ainsi que dans les
verticales). Toutes les lignes perpendiculaires au plan
figures mentionnées dans ce tableau.
de projection convergent vers le point de fuite, V,
coïncidant avec le point principal, C, (voir figure 3 et
7.2.1 et 7.3).
Tableau 1 — Symboles
o
N Terme Symbole Figure
5.2 Méthode à deux points
1)
Plan de projection T 1
La méthode de projection à deux points est une
1)
Plan de base G 1
projection centrale d’un objet ayant ses contours et
1)
Ligne de base X 1
arêtes verticaux parallèles au plan de projection
(position particulière). Toutes les lignes horizontales
3.4 Angle de projection b 5
d’une représentation convergent vers les multiples
1)
Plan d’horizon HT 1
points de fuite V , V , V , ., sur la ligne d’horizon (voir
1 2 3
1)
figure 4 et 7.2.2 et 7.4).
Ligne d’horizon h 1
3.1 Ligne d’alignement Vl 4
1)
Point principal C 1
5.3 Méthode à trois points
1)
Point de fuite V 4
La méthode de projection à trois points est une pro-
1)
Ligne de projection
jection centrale d’un objet qui n’a aucun contour ou
principale pL 1
arête parallèle au plan de projection (toute position). Si
1)
Centre de projection O 1
le plan de projection est incliné vers le centre de
projection, c’est-à-dire b > 90°, le point de fuite pour
3.2 Hauteur de projection H 1
les lignes verticales est situé au-dessous de la ligne
3.3 Distance horizontale d 1
d’horizon (voir figure 5 et 7.5.1 et 7.5.2).
1)
Cône de vision K 2
1)
Cercle de vision Ks 3
5.4 Méthode par coordonnées
1)
Angle de vision a 2
1)
Ligne de projection Pl 3 La méthode de représentation par coordonnées est
basée sur des proportions simples.
1)
Point de distance DP 13
3.5 Point d’échelle MP 14
Les coordonnées, relatives à la ligne de projection
principale de tous les points essentiels de l’objet à
3.6 Station d’observation Sp 1
représenter, sont relevées par la méthode graphique,
1) Termes définis dans l’ISO 10209-2.
à partir du plan de base et de l’élévation. À partir de
ces points de coordonnées, les coordonnées de
l’image sont obtenues par une méthode de calcul et
entrées à l’échelle. Les points de l’image sont reliés
entre eux pour aboutir à une représentation claire de
5 Méthodes de projection centrale
l’objet à représenter (voir figure 6).
Le mode de projection centrale dépend de la position
de l’objet à représenter par rapport au plan de projec-
tion.
6 Principe
Pour les positions possibles et les méthodes de
projection applicables, voir 5.1 à 5.4.
6.1 Emplacement et position du plan de
projection
5.1 Méthode à un point
La grandeur de l’image d’un objet peut varier par
La méthode de projection à un point est une projec- mouvement parallèle du plan de projection. Si l’objet
est placé devant le plan de projection, la représenta-
tion centrale d’un objet ayant sa face principale paral-
©
ISO ISO 5456-4:1996(F)
tion sera agrandie. L’objet placé derrière le plan de La figure 8 montre le changement de grandeur de
projection aboutira à une image plus petite. La figure 7 l’image en fonction de la méthode de représentation
montre les variations de grandeur de l’image en avec des plans de projection verticaux ou inclinés. b
fonction de la position de l’objet par rapport au plan de est l’angle compris entre le plan de projection et le
projection. plan de base près du centre de projection.
Figure 1 — Modèle de projection de la projection centrale
©
Figure 2 — Cône de vision et angle de vision du modèle de projection de la projection centrale
©
ISO ISO 5456-4:1996(F)
Figure 3 — Modèle de projection avec plan de projection vertical et un objet dans une position spéciale
par rapport au plan de projection
Figure 4 — Modèle de projection avec plan de projection vertical et un objet dans une position particulière
par rapport au plan de projection
©
Figure 5 — Modèle de projection avec plan de projection incliné et un objet dans une position quelconque
par rapport au plan de projection (b > 90°)
©
ISO ISO 5456-4:1996(F)
Figure 6 — Modèle de projection avec plan de projection vertical et un objet dans une position spéciale,
indiquant les longueurs utilisées dans la formule mathématique pour le calcul de la perspective de l’image
b = 90°, b > 90°; b < 90°
1 2
Figure 7 — Emplacement des plans de projection
Figure 8 — Position des plans de projection
©
Un objet peut être représenté en n’étant presque pas
6.2 Cercle de vision et cône de vision
déformé si les lignes de projection mènent à un
Pour obtenir une image pleinement instructive d’un
faisceau de rayons qui n’est pas incliné de plus de 30°
objet sans distorsion périphérique sur le plan de
par rapport à la ligne de projection principale. À cette
projection, l’objet doit être positionné dans un cône de
ouverture d’angle, le cône de vision donne seulement
vision dont l’ouverture ne dépasse pas 60°.
une petite distorsion sur le plan de projection.
Des distorsions périphériques importantes arrivent sur
Il convient que la ligne de projection principale attei-
les images qui se trouvent à l’extérieur du cercle de
gne l’objet à dessiner dans une partie qui est visuel-
vision; l’image n’apparaît pas pleinement instructive,
étant donné que la longueur, l’épaisseur et la hauteur lement importante, de façon que l’objet soit contenu
dans le cône de vision minimal.
ne correspondent pas aux proportions de l’objet (voir
figure 9).
Figure 9 — Objet, contenu dans un cube, à l’intérieur et à l’extérieur du cercle de vision
©
ISO ISO 5456-4:1996(F)
6.3 Distance
7 Principes et méthodes de représentation
Des distances relatives différentes influencent la
7.1 Méthode de percement
grandeur de l’image et son apparence. Si la distance
entre l’objet et le plan de projection est fixe et si le
En utilisant la méthode de percement, les points de
centre de projection et l’objet sont situés de part et
percement de lignes de projection avec le plan de
d’autre du plan de projection, l’accroissement de la
projection sont représentés par plan de base et par
distance (d) entre le centre de projection et le plan de
élévation, et peuvent être déterminés soit par cons-
projection donne des représentations agrandies et
truction, soit par calcul (voir figure 10).
aplaties. Si la distance (d) est fixe et si l’objet et le
centre de projection sont situés de part et d’autre du
plan de projection, l’accroissement de la distance La méthode de percement permet même aux objets
entre l’objet et le plan de projection donne des repré- complexes (formes rondes, hélicoïdes, etc.) d’être
facilement représentés dans la projection centrale.
sentations réduites et aplaties.
Figure 10 — Modèle de projection tourné dans la surface de dessin avec vue de côté
©
parallèles au plan de projection soit situé à l’infini et
7.2 Point de trace — méthodes par point de
que le point de fuite pour les arêtes qui sont perpen-
fuite
diculaires au plan de projection soit le point principal
(voir figure 11).
Avec le point de trace — méthodes par point de fuite,
les contours et les arêtes de l’objet à dessiner sont
7.2.2 Point de trace — méthode par point de fuite B
représentés à partir du plan de base et de l’élévation.
(position particulière de l’objet)
7.2.1 Point de trace — méthode par point de fuite A
Dans la méthode B, les faces horizontales de l’objet
(position spéciale de l’objet)
sont perpendiculaires au plan de projection vertical
(position particulière de l’objet par rapport au plan de
Dans la méthode A, une face verticale de l’objet est
parallèle au plan de projection vertical (position spé- projection), de façon que les lignes soient représen-
ciale de l’objet par rapport au plan de projection), de tées par leur trace sur le plan de projection et par leur
façon que le point de fuite pour les arêtes qui sont point de fuite (voir figure 12).
Figure 11 — Objet, contenu dans un cube (représenté par un trait mixte à deux points et un tiret long),
en position spéciale par rapport au plan de projection conformément à la méthode A
©
ISO ISO 5456-4:1996(F)
Figure 12 — Objet, contenu dans un cube (représenté par un trait mixte à deux points et un tiret long),
en position particulière par rapport au plan de projection conformément à la méthode B
©
tion (position spéciale). Le point de distance est à la
7.3 Méthode par point de distance
même distance du point principal que le centre de
(position spéciale de l’objet)
projection du plan de projection. Toutes lignes hori-
La méthode par point de distance donne la projection
zontales sont inclinées à 45° par rapport au plan de
centrale d’un objet sans plan de base, par placement projection aligné au point de distance. Le point de
d’une grille en perspective. Les contours et arêtes
fuite des lignes de profondeur de la grille est le point
sont parallèles ou perpendiculaires au plan de projec- principal (voir figure 13).
Figure 13 — Objet, contenu dans un cube (représenté par un trait mixte à deux points et un tiret long),
en pos
...
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