TECHNICAL SEMINAR REPORT
Submitted by
BOJA RAJU.T In partial fulfillment for the award of the
degree
of
BACHELOR OF ENGINEERING
IN
MECHANICAL ENGINEERING
SRI KRISHNA COLLEGE OF ENGINEERING AND
TECHNOLOGY
Kuniamuthur, Coimbatore.ANNA UNIVERSITY: COIMBATORE
OCTOBER 2011
ANNA UNIVERSITY: COIMBATORE
BONAFIDE CERIFICATE
Certified that this technical seminar report GRAPHICAL
PROJECTION AND ITS VARITIES is the bonafide work of BOJA RAJU.T
(090411123001) carried out the technical seminar under my
supervision.
Mr. Ashoka varathanan
Mr. R. Ramamoorthiprofessor
Assistant professor
Technical staff
Coordinator
Dr. A. Ramesh
Head of the department
Mechanical Engineering
INDEX
S.NOTITLEPAGE NO.
1ABSTRACT4
2GRAPHICAL PROJECTIONS5
3CLASSIFICATION5
4AXONOMETRIC PROJECTIONS7
5TYPES OF ANONOMETRIC9
6LIMITATIONS OF AXNOMETRIC10
7OBLIQUE PROJECTIONS11
8CAVALIER PROJECTIONS13
9CABINET PROJECTIONS13
10PERSPECTIVE PROJECTION15
11TYPES OF PRSPRCTIVE17
11CURVILINEAR PROJECTION23
12REVERSE PROJECTION25
13REFERENCES27
ABSTRACT:
The projection is achieved by the use of imaginary "projectors".
The projected, mental image becomes the technicians vision of the
desired, finished picture. By following the protocol the technician
may produce the envisioned picture on a planar surface such as
drawing paper. The protocols provide a uniform imaging procedure
among people trained in technical graphics (mechanical drawing,
computer aided design, etc.).
There are two types of graphical projection, categories each
with its own protocol:
parallel projection perspective projection
Isometric projection.
Oblique projection.
One-point GRAPHICAL PROJECTIONS:
Projection isthe representation of a line, figure, or solid on a
given plane as it would be seen from a particular direction or in
accordance with an accepted set of rules a.the process of showing
film on a screen b.the image or images shown Common projections
are
Orthographic projections.
&
Isometric projections.
Both these comes under parallel projections. CLASSIFICATION:
Parallel projection Orthographic projection Multiviews Plan, or
floor plan Section Elevation Auxiliary Axonometric projection (i.e.
pictorials) Isometric projection Dimetric projection Trimetric
projection Oblique projection Cavalier projection Cabinet
projection.Perspective projection I. Linear perspective One-point
perspective Two-point perspective Three-point perspective
Zero-point perspective Curvilinear perspective Reverse perspective
OTHER PROJECTIONS:
3D projection Stereographic projection Anamorphic
projectionAXONOMETRIC PROJECTIONS:
Axonometric projection is a type of parallel projection, more
specifically a type of orthographic projection, used to create a
pictorial drawing of an object, where the object is rotated along
one or more of its axes relative to the plane of projection.
There are three main types of axonometric projection: isometric,
dimetric, and trimetric projection.
"Axonometric" means "to measure along axes". Axonometric
projection shows an image of an object as viewed from a skew
direction in order to reveal more than one side in the same
picture.Whereas the term orthographic is sometimes reserved
specifically for depictions of objects where the axis or plane of
the object is parallel with the projection plane, in axonometric
projection the plane or axis of the object is always drawn not
parallel to the projection plane.
With axonometric projections the scale of distant features is
the same as for near features, such pictures will look distorted,
as it is not how our eyes or photography work. This distortion is
especially evident if the object to view is mostly composed of
rectangular features. Despite this limitation, axonometric
projection can be useful for purposes of illustration.
Optical-grinding engine model (1822), drawn in 30 isometric
perspective.
Trimetric projection of the design of the Time Pyramid in
Wemding, Germany
Three types of axonometric projections
The three types of axonometric projections are isometric
projection, dimetric projection, and trimetric projection,
depending on the exact angle at which the view deviates from the
orthogonal. Typically in axonometric drawing, one axis of space is
shown as the vertical.
In isometric projection, the most commonly-used form of
axonometric projection in engineering drawing,[9] the direction of
viewing is such that the three axes of space appear equally
foreshortened, of which the displayed angles among them and also
the scale of foreshortening are universally known. However in
creating a final, isometric instrument drawing, in most cases a
full-size scale, i.e., without using a foreshortening factor, is
employed to good effect because the resultant distortion is
difficult to perceive. Another advantage is that, in engineering
drawings, 60 angles are easier to construct using only a compass
and straightedge.
In dimetric projection, the direction of viewing is such that
two of the three axes of space appear equally foreshortened, of
which the attendant scale and angles of presentation are determined
according to the angle of viewing; the scale of the third direction
(vertical) is determined separately.
In trimetric projection, the direction of viewing is such that
all of the three axes of space appear unequally foreshortened. The
scale along each of the three axes and the angles among them are
determined separately as dictated by the angle of viewing.
Trimetric perspective is seldom used,[8] though it is found in some
video games (Fallout,[10] SimCity 4[11]).
Approximations are common in dimetric and trimetric
drawings.Limitations of axonometric projection
As with all types of parallel projection, objects drawn with
axonometric projection do not appear larger or smaller as they
extend closer to or away from the viewer. While advantageous for
architectural drawings, where measurements must be taken directly
from the image, the result is a perceived distortion, since unlike
perspective projection, this is not how our eyes or photography
normally work. It also can easily result in situations where depth
and altitude are difficult to gauge, as is shown in the
illustration to the right.
Drawing illustrating the limitations of axonometric
projection
In this isometric drawing, the blue sphere is two units higher
than the red one. However, this difference in elevation is not
apparent if one covers the right half of the picture, as the boxes
(which serve as clues suggesting height) are then obscured.
This visual ambiguity has been exploited in op art, including
"impossible object" drawings. M. C. Escher's Waterfall (1961) is a
well-known example, in which a channel of water seems to travel
unaided along a downward path, only to then paradoxically fall once
again as it returns to its source. The water thus appears to
disobey the law of conservation of energy.
OBLIQUE PROJECTIONS:
Oblique projection is a simple type of graphical projection used
for producing pictorial, two-dimensional images of
three-dimensional objects.
Overview:
Oblique projection is a type of parallel projection:
it projects an image by intersecting parallel rays
(projectors)
From the three-dimensional source object with the drawing
surface (projection plane).
In both oblique projection and orthographic projection, parallel
lines of the source object produce parallel lines in the projected
image. The projectors in oblique projection intersect the
projection plane at an oblique angle to produce the projected
image, as opposed to the perpendicular angle used in orthographic
projection.
Oblique drawing is also the crudest "3D" drawing method but the
easiest to master. Oblique is not really a 3D system but a 2
dimensional view of an object with 'forced depth'. One way to draw
using an oblique view is to draw the side of the object you are
looking at in two dimensions, i.e. flat, and then draw the other
sides at an angle of 45 degrees, but instead of drawing the sides
full size they are only drawn with half the depth creating 'forced
depth' - adding an element of realism to the object. Even with this
'forced depth', oblique drawings look very unconvincing to the eye.
For this reason oblique is rarely used by professional designers
and engineers.Oblique pictorial:In an oblique pictorial drawing,
the angles displayed among the axes, as well as the foreshortening
factors (scale) are arbitrary. More precisely, any given set of
three coplanar segments originating from the same point may be
construed as forming some oblique perspective of three sides of a
cube. This result is known as Pohlke's theorem, from the German
mathematician Pohlke, who published it in the early 19th
century.
The resulting distortions make the technique unsuitable for
formal, working drawings. Nevertheless, the distortions are
partially overcome by aligning one plane of the image parallel to
the plane of projection. Doing so creates a true shape image of the
chosen plane. This specific category of oblique projections,
whereby lengths along the directions x and y are preserved, but
lengths along direction z are drawn at angle using a reduction
factor is very much in use for industrial drawings.
Cavalier projection is the name of such a projection, where the
length along the z axis remains unscaled.
Cabinet projection, popular in furniture illustrations, is an
example of such a technique, wherein the receding axis is scaled to
half-size (sometimes also two thirds the original).Cavalier
projections:In cavalier projection (sometimes cavalier perspective
or high view point) a point of the object is represented by three
coordinates, x, y and z. On the drawing, it is represented by only
two coordinates, x" and y". On the flat drawing, two axes, x and z
on the figure, are perpendicular and the length on these axes are
drawn with a 1:1 scale; it is thus similar to the dimetric
projections, although it is not an orthographic projection, as the
third axis, here y, is drawn in diagonal, making an arbitrary angle
with the x" axis, usually 30 or 45. The length of the third axis is
not scaled.
It is very easy to draw, especially with pen and paper. It is
thus often used when a figure must be drawn by hand, e.g. on a
black board (lesson, oral examination).
The representation was initially used for military
fortifications. In French, the cavalier (literally rider, horseman,
see Cavalry) is an artificial hill behind the walls that allows to
see the enemy above the walls. The cavalier perspective was the way
the things were seen from this high point. Some also explain the
name by the fact that it was the way a rider could see a small
object on the ground from his horseback.
Cabinet projection:The term cabinet projection (sometimes
cabinet perspective) stems from its use in illustrations by the
furniture industry. Like cavalier perspective, one face of the
projected object is parallel to the viewing plane, and the third
axis is projected as going off in an angle (typical 30 or 45).
Unlike cavalier projection, where the third axis keeps its length,
with cabinet projection the length of the receding lines is cut in
half.Examples:Besides technical drawing and illustrations, video
games (especially those preceding the advent of 3D games) also
often use a form of oblique projection. Examples include SimCity,
Ultima VII, EarthBound, and Paperboy.
The figures to the left are orthographic projections. The figure
to the right is an oblique projection with an angle of 30 and a
ratio of 0.5.
Potting bench drawn in cabinet projection: an oblique projection
with an angle of 30 and a ratio of 0.5.
Pieces of fortification in cavalier perspective (Cyclopaedia
vol. 1, 1728).
PERSPECTIVE PROJECTIONS:
Perspective in the graphic arts, such as drawing, is an
approximate representation, on a flat surface (such as paper), of
an image as it is seen by the eye. The two most characteristic
features of perspective are that objects are drawn:
Smaller as their distance from the observer increases
Foreshortened: the size of an object's dimensions along the line
of sight are relatively shorter than dimensions across the line of
sight
OVERVIEW:
Linear perspective works by representing the light that passes
from a scene through an imaginary rectangle (the painting), to the
viewer's eye. It is similar to a viewer looking through a window
and painting what is seen directly onto the windowpane. If viewed
from the same spot as the windowpane was painted, the painted image
would be identical to what was seen through the unpainted window.
Each painted object in the scene is a flat, scaled down version of
the object on the other side of the window. Because each portion of
the painted object lies on the straight line from the viewer's eye
to the equivalent portion of the real object it represents, the
viewer cannot perceive (sans depth perception) any difference
between the painted scene on the windowpane and the view of the
real scene. All perspective drawings assume the viewer is a certain
distance away from the drawing. Objects are scaled relative to that
viewer. Additionally, an object is often not scaled evenly: a
circle often appears as an ellipse and a square can appear as a
trapezoid. This distortion is referred to as foreshortening.
A cube in two-point perspective
Perspective drawings typically have an -often implied- horizon
line. This line, directly opposite the viewer's eye, represents
objects infinitely far away. They have shrunk, in the distance, to
the infinitesimal thickness of a line. It is analogous to (and
named after) the Earth's horizon.
Any perspective representation of a scene that includes parallel
lines has one or more vanishing points in a perspective drawing. A
one-point perspective drawing means that the drawing has a single
vanishing point, usually (though not necessarily) directly opposite
the viewer's eye and usually (though not necessarily) on the
horizon line. All lines parallel with the viewer's line of sight
recede to the horizon towards this vanishing point. This is the
standard "receding railroad tracks" phenomenon. A two-point drawing
would have lines parallel to two different angles. Any number of
vanishing points is possible in a drawing, one for each set of
parallel lines that are at an angle relative to the plane of the
drawing.In contrast, natural scenes often do not have any sets of
parallel lines. Such a perspective would thus have no vanishing
points.
Types of perspective:Of the many types of perspective drawings,
the most common categorizations of artificial perspective are one-,
two- and three-point. The names of these categories refer to the
number of vanishing points in the perspective drawing.
One-point perspective:
One vanishing point is typically used for roads, railway tracks,
hallways, or buildings viewed so that the front is directly facing
the viewer. Any objects that are made up of lines either directly
parallel with the viewer's line of sight or directly perpendicular
(the railroad slats) can be represented with one-point
perspective.
One-point perspective exists when the painting plate (also known
as the picture plane) is parallel to two axes of a rectilinear (or
Cartesian) scene a scene which is composed entirely of linear
elements that intersect only at right angles. If one axis is
parallel with the picture plane, then all elements are either
parallel to the painting plate (either horizontally or vertically)
or perpendicular to it. All elements that are parallel to the
painting plate are drawn as parallel lines. All elements that are
perpendicular to the painting plate converge at a single point (a
vanishing point) on the horizon.
Some examples:
Two-point perspective
Walls in 2-pt perspective.
Two-point perspective can be used to draw the same objects as
one-point perspective, rotated: looking at the corner of a house,
or looking at two forked roads shrink into the distance, for
example. One point represents one set of parallel lines, the other
point represents the other. Looking at a house from the corner, one
wall would recede towards one vanishing point, the other wall would
recede towards the opposite vanishing point.
Two-point perspective exists when the painting plate is parallel
to a Cartesian scene in one axis (usually the z-axis) but not to
the other two axes. If the scene being viewed consists solely of a
cylinder sitting on a horizontal plane, no difference exists in the
image of the cylinder between a one-point and two-point
perspective.
Two-point perspective has one set of lines parallel to the
picture plane and two sets oblique to it. Parallel lines oblique to
the picture plane converge to a vanishing point,which means that
this set-up will require two vanishing points.Three-point
perspective
Three-point perspective rendered from computer model
Three-point perspective is usually used for buildings seen from
above (or below). In addition to the two vanishing points from
before, one for each wall, there is now one for how those walls
recede into the ground. This third vanishing point will be below
the ground. Looking up at a tall building is another common example
of the third vanishing point. This time the third vanishing point
is high in space.
Three-point perspective exists when the perspective is a view of
a Cartesian scene where the picture plane is not parallel to any of
the scene's three axes. Each of the three vanishing points
corresponds with one of the three axes of the scene. Image
constructed using multiple vanishing points.One-point, two-point,
and three-point perspectives appear to embody different forms of
calculated perspective. The methods required to generate these
perspectives by hand are different. Mathematically, however, all
three are identical: The difference is simply in the relative
orientation of the rectilinear scene to the viewer.
Four-point perspective:Four-point perspective, also called
infinite-point perspective, is the curvilinear variant of two-point
perspective. As the result when made into an infinite point version
(i.e. when the amount of vanishing points exceeds the minimum
amount required), a four point perspective image becomes a panorama
that can go to a 360 degree view and beyond - when going beyond the
360 degree view the artist might depict an "impossible" room as the
artist might depict something new when it's supposed to show part
of what already exists within those 360 degrees. This elongated
frame can be used both horizontally and vertically and when used
vertically can be described as an image that depicts both a worm's-
and bird's-eye view of a scene at the same time.
As all other foreshortened variants of perspective (respectively
one- to six-point perspective), it starts off with a horizon line,
followed by four equally spaced vanishing points to delineate four
vertical lines created in a 90 degree relation to the horizon
line.The vanishing points made to create the curvilinear
orthogonals are thus made ad hoc on the four vertical lines placed
on the opposite side of the horizon line. The only dimension not
foreshortened in this type of perspective being the rectilinear and
parallel lines at a 90 degree angle to the horizon line - similar
to the vertical lines used in two-point perspective.
Zero-point perspective:Because vanishing points exist only when
parallel lines are present in the scene, a perspective without any
vanishing points ("zero-point" perspective) occurs if the viewer is
observing a nonlinear scene. The most common example of a nonlinear
scene is a natural scene (e.g., a mountain range) which frequently
does not contain any parallel lines. A perspective without
vanishing points can still create a sense of "depth," as is clearly
apparent in a photograph of a mountain range (more distant
mountains have smaller scale features).
Other varieties of linear perspective:One-point, two-point, and
three-point perspective are dependent on the structure of the scene
being viewed. These only exist for strict Cartesian (rectilinear)
scenes. By inserting into a Cartesian scene a set of parallel lines
that are not parallel to any of the three axes of the scene, a new
distinct vanishing point is created. Therefore, it is possible to
have an infinite-point perspective if the scene being viewed is not
a Cartesian scene but instead consists of infinite pairs of
parallel lines, where each pair is not parallel to any other
pair.
A: No perspective foreshortening, and B: Perspective
foreshortening
Foreshortening:Foreshortening refers to the visual effect or
optical illusion that an object or distance appears shorter than it
actually is because it is angled toward the viewer.
Although foreshortening is an important element in art where
visual perspective is being depicted, foreshortening occurs in
other types of two-dimensional representations of three-dimensional
scenes. Some other types where foreshortening can occur include
oblique parallel projection drawings.
Figure F1 shows two different projections of a stack of two
cubes, illustrating oblique parallel projection foreshortening
("A") and perspective foreshortening ("B").
Foreshortening also occurs when imaging rugged terrain using
Synthetic Aperture Radar systems.
This technique was often used in Renaissance
painting.CURVILINEAR PERSPECTIVE:
Curvilinear perspective is a graphical projection used to draw
3D objects on 2D surfaces. It was formally codified in 1968 by the
artists and art historians Andr Barre and Albert Flocon in the book
La Perspective curviligne,[1] which was translated into English in
1987 as Curvilinear Perspective: From Visual Space to the
Constructed Image and published by the University of California
Press.[2]Horizon and vanishing points:A comparison of the same
object displayed, on the left using a curvilinear perspective and
on the right, using a vanishing point
Curvilinearity in photography:
The system uses curving perspective lines instead of straight
converging ones to approximate the image on the retina of the eye,
which is itself spherical, more accurately than the traditional
linear perspective, which uses straight lines and gets very
strangely distorted at the edges.
It uses either four or five vanishing points:
In five-point (fisheye) perspective: Four vanishing points are
placed around in a circle, they are named N, W, S, E, and one
vanishing point in the center of the circle.
Four, or infinite-point perspective is the one that (arguably)
most approximates the perspective of the human eye, while at the
same time being effective for making impossible spaces, while five
point is the curvilinear equivalent of one point perspective, so is
four point the equivalent of two point perspective.
This technique can, like two-point perspective, use a vertical
line as a horizon line, creating both a worms and birds eye view at
the same time. It uses four or more points equally spaced along an
horizon line, all vertical lines are made perpendicular to the
horizon line, while orthogonals are created using a compass set on
a line made at a 90-degree angle through each of the four vanishing
points.Reverse perspective:Reverse perspective, also called inverse
perspective, inverted perspective or Byzantine perspective, is a
convention of perspective drawing where the further the objects
are, the larger they are drawn. The lines diverge against the
horizon, rather than converge as in linear perspective.
Technically, the vanishing points are placed outside the painting
with the illusion that they are "in front of" the painting.
The name Byzantine perspective comes from the use of this
perspective in Byzantine and Russian Orthodox icons; it is also
found in East Asian art, and was sometimes used in Cubism and other
movements of modern art. The reasons for the convention are still
debated among art historians; since the artists concerned in
forming the convention did not have access to the more realistic
linear perspective convention it is not clear how deliberate the
effects achieved were. The scheme shows the image content as
opening up and expanding, increasing the viewer's sense of awe. One
interpretation is that as the vanishing point of the perspective
scheme is near the viewer, it shows God looking upon him, rather
than the viewer looking upon God.[citation needed] It displays the
spiritual rather than the physical reality.
An alternative interpretation would be that as God is
omnipresent, his view converges from everywhere, rather than
scanning out from a point. According to this interpretation, the
reverse perspective would be imitative of the conception and/or
sensorium of God.
A practical effect of reverse perspective is that since our
vision has its greatest acuity at the focus, a visual
representation which enlarges things which are not at the center
will tend to even out the lack of discernment of detail, thus
aiding in the envisionment of the image as a gestalt.REFERENCES:
Engineering drawing by, Maurice Arthur Parker, F. Pickup
Geometric and Engineering Drawing by, K. Morling
www.wikipedia.com www.youtube.com24