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