Parallel projection
Encyclopedia
Parallel projections have lines of projection that are parallel both in reality and in the projection plane.
Parallel projection corresponds to a perspective projection with an infinite focal length
(the distance from the image plane to the projection point), or "zoom
".
Within parallel projection there is an ancillary category known as "pictorials". Pictorials show an image of an object as viewed from a skew direction in order to reveal all three directions (axes) of space in one picture. Because pictorial projections innately contain this distortion, in the rote, drawing instrument for pictorials, some liberties may be taken for economy of effort and best effect.
The orthographic projection
is derived from the principles of descriptive geometry
, and is a type of parallel projection where the projection rays are perpendicular to the projection plane. It is the projection type of choice for working drawings
.
The term orthographic is also sometimes reserved specifically for depictions of objects where the axis or plane of the object is also parallel with the projection plane.
is a type of orthographic projection where the plane or axis of the object depicted is not parallel to the projection plane, such that multiple sides of an object are visible in the same image. It is further subdivided into three groups: isometric, dimetric and trimetric projection, depending on the exact angle at which the view deviates from the orthogonal. A typical characteristic of axonometric pictorials is that one axis of space is usually displayed as vertical.
), the most common form of axonometric projection, 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.
s the parallel projection rays are not perpendicular to the viewing plane as with orthographic projection, but strike the projection plane at an angle other than ninety degrees. In both orthographic and oblique projection, parallel lines in space appear parallel on the projected image. Because of its simplicity, oblique projection is used exclusively for pictorial purposes rather than for formal, working drawings. In an oblique pictorial drawing, the displayed angles among the axes as well as the foreshortening factors (scale) are arbitrary. The distortion created thereby is usually attenuated by aligning one plane of the imaged object to be parallel with the plane of projection thereby creating a true shape, full-size image of the chosen plane. Special types of oblique projections are cavalier projection and cabinet projection.
s, 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.
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 an 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
.
Parallel projection corresponds to a perspective projection with an infinite focal length
Focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...
(the distance from the image plane to the projection point), or "zoom
Zoom lens
A zoom lens is a mechanical assembly of lens elements for which the focal length can be varied, as opposed to a fixed focal length lens...
".
Within parallel projection there is an ancillary category known as "pictorials". Pictorials show an image of an object as viewed from a skew direction in order to reveal all three directions (axes) of space in one picture. Because pictorial projections innately contain this distortion, in the rote, drawing instrument for pictorials, some liberties may be taken for economy of effort and best effect.
Orthographic projection
Orthographic projection
Orthographic projection is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface...
is derived from the principles of descriptive geometry
Descriptive geometry
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art...
, and is a type of parallel projection where the projection rays are perpendicular to the projection plane. It is the projection type of choice for working drawings
Plans (drawings)
Plans are a set of drawings or two-dimensional diagrams used to describe a place or object, or to communicate building or fabrication instructions. Usually plans are drawn or printed on paper, but they can take the form of a digital file.- Overview :...
.
The term orthographic is also sometimes reserved specifically for depictions of objects where the axis or plane of the object is also parallel with the projection plane.
Axonometric projection
Axonometric projectionAxonometric projection
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....
is a type of orthographic projection where the plane or axis of the object depicted is not parallel to the projection plane, such that multiple sides of an object are visible in the same image. It is further subdivided into three groups: isometric, dimetric and trimetric projection, depending on the exact angle at which the view deviates from the orthogonal. A typical characteristic of axonometric pictorials is that one axis of space is usually displayed as vertical.
Isometric projection
In isometric pictorials (for protocols see isometric projectionIsometric projection
Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings...
), the most common form of axonometric projection, 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.
Dimetric projection
In dimetric pictorials (for protocols see 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. Approximations are common in dimetric drawings.Trimetric projection
In trimetric pictorials (for protocols see 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. Approximations in trimetric drawings are common, and trimetric perspective is seldom used.Oblique projection
In oblique projectionOblique projection
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:...
s the parallel projection rays are not perpendicular to the viewing plane as with orthographic projection, but strike the projection plane at an angle other than ninety degrees. In both orthographic and oblique projection, parallel lines in space appear parallel on the projected image. Because of its simplicity, oblique projection is used exclusively for pictorial purposes rather than for formal, working drawings. In an oblique pictorial drawing, the displayed angles among the axes as well as the foreshortening factors (scale) are arbitrary. The distortion created thereby is usually attenuated by aligning one plane of the imaged object to be parallel with the plane of projection thereby creating a true shape, full-size image of the chosen plane. Special types of oblique projections are cavalier projection and cabinet projection.
Limitations
Objects drawn with parallel projection do not appear larger or smaller as they extend closer to or away from the viewer. While advantageous for architectural drawingArchitectural drawing
An architectural drawing or architect's drawing is a technical drawing of a building that falls within the definition of architecture...
s, 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.
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
Op art
Op art, also known as optical art, is a style of visual art that makes use of optical illusions."Optical art is a method of painting concerning the interaction between illusion and picture plane, between understanding and seeing." Op art works are abstract, with many of the better known pieces made...
, including "impossible object" drawings. M. C. Escher
M. C. Escher
Maurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
's Waterfall
Waterfall (M. C. Escher)
Waterfall is a lithography print by the Dutch artist M. C. Escher which was first printed in October, 1961. It shows an apparent paradox where water from the base of a waterfall appears to run downhill before reaching the top of the waterfall....
(1961) is a well-known example, in which a channel of water seems to travel unaided along an 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
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
.