Graphical projection
Encyclopedia
Graphical projection is a protocol by which an image of a three-dimensional
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...

 object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing
Technical drawing
Technical drawing, also known as drafting or draughting, is the act and discipline of composing plans that visually communicate how something functions or has to be constructed.Drafting is the language of industry....

.

Overview

The projection is achieved by the use of imaginary "projectors". The projected, mental image becomes the technician’s 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
    Parallel projection
    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 , or "zoom".Within parallel projection there is an ancillary category known as "pictorials"...

  • perspective projection
    Perspective (graphical)
    Perspective in the graphic arts, such as drawing, is an approximate representation, on a flat surface , of an image as it is seen by the eye...


Types of projection

Parallel projection

In parallel projection
Parallel projection
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 , or "zoom".Within parallel projection there is an ancillary category known as "pictorials"...

, the lines of sight from the object to the projection plane are parallel to each other. 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

The 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 two-dimensional representation of a three-dimensional object. It is a parallel projection (the lines of projection are parallel both in reality and in 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 :...

.
Axonometric projection


Within parallel projection there is a subcategory 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. Parallel projection pictorial instrument drawings are often used to approximate graphical perspective projections, but there is attendant distortion in the approximation. Because pictorial projections inherently have this distortion, in the instrument drawing of pictorials, great liberties may then be taken for economy of effort and best effect. Parallel projection pictorials rely on the technique of axonometric projection ("to measure along axes").
Isometric projection

In isometric pictorials (for protocols see isometric projection
Isometric projection
Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings...

), 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.
Oblique projection

In oblique projection
Oblique 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.

Perspective projection

Perspective projection
Perspective (graphical)
Perspective in the graphic arts, such as drawing, is an approximate representation, on a flat surface , of an image as it is seen by the eye...

 is a type of projection where three dimensional objects are not projected along parallel lines, but along lines emerging from a single point. This has the effect that distant objects appear smaller than nearer objects.

It also means that lines which are parallel in nature appear to intersect in the projected image, for example if railways are pictured with perspective projection, they appear to converge towards a single point, called vanishing point
Vanishing point
A vanishing point is a point in a perspective drawing to which parallel lines not parallel to the image plane appear to converge. The number and placement of the vanishing points determines which perspective technique is being used...

. Photographic lenses and the human eye work in the same way, therefore perspective projection looks most realistic.

Perspective projection is usually categorized into one-point, two-point and three-point perspective, depending on the orientation of the projection plane towards the axes of the depicted object.

See also

  • Curvilinear perspective
    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 André Barre and Albert Flocon in the book La Perspective curviligne, which was translated into English in 1987 as Curvilinear Perspective:...

    ,
  • Engineering drawing
    Engineering drawing
    An engineering drawing, a type of technical drawing, is used to fully and clearly define requirements for engineered items.Engineering drawing produces engineering drawings . More than just the drawing of pictures, it is also a language—a graphical language that communicates ideas and information...

    ,
  • 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...

    ,
  • Map projection
    Map projection
    A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...

     (including Cylindrical projection),

  • Multiview orthographic projection
    Multiview orthographic projection
    With multiview orthographic projections, up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes of the object....

    ,
  • Plans (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 :...

    ,
  • Technical drawing
    Technical drawing
    Technical drawing, also known as drafting or draughting, is the act and discipline of composing plans that visually communicate how something functions or has to be constructed.Drafting is the language of industry....

    .
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