Graphical projection

Views
Graphical projections Planar projection Perspective projection Parallel projection Orthographic projection Multiviews Plan, or floor plan Section Elevation Auxiliary view Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier perspective Cabinet projection 3D projection Fisheye Stereoscopic Projection Anamorphic projection Map projection
Other views Bird's-eye view/Aerial view Top-down perspective Worm's-eye view
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Graphical projection is a protocol by which an image of an imaginary three-dimensional object is projected onto a planar surface without the aid of mathematical calculation. Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three dimensional space to points on a two-dimensional projection plane Perspective (from Latin perspicere to see through in the graphic arts such as drawing is an approximate representation on a flat surface (such as paper of an image as it is perceived Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D A plan is an Orthographic projection of a 3-dimensional object from the position of a horizontal plane through the object A floor plan ( floorplan) in Architecture and Building engineering is a Diagram, usually to scale, of the relationships between rooms In Geometry, a cross section is the intersection of a body in 2-dimensional space with a line or of a body in 3-dimensional space with a plane etc An elevation is an Orthographic projection of a 3-dimensional object from the position of a horizontal plane beside an object An auxiliary view is an angle at which one can view an object that is not one of the primary views for an Orthographic projection. Axonometric projection ("to measure along axes" is a technique used in orthographic pictorials Isometric projection is a form of Graphical projection —more specifically an Axonometric projection. Dimetric projection is a form of Axonometric projection, in which its direction of viewing is such that two of the three axes of space appear equally foreshortened of which Trimetric projection is a form of Axonometric projection, where the direction of viewing is such that all of the three axes of space appear unequally foreshortened This article discusses imaging of three-dimensional objects For an abstract mathematical discussion see Projection (linear algebra. The cavalier perspective, also called cavalier projection or high view point, is a way to represent a three dimensional object on a flat drawing and more specifically Cabinet projection or sometimes cabinet perspective is a type of Oblique projection. 3D projection is any method of mapping three-dimensional points to a two-dimensional plane Owned by Atlassian Software Systems, FishEye is a Revision control browser and search engine Stereoscopy, stereoscopic imaging or 3-D (three-dimensional imaging is any technique capable of recording three-dimensional visual Anamorphosis is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point to reconstitute the image A map projection is any method of representing the Surface of a sphere or other shape on a plane. A bird's-eye view is a View of an object from above as though the observer were a Bird, often used in the making of Blueprints, Floor plans Top-down perspective, also sometimes referred to as bird's-eye view, overhead view or helicopter view, A worm's-eye view is a View of an object from below as though the observer were a Worm. Three-dimensional space is a geometric model of the physical Universe in which we live 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. ).

Graphical projection contains three broad categories each with its own protocol: orthographic (for protocol, see orthographic projection), oblique (for protocol see oblique projection) and perspective (for protocol, see perspective projection). Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D This article discusses imaging of three-dimensional objects For an abstract mathematical discussion see Projection (linear algebra. Perspective (from Latin perspicere to see through in the graphic arts such as drawing is an approximate representation on a flat surface (such as paper of an image as it is perceived

1 Orthographic projection
- 1.1 Pictorials
2 Oblique projection
3 Perspective
4 References
5 See also

Orthographic projection

Main article: Orthographic projection

Orthographic projection is derived from the principles of descriptive geometry and may produce an image of a specified, imaginary object as viewed from any direction of space. Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D 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 It is distinguished by parallel projectors from the imaged object and which intersect a plane of projection at right-angles. It is the projection type of choice for working drawings. Plans are a set of two-dimensional diagrams or drawings used to describe a place or object or to communicate building or fabrication instructions

Pictorials

Main article: Axonometric projection

Within orthographic projection there is an ancillary category known as pictorials. Axonometric projection ("to measure along axes" is a technique used in orthographic 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. Orthographic pictorial, rote, instrument drawings are often used to approximate graphical perspective projections, but there is attendant distortion in the approximation. Because Pictorial projections innately contain this distortion, in the rote, instrument drawing of Pictorials, great liberties may then be taken for economy of effort and best effect. Orthographic pictorials rely upon the technique of axonometric ("to measure along axes") projection.

A characteristic of axonometric projections/drawing is, one axis of space usually displays as vertical.

There are three categories of Pictorials within axonometric projection/drawing: isometric, diametric and trimetric.

Isometric

In isometric pictorials (for protocols see isometric 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. Isometric projection is a form of Graphical projection —more specifically an Axonometric projection. 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

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. Dimetric projection is a form of Axonometric projection, in which its direction of viewing is such that two of the three axes of space appear equally foreshortened of which Approximations are common in dimetric drawings.

Trimetric

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. Trimetric projection is a form of Axonometric projection, where 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

Main article: Oblique projection

In oblique projections 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. This article discusses imaging of three-dimensional objects For an abstract mathematical discussion see Projection (linear algebra. In both orthographic and oblique projection, parallel lines in space appear parallel on the final, 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. The cavalier perspective, also called cavalier projection or high view point, is a way to represent a three dimensional object on a flat drawing and more specifically Cabinet projection or sometimes cabinet perspective is a type of Oblique projection.

Perspective

Main article: Perspective (graphical)

Perspective projection is a type of projection where three dimensional objects are not projected along parallel lines, but along lines emerging from a single point. Perspective (from Latin perspicere to see through in the graphic arts such as drawing is an approximate representation on a flat surface (such as paper of an image as it is perceived 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. A vanishing point is a point in a perspective drawing to which Parallel lines appear to converge Photographic lenses and the human eye work in the same way, therefore perspective projection looks most realistic ^[1]. 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^[2].

References

^ Hearn, D., & Baker, M. (1997). Computer Graphics, C Version. Englewood Cliffs: Prentice Hall, chapter 9
^ Foley, James (1997). Computer Graphics. Boston: Addison-Wesley. ISBN 0201848406, chapter 6

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