Cabinet projection - Citizendia

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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Cabinet projection or sometimes cabinet perspective is a type of oblique projection. 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 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. This article discusses imaging of three-dimensional objects For an abstract mathematical discussion see Projection (linear algebra. The term stems from the use for illustrations in furniture industry. This projection has been used in early video games like Paperboy. Paperboy is a 1984 Arcade game by Atari Games. The players take the role of a Paperboy who delivers Newspapers along a

The figures to the left are orthographic projections. Orthographic projection is a means of representing a three- Dimensional (3D object in two dimensions (2D The figure to the right is an oblique projection with an angle of 30° and a ratio of 0. This article discusses imaging of three-dimensional objects For an abstract mathematical discussion see Projection (linear algebra. 5

Principle

Like Cavalier perspective, cabinet projection is an oblique projection, where 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°). 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 Unlike Cavalier projection, where the third axis keeps its length, with cabinet projection the length of the receding lines is cut in half.

Mathematical formula

As formula, if the plane facing the viewer is $x y$ , and the receding axis is $z$ , then a point $P$ is project like this:

$P \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} x + 0.5 \cdot z \cdot cos \alpha \\ y + 0.5 \cdot z \cdot sin \alpha \\ 0 \end{pmatrix}$

Where $α$ is the mentioned angle.

The transformation matrix is:

$P = \begin{bmatrix} 1 & 0 & 0.5 \cdot \cos \alpha \\ 0 & 1 & 0.5 \cdot \sin \alpha \\ 0 & 0 & 0 \end{bmatrix}$

References

Potting bench drawn in cabinet view

Illustrator Draftsman 3 & 2 - Volume 2 Standard Practices and Theory, page 68 from http://www.tpub.com
Ingrid Carlbom, Joseph Paciorek, Planar Geometric Projections and Viewing Transformations, ACM Computing Surveys (CSUR), v. In Linear algebra, Linear transformations can be represented by matrices. A Potting bench or gardening table is a kind of Workbench used for small gardening tasks such as transplanting seedlings 10 n. 4, p. 465-502, Dec. 1978
Foley, James (1997). Computer Graphics. Boston: Addison-Wesley. ISBN 0201848406.

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