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Vector projection. The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as or a∥b. The vector component or vector resolute of a perpendicular to b, sometimes ...
A projection on a vector space is a linear operator such that . When has an inner product and is complete, i.e. when is a Hilbert space, the concept of orthogonality can be used. A projection on a Hilbert space is called an orthogonal projection if it satisfies for all .
Properties. The projection matrix has a number of useful algebraic properties. [5][6] In the language of linear algebra, the projection matrix is the orthogonal projection onto the column space of the design matrix . [4] (. Note that is the pseudoinverse of X.) Some facts of the projection matrix in this setting are summarized as follows: [4] and.
In video projection terminology, throw is the distance between a video projector lens and the screen on which it shines. It is given as a ratio (called throw ratio), which describes the relationship between the distance to the screen and the width of the screen (assuming the image is to fill the screen fully). Throw ratio is a characteristic of ...
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. 3D projections use the primary qualities of an object's basic ...
The scalar projection is a scalar, equal to the length of the orthogonal projection of on , with a negative sign if the projection has an opposite direction with respect to . Multiplying the scalar projection of on by converts it into the above-mentioned orthogonal projection, also called vector projection of on .
Reflective surface to send light back to viewer. (In a backlit LCD, this layer is replaced or complemented with a light source.) A liquid-crystal display (LCD) is a flat-panel display or other electronically modulated optical device that uses the light-modulating properties of liquid crystals combined with polarizers.
Camera matrix. In computer vision a camera matrix or (camera) projection matrix is a matrix which describes the mapping of a pinhole camera from 3D points in the world to 2D points in an image. Let be a representation of a 3D point in homogeneous coordinates (a 4-dimensional vector), and let be a representation of the image of this point in the ...