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The point P is the inversion point of Q; the polar is the line through P that is perpendicular to the line containing O, P and Q. If point R is the inverse of point P then the lines perpendicular to the line PR through one of the points is the polar of the other point (the pole). Poles and polars have several useful properties:
If the original curve is a line then the inverse curve will pass through the center of inversion. If the original curve passes through the center of inversion then the inverted curve will be a line. The inverted curve will be the same as the original exactly when the curve intersects the circle of inversion at right angles.
In computer science, an inverted index (also referred to as a postings list, postings file, or inverted file) is a database index storing a mapping from content, such as words or numbers, to its locations in a table, or in a document or a set of documents (named in contrast to a forward index, which maps from documents to content). [1]
For example, Plücker coordinates are used to determine the position of a line in space. [11] When there is a need, the type of figure being described is used to distinguish the type of coordinate system, for example the term line coordinates is used for any coordinate system that specifies the position of a line.
Reverse perspective, also called inverse perspective, [1] inverted perspective, [2] divergent perspective, [3] [4] or Byzantine perspective, [5] is a form of perspective drawing where the objects depicted in a scene are placed between the projective point and the viewing plane.
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.
The word horizontal is derived from the Latin horizon, which derives from the Greek ὁρῐ́ζων, meaning 'separating' or 'marking a boundary'. [2] The word vertical is derived from the late Latin verticalis, which is from the same root as vertex, meaning 'highest point' or more literally the 'turning point' such as in a whirlpool.
The forward index is sorted to transform it to an inverted index. The forward index is essentially a list of pairs consisting of a document and a word, collated by the document. Converting the forward index to an inverted index is only a matter of sorting the pairs by the words. In this regard, the inverted index is a word-sorted forward index.