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The collinearity equations are a set of two equations, used in photogrammetry and computer stereo vision, to relate coordinates in a sensor plane (in two dimensions) to object coordinates (in three dimensions).
In geometry, collinearity of a set of points is the property of their lying on a single line. [1] A set of points with this property is said to be collinear (sometimes spelled as colinear [ 2 ] ). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row".
An automorphic collineation is a map that, in coordinates, ... The idea of a line was abstracted to a ternary relation determined by collinearity ...
Pappus's hexagon theorem: Points X, Y and Z are collinear on the Pappus line. The hexagon is AbCaBc. Pappus's theorem: affine form, In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that
Trilinear coordinates are an example of homogeneous coordinates. The ratio x : y is the ratio of the perpendicular distances from the point to the sides (extended if necessary) opposite vertices A and B respectively; the ratio y : z is the ratio of the perpendicular distances from the point to the sidelines opposite vertices B and C ...
In photogrammetry and computer stereo vision, bundle adjustment is simultaneous refining of the 3D coordinates describing the scene geometry, the parameters of the relative motion, and the optical characteristics of the camera(s) employed to acquire the images, given a set of images depicting a number of 3D points from different viewpoints.
That day, in August 2013, Patrick got in the car and put the duffel bag on a seat. Inside was a talisman he’d been given by the treatment facility: a hardcover fourth edition of the Alcoholics Anonymous bible known as “The Big Book.”
The cross-ratio does not generalize in a simple manner to higher dimensions, due to other geometric properties of configurations of points, notably collinearity – configuration spaces are more complicated, and distinct k-tuples of points are not in general position.