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Coplanarity. In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
Collinearity equation. Light beams passing through the pinhole of a pinhole camera. 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). The equations originate from the central projection ...
Collinearity of points whose coordinates are given. In coordinate geometry, in n -dimensional space, a set of three or more distinct points are collinear if and only if, the matrix of the coordinates of these vectors is of rank 1 or less. For example, given three points. if the matrix. is of rank 1 or less, the points are collinear.
Euclidean distance matrix. In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points in k -dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them. That is. where denotes the Euclidean norm on ℝk.
Principal symbol. The variation formula computations above define the principal symbol of the mapping which sends a pseudo-Riemannian metric to its Riemann tensor, Ricci tensor, or scalar curvature. The principal symbol of the map assigns to each a map from the space of symmetric (0,2)-tensors on to the space of (0,4)-tensors on given by.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates (x, y) with respect to the ...
As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range of 180°, running from 0° to 180°, and does not pose any problem when calculated from an arccosine, but beware for an arctangent. If, in the alternative definition, θ is chosen to run from − ...
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...