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Flatness deviation may be defined in terms of least squares fit to a plane ("statistical flatness") or worst-case (the distance between the two closest parallel planes within). It can be specified for a given area and/or over an entire surface.
The lap or lapping plate in this machine is 30 cm (12 in) in diameter, about the smallest size available commercially. At the other end of the size spectrum, machines with 2.4-to-3.0-metre-diameter (8 to 10 ft) plates are not uncommon, and systems with tables 9 m (30 ft) in diameter have been constructed.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
The distance of closest approach is sometimes referred to as the contact distance. For the simplest objects, spheres, the distance of closest approach is simply the sum of their radii. For non-spherical objects, the distance of closest approach is a function of the orientation of the objects, and its calculation can be difficult.
In geometry, the sagitta (sometimes abbreviated as sag [1]) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. [2] It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror ...
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
where n is the local refractive index as a function of distance along the path C. An electromagnetic wave propagating along a path C has the phase shift over C as if it was propagating a path in a vacuum , length of which, is equal to the optical path length of C .
is of rank 2 or less, the four points are coplanar. In the special case of a plane that contains the origin, the property can be simplified in the following way: A set of k points and the origin are coplanar if and only if the matrix of the coordinates of the k points is of rank 2 or less.