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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 ...
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).
The ITRS defines a geocentric system of coordinates using the SI system of measurement. An International Terrestrial Reference Frame (ITRF) is a realization of the ITRS. Its origin is at the center of mass of the whole earth including the oceans and atmosphere.
Barycentric coordinates are strongly related to Cartesian coordinates and, more generally, affine coordinates.For a space of dimension n, these coordinate systems are defined relative to a point O, the origin, whose coordinates are zero, and n points , …,, whose coordinates are zero except that of index i that equals one.
a special case of barycentric coordinates for a triangle, in which case it is known as a ternary plot or areal coordinates, among other names; Trilinear coordinates, in which the coordinates of a point in a triangle are its relative distances from the three sides; Synergetics coordinates
Let ABC be a plane triangle and let x : y : z be the trilinear coordinates of an arbitrary point in the plane of triangle ABC.. A straight line in the plane of ABC whose equation in trilinear coordinates has the form (,,) + (,,) + (,,) = where the point with trilinear coordinates (,,): (,,): (,,) is a triangle center, is a central line in the plane of ABC relative to ABC.
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass.
The international standard convention —that east is positive—is consistent with a right-handed Cartesian coordinate system, with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the northern hemisphere ) to give a precise position on the Earth's surface.