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In geometry, a Cartesian coordinate system (UK: / k ɑːr ˈ t iː zj ə n /, US: / k ɑːr ˈ t iː ʒ ə n /) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines ...
A Cartesian grid is a special case where the elements are unit squares or unit cubes, and the vertices are points on the integer lattice. A rectilinear grid is a tessellation by rectangles or rectangular cuboids (also known as rectangular parallelepipeds ) that are not, in general, all congruent to each other.
Comparison between Cartesian and curvilinear grids shows that in Cartesian grid cells are wasted in dealing with objects. The distribution of function is very fine in curvilinear grid. The resources required in curvilinear grids are less as compared to Cartesian grids thus saving much memory.
In three-dimensional space the intersection of two coordinate surfaces is a coordinate curve. In the Cartesian coordinate system we may speak of coordinate planes. Similarly, coordinate hypersurfaces are the (n − 1)-dimensional spaces resulting from fixing a single coordinate of an n-dimensional coordinate system. [14]
A projected coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of spatial reference system that represents locations on Earth using Cartesian coordinates (x, y) on a planar surface created by a particular map projection. [1]
A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane. The set R 2 {\displaystyle \mathbb {R} ^{2}} of the ordered pairs of real numbers (the real coordinate plane ), equipped with the dot product , is often called the Euclidean plane or standard Euclidean plane , since every Euclidean plane is isomorphic to it.
Transformation of geographic coordinates (longitude and latitude) to Cartesian (x,y) or polar (r, θ) plane coordinates. In large-scale maps, Cartesian coordinates normally have a simple relation to eastings and northings defined as a grid superimposed on the projection. In small-scale maps, eastings and northings are not meaningful, and grids ...
A square grid graph is a Cartesian product of graphs, namely, of two path graphs with n − 1 and m − 1 edges. [2] Since a path graph is a median graph, the latter fact implies that the square grid graph is also a median graph.