A spatial point is an entity with a location in space but no extent (volume,
area or length). In geometry, a point therefore captures the notion of location;
no further information is captured. Points are used in the basic language of
geometry, physics, vector graphics (both 2d and 3d), and many other fields. In
mathematics generally, any form of space is considered as made up of points as
Points in Euclidean geometry
A point in Euclidean geometry has no
size, orientation, or any other feature except position. Euclid's axioms or
postulates assert in some cases that points exist: for example, they assert that
if two lines on a plane
are not parallel, there is exactly one point that lies on both of them.
Points in Cartesian geometry
Intuitively one can understand a location in 3d space. This location could be
described with three real number coordinates: for instance
P = (2, 6, 9)
But one can also describe points in 1, 2 or more than 3 dimensions.
description of a point is quite similar to the description of a
which also can exist in space with dimensions from one to many. The conceptual difference between these notions is significant, though: a
point indicates a location, while a vector indicates a direction and length. If
a distinguished point (the origin) is given, one can describe a location by
giving the direction and distance from the
origin to that point.