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The three coordinate planes ( x = 0, y = 0, z = 0) divide the space into eight octants. They are identified by the eight cube-corner coordinates of the shape (±, ±, ±). In the horizontal coordinate plane you can see the four quadrants between the x and y axes. (The numbering of the points is balanced ternary with the smallest digit on the left, i.e. little-endian .)
In geometry , three-dimensional space is broken down into 8 parts by the coordinate planes of a Cartesian coordinate system , which are called octants . Since the limiting coordinate planes usually do not belong to any octant, the respective signs of the coordinates of a point in three-dimensional space indicate in which of the eight octants a point is located.
numbering
The octant of the three axes is positive (analogously to the first quadrant ) as the first designated. But there is no convention for numbering the other octants.
The following table shows the signed tuples together with possible numbering. A binary numbering with - as 1 can easily be generalized to different dimensions. A binary numbering with + as 1 defines the same order as a balanced ternary . The Roman numbering of the quadrants puts the pairs of signs in Gray-Code order. Therefore the corresponding order is also in the table of octants.
Occasionally two-dimensional space is also divided into octants. The four quadrants are divided on the straight lines and . The octants defined in this way are numbered counterclockwise from I to VIII, starting with the lower half of the first quadrant.
