### 12.12.4 The coordinates of a point, vector or line in space: coordinates

See section 11.13.4 for coordinates in
two-dimensional geometry.

The coordinates command takes as argument a point, vector or line.

If the argument is a point,
coordinates returns a list consisting of the abscissa,
ordinate and cote.

Input:

coordinates(point(1,2,3))

Output:

[1,2,3]

If the argument is a vector, for example from point A to
point B, then coordinates returns a list of the
coordinates of B-A.

Input:

coordinates(vector(point(1,2,3),point(2,4,7)))

Output:

[1,2,4]

If the argument is a line, coordinates returns a list of
two points on the line, in the order determined by the direction of
the line.

Input:

coordinates(line(point(-1,1,0),point(1,2,3)))

Output:

[[-1,1,0],[1,2,3]]

Input:

coordinates(line(x-2*y+3=0, 6*x + 3*y - 5*z + 3 = 0))

Output:

[[-1,1,0],[9,6,15]]

coordinates can also take a sequence or list of points as an
argument; it then returns a sequence or list of the coordinates of
the points.

Input:

coordinates(point(0,1,2),point(1,2,4))

Output:

[0,1,2], [1,2,4]

Note that if the argument is a list of real numbers, it is
interpreted as a list of points on the real axis of the plane.

Input:

coordinates([1,2,4])

Output:

[[1,0],[2,0],[4,0]]