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

See Section 13.13.4 for coordinates in two-dimensional geometry.

The coordinates command takes finds the coordinates of a point.

• coordinates takes one argument:
  P, which can be a point (or a sequence or list of points), a vector, or a line.
• If P is a point, then coordinates(P) returns a list consisting of the abscissa, ordinate and cote. If P is a list or sequence of points, then the command returns a list or sequence of such lists.
• If P is a vector, for example from A to B, then coordinates(P) returns a list of the coordinates of B−A.
• If P is a line, then coordinates(P) returns a list of two points on the line, in the order determined by the direction of the line.

Examples.

• Input:
  coordinates(point(1,2,3))
  Output:

  ⎡ ⎣

  1,2,3

  ⎤ ⎦

• 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

  ⎤ ⎥ ⎥ ⎦

• Input:
  coordinates(vector(point(1,2,3),point(2,4,7)))
  Output:

  ⎡ ⎣

  1,2,4

  ⎤ ⎦

• 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

  ⎤ ⎦

  ⎤ ⎦