14.14.8  Orthogonal projection in space: projection

See Section 13.15.8 for projections in the plane.

The projection command creates a projection.

• projection takes one mandatory argument and one optional argument:
  • O, a geometrix object.
  • Optionally, P, a point.
• projection(O) returns a new command which projects points onto O.
• projection(O,P) returns and draws the projection of P onto O.

Examples.

• Input:
  P:=point(0,0,1); p1:= projection(line(point(0,0,0), point(1,1,1))) coordinates(p1(P))
  Output:

  ⎡ ⎢ ⎢ ⎣

  1 3

  ,

  1 3

  ,

  1 3

  ⎤ ⎥ ⎥ ⎦

  which is the projection of (0,0,1) onto the line.
• Input:
  coordinates(projection(plane(point(1,0,0),point(0,0,0),point(1,1,1)),point(0,0,1)))
  Output:

  ⎡ ⎢ ⎢ ⎣

  0,

  1 2

  ,

  1 2

  ⎤ ⎥ ⎥ ⎦

  which is the projection of the point (0,0,1) onto the plane.