load (draw);
load(vector_rebuild);
listarith : true;
domxmxops: true;

A : [1,1,1];

netzberechnen(a) := block ([],
  n : [a,2,3],

  u1 : [n[2], -n[1], 0],
  u2 : [0, n[3], -n[2]],
  u3 : [n[1], 0, -n[3]],

  u : u1,
  v : u2,

  if (u1 = [0,0,0]) then (
    u : u2,
    v : u3
    ),
  if (u2 = [0,0,0]) then (
    u : u1,
    v : u3
    ),
  if (u3 = [0,0,0]) then (
    u : u1,
    v : u2
    ),
  /* Länge der Richtungsvektoren */
  u : u * (6 / (sqrt (u.u))),
  v : v * (6 / (sqrt (v.v))),
  array(P, 4, 4),
  for i : 0 while i < 4 do (
    for k : 0 while k < 4 do (
      P[i+1, k+1] : A + i * u + k * v
    )
  ),

  array(t, 4),
  graphlist : [],
  for i : 1 while i <= 3 do (
    tmplist: [],
    for k : 1 while k <= 3 do 
      tmplist : append (tmplist, [P[i, k]]),
    graphlist : append (graphlist, [points (tmplist)])
  ),
  for i : 1 while i <= 3 do (
    tmplist: [],
    for k : 1 while k <= 3 do 
      tmplist : append (tmplist, [P[k, i]]),
    graphlist : append (graphlist, [points (tmplist)])
  ),
  graphlist : append (graphlist, [vector (A, n)]),
  graphlist : append (graphlist, [vector (A, n)]),
  tmptxt : concat ("a=", a),
  graphlist : append (graphlist, [label ([tmptxt, 8, 15, 4]) ]),
  graphlist : append (graphlist, [label (["n", n[1], n[2], n[3]]) ])
);


bilderstellen() := block ([],
  [gr3d(
     xrange = [0,30],
     yrange = [-20,20],
     zrange = [-10,15],
     points_joined = true,
     point_size = 0,
     color = black,
     head_length = 0.4,
     line_width = 2,
     vector ([0,0,0], A),
     color = blue,
     vector (A, u),
     color = green,
     vector (A, v),
     color = black,
     line_width = 1,
     head_length = 0.5,
     font_size = 25,
     label (["A", A[1] - 3, A[2], A[3]]),
     graphlist
  )]
);


bildliste : [];
for i : 0 step 4 while i <= 32 do
  block ([],
    netzberechnen (i),
    bild : bilderstellen (),
    bildliste : append (bildliste, bild)
  );

graphlist;

bildliste;

draw (
  dimensions = [400,400],
  bildliste,
  file_name = "ebene1",
  delay = 100,
  terminal = 'animated_gif
);