load (draw);
load (vector_rebuild);
listarith : true;
bildanfang : 10;
bildende : 10;

n1 : [1,2,2];
n2 : [-1,-1,2];
nv : [0,0,0];

/* Schnittgerade g */
A : [1,1,1];
v : n1 ~ n2 / | n1 ~ n2 |;
g : A + t*v;
g1 : g, t=-8, vector_simp;
g2 : g, t=8, vector_simp;

rv1 : v ~ n1 / | n1 ~ v |;
rv2 : n2 ~ v / | n2 ~ v |;

P1 : A + 4 * rv1, vector_simp;
P2 : A + 4 * rv2, vector_simp;

eq : extract_equations (P1 + a1 * n1 = P2 + a2 * n2);
lsg : solve (eq, [a1, a2]);
b1 : rhs (lsg[1][1] ), numer;
b2 : rhs (lsg[1][2] ), numer;
n11 : b1 * n1, vector_simp, numer;
n21 : b2 * n2, vector_simp, numer;

/* Rechtecke */
r11 : P1 - 4*rv1 - 2*v, vector_simp, numer;
r12 : P1 - 4*rv1 + 2*v, vector_simp, numer;
r13 : P1 + 4*rv1 - 2*v, vector_simp, numer;
r14 : P1 + 4*rv1 + 2*v, vector_simp, numer;
r21 : P2 - 4*rv2 - 2*v, vector_simp, numer;
r22 : P2 - 4*rv2 + 2*v, vector_simp, numer;
r23 : P2 + 4*rv2 - 2*v, vector_simp, numer;
r24 : P2 + 4*rv2 + 2*v, vector_simp, numer;

Sn : P1 + n11;

draw3d (
/*
  xrange = [bildanfang, bildende],
  yrange = [bildanfang, bildende],
  zrange = [bildanfang, bildende],
*/
  xtics = false,
  ytics = false,
  ztics = false,
  points_joined = true,
  head_length = 0.2,
  vector (P1, n11),
  vector (P2, n21),
  mesh ([r11, r12], [r13, r14]),
  mesh ([r21, r22], [r23, r24]),
/*
  points ([g1, g2]),
*/
  line_width = 2,
  color = red,
  points ([A, P1, Sn, P2, A]),
  view = [52, 44],
  dimensions = [600,600],
  file_name = "eewinkel",
  terminal = png
);