/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 0.8.5 ] */

/* [wxMaxima: title   start ]
Eulersche Winkel
   [wxMaxima: title   end   ] */

/* [wxMaxima: comment start ]
(A. Filler, Elementare Lineare Algebra, Kapitel 7, Abschnitt 7.4)

Die folgende Befehlsfolge stellt die drei Vektoren der Standardbasis von R3 
(blau) und ihre Bildvektoren (rot) bei einer Isometrie dar. Außerdem
werden ein Quadrat in der x-y-Ebene und sein Bild (ebenfalls blau->rot) 
dargestellt.

Verändern Sie die Werte der Eulerschen Winkel alphaZ, alphaY, und alphaX, um 
unterschiedliche gleichsinnige Isometrien zu untersuchen.

Sie können auch d:-1$ setzen, um eine ungleichsinnige Isometrie zu betrachten.
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
alphaZ:45$
alphaY:30$
alphaX:60$
d:1$
v:matrix([0],[0],[0])$
A:matrix([cos(alphaZ*%pi/180),-sin(alphaZ*%pi/180),0],
         [sin(alphaZ*%pi/180),cos(alphaZ*%pi/180),0],[0,0,1]).
  matrix([cos(alphaY*%pi/180),0,sin(alphaY*%pi/180)],[0,1,0],
         [-sin(alphaY*%pi/180),0,cos(alphaY*%pi/180)]).
  matrix([1,0,0],[0,cos(alphaX*%pi/180),-sin(alphaX*%pi/180)],
           [0,sin(alphaX*%pi/180),cos(alphaX*%pi/180)]).
  matrix([1,0,0],[0,1,0],[0,0,d]);
fx(x,y,z):= x*A[1,1] + y*A[1,2] + z*A[1,3] + v[1,1]$
fy(x,y,z):= x*A[2,1] + y*A[2,2] + z*A[2,3] + v[2,1]$
fz(x,y,z):= x*A[3,1] + y*A[3,2] + z*A[3,3] + v[3,1]$
load(draw)$
O:[0,0,0]$
E1:[1,0,0]$ E2:[0,1,0]$ E3:[0,0,1]$
E1f:[fx(1,0,0),fy(1,0,0),fz(1,0,0)]$
E2f:[fx(0,1,0),fy(0,1,0),fz(0,1,0)]$
E3f:[fx(0,0,1),fy(0,0,1),fz(0,0,1)]$
A1:[-1,-1,0]$ B1:[1,-1,0]$ C1:[1,1,0]$ D1:[-1,1,0]$
A2:[fx(-1,-1,0),fy(-1,-1,0),fz(-1,-1,0)]$ 
B2:[fx(1,-1,0),fy(1,-1,0),fz(1,-1,0)]$
C2:[fx(1,1,0),fy(1,1,0),fz(1,1,0)]$
D2:[fx(-1,1,0),fy(-1,1,0),fz(-1,1,0)]$
draw3d( user_preamble = ["set size ratio 1"], grid=true,
        xaxis=true, yaxis=true,
        xrange = [-2.4,2.4], yrange = [-2.4,2.4], zrange = [-1.5,1.5],
        color = blue, line_width = 2,
        points_joined = true,point_type=none,
        points([A1,B1,C1,D1,A1]),
        color = red,
        points([A2,B2,C2,D2,A2]),
        point_type=none, color = blue, line_width = 3,
        points([O,E1]),points([O,E2]),points([O,E3]),
        color = red,
        points([O,E1f]),points([O,E2f]),points([O,E3f]),
        point_type=circle, point_size=0.7,
        color = black, points([O]),
        color = grey, points([E1]),points([E1f]),
        color = green, points([E2]),points([E2f]),
        color = yellow, points([E3]),points([E3f])
    )$
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$