ForSuffixes.mp
u:=25; % 25 = 25bp = 25 PostScript points = 30/72 in
wi:=10; % width in units u
he:=9; % height in units u
hoehe:=he*u; % height
breite:=wi*u; % width
transform t, Txy;
pair P[];
path p[];
color wuerfel[], versch; % 3D vectors: MetaPost type ``color''
rotX:=45; % angle of rotation around the x axis
rotY:=45; % angle of rotation around the y axis
rotZ:=45; % angle of rotation around the z axis
versch:=(1.6, 1, 2.7); % translation (in mathematical units)
P0=(3.2, 2.2)*u; % origin in MetaPost coordinates (bp)
P1=(-.6, -.4)/1.5; % x axis in mathematical coordinates
t:=identity % t: maps mathematical 2D coordinates
scaled u % onto MetaPost coordinates (bp)
shifted P0;
Txy:=identity % Txy: maps 3D coordinates x,y onto
reflectedabout((0,0), (1,1)) % MetaPost coordinates
yscaled ypart P1
slanted (xpart P1/ypart P1)
transformed t;
vardef dreheX(expr SpaceVector, winkel) = % rotation of 3D vector
pair yz; % ``SpaceVector'' around
yz:=(greenpart SpaceVector, bluepart SpaceVector); % the x axis by the
yz:=yz rotated winkel; % angle ``winkel''
(redpart SpaceVector, xpart yz, ypart yz)
enddef;
vardef dreheY(expr SpaceVector, winkel) = % rotation around the y axis
pair zx;
zx:=(bluepart SpaceVector, redpart SpaceVector);
zx:=zx rotated winkel;
(ypart zx, greenpart SpaceVector, xpart zx)
enddef;
vardef dreheZ(expr SpaceVector, winkel) = % rotation around the z axis
pair xy;
xy:=(redpart SpaceVector, greenpart SpaceVector);
xy:=xy rotated winkel;
(xpart xy, ypart xy, bluepart SpaceVector)
enddef;
vardef getPixel(expr SpaceVector) = % returns MetaPost coordinates (bp)
% SpaceVector: type ``color'' % of spatial projection of
(redpart SpaceVector, greenpart SpaceVector) % 3D point
transformed Txy % with coordinates ``SpaceVector''
shifted (0, u*bluepart SpaceVector)
enddef;
vardef Zyklus(text t) = % returns cyclic path formed of the
forsuffixes $=t: z$-- endfor % z points with suffixes in argument t
cycle
enddef;
%
% The following construction copies the possibilities one has in Java with
%
% main(String[] args) {
% k = args.length;
%
vardef Pfad(text t) = % returns path formed of the
k:=0; % z points with suffixes in argument t
forsuffixes $=t: k:=k+1; endfor % count number of arguments first
i:=1;
forsuffixes $=t: % problem: the last z must not be followed by --
if i‹k: z$-- else: z$ fi
hide(i:=i+1) % hide: to prevent ``i:=i+1'' to be written into the path
endfor % no ; after ``)'' (would be written into path)
enddef;
def lot(expr n) = % draws perpendicular line from point wuerfel[n]
color SpaceVector; % to (x,y) plane
SpaceVector:=wuerfel[n];
draw getPixel(SpaceVector)--getPixel((redpart SpaceVector,greenpart SpaceVector, 0));
draw_point(getPixel(SpaceVector), white, black);
draw_point( getPixel((redpart SpaceVector,greenpart SpaceVector, 0)), white, black);
enddef;
def draw_point(expr P, colInt, colPer) =
fill fullcircle scaled 1mm shifted P withcolor colInt;
draw fullcircle scaled 1mm shifted P withcolor colPer;
enddef;
def Lote(text t) = % invokes lot(n) for all the suffixes in
forsuffixes $=t: % argument t
lot($);
endfor
enddef;
wuerfel0:=(2.8, 0, 0); % definition of cube ``wuerfel''
wuerfel1:=(2.8, 2.8, 0); % (array of type color)
wuerfel2:=(0, 2.8, 0); % in mathematical 3D coordinates
wuerfel3:=(0, 0, 0);
wuerfel4:=(2.8, 0, 2.8);
wuerfel5:=(2.8, 2.8, 2.8);
wuerfel6:=(0, 2.8, 2.8);
wuerfel7:=(0, 0, 2.8);
beginfig(1)
for i=0 upto 7: % z0,...,z7: MetaPost coordinates of
z[i]=getPixel(wuerfel[i]); % cube in original position
endfor
for i=0 upto 7: % rotation and translation
wuerfel[i]:=dreheX(wuerfel[i], rotX); % of cube
wuerfel[i]:=dreheY(wuerfel[i], rotY);
wuerfel[i]:=dreheZ(wuerfel[i], rotZ);
wuerfel[i]:=wuerfel[i]+versch;
endfor
for i=0 upto 7: % z100,...,z107: MetaPost coordinates of
z[i+100]=getPixel(wuerfel[i]); % cube after rotation
endfor
% --- Grid ---
for i=0 upto 5:
draw getPixel((i,0,0))--getPixel((i,5,0)) withcolor .7white;
draw getPixel((0,i,0))--getPixel((5,i,0)) withcolor .7white;
draw getPixel((0,i,0))--getPixel((0,i,5)) withcolor .7white;
draw getPixel((0,0,i))--getPixel((0,5,i)) withcolor .7white;
draw getPixel((0,0,i))--getPixel((5,0,i)) withcolor .7white;
draw getPixel((i,0,0))--getPixel((i,0,5)) withcolor .7white;
endfor
% --- End Grid ---
% --- Frame ---
draw (0, 0)--(breite, 0)--(breite, hoehe)--(0, hoehe)--cycle;
% --- Axes ---
drawarrow getPixel((0, 0, 0))--getPixel((6, 0, 0));
label.llft(btex $x$ etex, getPixel((6, 0, 0))+(0, 1mm));
drawarrow getPixel((0, 0, 0))--getPixel((0, 6, 0));
label.rt (btex $y$ etex, getPixel((0, 6, 0)));
drawarrow getPixel((0, 0, 0))--getPixel((0, 0, 6));
label.top (btex $z$ etex, getPixel((0, 0, 6)));
% --- Cube in original position ---
fill Zyklus(0, 1, 5, 4) withcolor .7green;
fill Zyklus(4, 5, 6, 7) withcolor .9green;
fill Zyklus(1, 2, 6, 5) withcolor .5green;
draw Pfad(0, 3, 2) dashed evenly;
draw Pfad(3, 7) dashed evenly;
draw Zyklus(1, 2, 6, 7, 4, 0) ;
draw Pfad(4, 5, 1, 5, 6);
% --- Cube after rotation ---
fill Zyklus(104, 105, 106, 107) withcolor .9red;
fill Zyklus(101, 102, 106, 105) withcolor .7red;
fill Zyklus(100, 101, 105, 104) withcolor .5red;
draw Pfad(100, 103, 102) dashed evenly;
draw Pfad(103, 107) dashed evenly;
draw Pfad(104, 105, 101, 105, 106);
draw Zyklus(101, 102, 106, 107, 104, 100);
Lote(0, 1, 4, 5, 7); % suffixes of ``wuerfel''
endfig;
end