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%!PS-Adobe-3.0
%
% ********************************************************************************
%
% Figure 5.9(a)-(d) from the book: "The Theory of the Moire Phenomenon, Vol. II"
% by I. Amidror, published by Springer, 2007.
%
% * * * Copyright (c) 2007 EPFL * * *
%
% Author: I. Amidror
%
% Modified: March 21, 2007
%
% ********************************************************************************
%
% Superpositions of two dot screens - first layer only
%
% ********************************************************************************
%
/inch {72 mul} def
/centiinch {0.72 mul} def
1.2 centiinch setlinewidth
/dim 250 def % dimensions of the screen in centiinches
/dim2 125 def % dim/2
/myrand {rand 2147483647 div 2 mul 1 sub} def % random number between -1...1
1 setlinecap
/Helvetica findfont
10 scalefont setfont
0 inch 0 inch translate
% ************************************** Fig. (a):
/alpha 0 def
/theta1 0 def
/theta2 0 def
/rot 0 def % general rotation to prevent printer artifacts
/p1 3 def % period for first (reference) dot screen
/p2 3 def % period for second dot screen
/p1y 3 def % period for first (reference) dot screen
/p2y 3 def % period for second dot screen
/xshift1 0 p1 mul def % x phase shift for first dot screen (e.g. 0.5)
/yshift1 0 p1y mul def % y phase shift for first dot screen (e.g. 0.5)
/xshift2 0 p2 mul def % x phase shift for second dot screen
/yshift2 0 p2y mul def % y phase shift for second dot screen
/xmax 3 def % the x axis units will be scaled before applying the mappings so
% that the max. axis value becomes "xmax units" rather than "dim2 ci".
/ymax 3 def % the y axis units will be scaled before applying the mappings so
% that the max. axis value becomes "ymax units" rather than "dim2 ci".
/rr 1 def % random numbers will be generated in the range -rr...rr
% (in PostScript points!)
% draw first (reference) dot screen:
8 srand % seed for rand
/y dim2 neg def
gsave
2.5 inch 9.4 inch translate
theta1 rot add rotate
gsave
0 p1y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p1y div round p1y mul sub def
0 p1 dim % draw a horizontal line of dots
{/xsave exch dim2 p1 div round p1 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul add % g1(x,y)
add xshift1 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul add % g2(x,y)
add yshift1 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p1 add def
} for
stroke
/y y p1y add def
} for
-1.4 inch -1.35 inch moveto
%(A) show
grestore
gsave
/Times-Roman findfont
12 scalefont setfont
-0.07 inch -1.6 inch moveto
((a)) show
grestore
grestore
% draw second dot screen:
8 srand % same seed for rand
/y dim2 neg def
gsave
2.5 inch 9.4 inch translate
theta2 rot add rotate
0 p2y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p2y div round p2y mul sub def
0 p2 dim % draw a horizontal line of dots
{/xsave exch dim2 p2 div round p2 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul sub % g3(x,y)
add xshift2 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul sub % g4(x,y)
add yshift2 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p2 add def
} for
% stroke
/y y p2y add def
} for
-1.4 inch -1.35 inch moveto
%(B) show
grestore
% ****************************************** Fig. (b):
/alpha 0 def
/theta1 0 def
/theta2 0 def
/rot 0 def % general rotation to prevent printer artifacts
/p1 3 def % period for first (reference) dot screen
/p2 3 def % period for second dot screen
/p1y 3 def % period for first (reference) dot screen
/p2y 3 def % period for second dot screen
/xshift1 0 p1 mul def % x phase shift for first dot screen (e.g. 0.5)
/yshift1 0 p1y mul def % y phase shift for first dot screen (e.g. 0.5)
/xshift2 0 p2 mul def % x phase shift for second dot screen
/yshift2 0 p2y mul def % y phase shift for second dot screen
/xmax 3 def % the x axis units will be scaled before applying the mappings so
% that the max. axis value becomes "xmax units" rather than "dim2 ci".
/ymax 3 def % the y axis units will be scaled before applying the mappings so
% that the max. axis value becomes "ymax units" rather than "dim2 ci".
/rr 0 def % random numbers will be generated in the range -rr...rr
% (in PostScript points!)
% draw first (reference) dot screen:
8 srand % seed for rand
/y dim2 neg def
gsave
5.7 inch 9.4 inch translate
theta1 rot add rotate
gsave
0 p1y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p1y div round p1y mul sub def
0 p1 dim % draw a horizontal line of dots
{/xsave exch dim2 p1 div round p1 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul add % g1(x,y)
add xshift1 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul add % g2(x,y)
add yshift1 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p1 add def
} for
stroke
/y y p1y add def
} for
-1.4 inch -1.35 inch moveto
%(A) show
grestore
gsave
/Times-Roman findfont
12 scalefont setfont
-0.07 inch -1.6 inch moveto
((b)) show
grestore
grestore
% draw second dot screen:
8 srand % same seed for rand
/y dim2 neg def
gsave
5.7 inch 9.4 inch translate
theta2 rot add rotate
0 p2y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p2y div round p2y mul sub def
0 p2 dim % draw a horizontal line of dots
{/xsave exch dim2 p2 div round p2 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul sub % g3(x,y)
add xshift2 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul sub % g4(x,y)
add yshift2 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p2 add def
} for
% stroke
/y y p2y add def
} for
-1.4 inch -1.35 inch moveto
%(B) show
grestore
% ************************************** Fig. (c):
/alpha 0 def
/theta1 0 def
/theta2 0 def
/rot 0 def % general rotation to prevent printer artifacts
/p1 3 def % period for first (reference) dot screen
/p2 3 def % period for second dot screen
/p1y 3 def % period for first (reference) dot screen
/p2y 3 def % period for second dot screen
/xshift1 0 p1 mul def % x phase shift for first dot screen (e.g. 0.5)
/yshift1 1 p1y mul def % y phase shift for first dot screen (e.g. 0.5)
/xshift2 0 p2 mul def % x phase shift for second dot screen
/yshift2 0 p2y mul def % y phase shift for second dot screen
/xmax 3 def % the x axis units will be scaled before applying the mappings so
% that the max. axis value becomes "xmax units" rather than "dim2 ci".
/ymax 3 def % the y axis units will be scaled before applying the mappings so
% that the max. axis value becomes "ymax units" rather than "dim2 ci".
/rr 1 def % random numbers will be generated in the range -rr...rr
% (in PostScript points!)
% draw first (reference) dot screen:
8 srand % seed for rand
/y dim2 neg def
gsave
2.5 inch 6.0 inch translate
theta1 rot add rotate
gsave
0 p1y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p1y div round p1y mul sub def
0 p1 dim % draw a horizontal line of dots
{/xsave exch dim2 p1 div round p1 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul add % g1(x,y)
add xshift1 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul add % g2(x,y)
add yshift1 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p1 add def
} for
stroke
/y y p1y add def
} for
-1.4 inch -1.35 inch moveto
%(A) show
grestore
gsave
/Times-Roman findfont
12 scalefont setfont
-0.07 inch -1.6 inch moveto
((c)) show
grestore
grestore
% draw second dot screen:
8 srand % same seed for rand
/y dim2 neg def
gsave
2.5 inch 6.0 inch translate
theta2 rot add rotate
0 p2y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p2y div round p2y mul sub def
0 p2 dim % draw a horizontal line of dots
{/xsave exch dim2 p2 div round p2 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul sub % g3(x,y)
add xshift2 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul sub % g4(x,y)
add yshift2 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p2 add def
} for
% stroke
/y y p2y add def
} for
-1.4 inch -1.35 inch moveto
%(B) show
grestore
% ****************************************** Fig. (d):
/alpha 0 def
/theta1 0 def
/theta2 0 def
/rot 0 def % general rotation to prevent printer artifacts
/p1 3 def % period for first (reference) dot screen
/p2 3 def % period for second dot screen
/p1y 3 def % period for first (reference) dot screen
/p2y 3 def % period for second dot screen
/xshift1 0 p1 mul def % x phase shift for first dot screen (e.g. 0.5)
/yshift1 1 p1y mul def % y phase shift for first dot screen (e.g. 0.5)
/xshift2 0 p2 mul def % x phase shift for second dot screen
/yshift2 0 p2y mul def % y phase shift for second dot screen
/xmax 3 def % the x axis units will be scaled before applying the mappings so
% that the max. axis value becomes "xmax units" rather than "dim2 ci".
/ymax 3 def % the y axis units will be scaled before applying the mappings so
% that the max. axis value becomes "ymax units" rather than "dim2 ci".
/rr 0 def % random numbers will be generated in the range -rr...rr
% (in PostScript points!)
% draw first (reference) dot screen:
8 srand % seed for rand
/y dim2 neg def
gsave
5.7 inch 6.0 inch translate
theta1 rot add rotate
gsave
0 p1y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p1y div round p1y mul sub def
0 p1 dim % draw a horizontal line of dots
{/xsave exch dim2 p1 div round p1 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul add % g1(x,y)
add xshift1 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul add % g2(x,y)
add yshift1 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p1 add def
} for
stroke
/y y p1y add def
} for
-1.4 inch -1.35 inch moveto
%(A) show
grestore
gsave
/Times-Roman findfont
12 scalefont setfont
-0.07 inch -1.6 inch moveto
((d)) show
grestore
grestore
% draw second dot screen:
8 srand % same seed for rand
/y dim2 neg def
gsave
5.7 inch 6.0 inch translate
theta2 rot add rotate
0 p2y dim % draw horizontal lines of dots
{newpath
/x dim2 neg def
/ysave exch dim2 p2y div round p2y mul sub def
0 p2 dim % draw a horizontal line of dots
{/xsave exch dim2 p2 div round p2 mul sub def
/x1 x dim2 div xmax mul def
/y1 y dim2 div ymax mul def
xsave x sub
x 2 x1 mul y1 mul 0.5 mul sub % g3(x,y)
add xshift2 add
centiinch myrand rr mul sub
ysave y sub
y x1 x1 mul y1 y1 mul sub 0.5 mul sub % g4(x,y)
add yshift2 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p2 add def
} for
% stroke
/y y p2y add def
} for
-1.4 inch -1.35 inch moveto
%(B) show
grestore
gsave
1.75 inch 2.3 inch translate
0 inch 0 inch moveto
/Times-Bold findfont
12 scalefont setfont
(Figure 5.9(a)-(d)) show
/Times-Roman findfont
12 scalefont setfont
( from the book: ) show
/Times-Italic findfont
12 scalefont setfont
(The Theory of the Moire) show
-0.06 inch 0 inch rmoveto
(\302 Phenomenon) show
0.05 inch -0.25 inch moveto
(Vol. II: Aperiodic Layers,) show
/Times-Roman findfont
12 scalefont setfont
( by I. Amidror, published by Springer, 2007.) show
1.7 inch -0.65 inch moveto
((First layer only.)) show
grestore
showpage