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%!PS-Adobe-3.0
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% Figure 3.2(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 - second layer only
%
% ********************************************************************************
%
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1.2 centiinch setlinewidth
/dim 180 def % dimensions of the screen in centiinches
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1 setlinecap
/Helvetica findfont
10 scalefont setfont
0.5 inch 0.9 inch translate
% ************************************** Fig. (a):
/alpha 6 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)
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/yshift2 0 p2y mul def % y phase shift for second dot screen
/rr 1 def % random numbers will be generated in the range -rr...rr
% (in PostScript points!)
% draw first (reference) dot screen:
25 srand % seed for rand
/y dim2 neg def
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2.5 inch 8.7 inch translate
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((a)) show
grestore
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% draw second dot screen:
25 srand % same seed for rand
/y dim2 neg def
gsave
2.5 inch 8.7 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
xsave x sub
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add xshift2 add
centiinch myrand rr mul sub
ysave y sub
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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
alpha rotate % rotate the letter B
-1.01 inch -0.95 inch moveto
(B) show
grestore
% ****************************************** Fig. (b):
/alpha 6 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 0.5 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
/rr 1 def % random numbers will be generated in the range -rr...rr
% (in PostScript points!)
% draw first (reference) dot screen:
25 srand % seed for rand
/y dim2 neg def
gsave
5 inch 8.7 inch translate
% draw cross:
gsave
newpath
2.5 centiinch setlinewidth
0.1 inch 0 inch moveto
-0.2 inch 0 inch rlineto
0 inch 0.1 inch moveto
0 inch -0.2 inch rlineto
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1.2 centiinch setlinewidth
% draw surrounding crosses:
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0.5 centiinch setlinewidth
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-1.150 inch -1.050 inch moveto
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-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch -1.200 inch moveto
0.950 inch -1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%-1.400 inch 1.200 inch moveto
-1.150 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch 1.200 inch moveto
0.950 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
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0 inch 0.2 inch rlineto
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% draw shifted surrounding crosses:
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0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch -1.200 inch moveto
0.950 inch -1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%-1.400 inch 1.200 inch moveto
-1.150 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch 1.200 inch moveto
0.950 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
stroke
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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
xsave x sub
x % g1(x,y)
add xshift1 add
centiinch myrand rr mul sub
ysave y sub
y % g2(x,y)
add yshift1 add
centiinch myrand rr mul sub moveto
0 0 rlineto
/x x p1 add def
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% stroke
/y y p1y add def
} for
-1.01 inch -0.91 inch moveto
%(A) show
grestore
gsave
/Times-Roman findfont
12 scalefont setfont
-0.07 inch -1.15 inch moveto
((b)) show
grestore
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% draw second dot screen:
25 srand % same seed for rand
/y dim2 neg def
gsave
5 inch 8.7 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
xsave x sub
alpha cos x mul alpha sin y mul sub % g3(x,y)
add xshift2 add
centiinch myrand rr mul sub
ysave y sub
alpha sin x mul alpha cos y mul add % 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
alpha rotate % rotate the letter B
-1.01 inch -0.95 inch moveto
(B) show
grestore
% ************************************** Fig. (c):
/alpha 6 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 0.5 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
/rr 1 def % random numbers will be generated in the range -rr...rr
% (in PostScript points!)
% draw first (reference) dot screen:
25 srand % seed for rand
/y dim2 neg def
gsave
2.5 inch 6.1 inch translate
% draw cross:
gsave
newpath
2.5 centiinch setlinewidth
0.1 inch 0 inch moveto
-0.2 inch 0 inch rlineto
0 inch 0.1 inch moveto
0 inch -0.2 inch rlineto
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1.2 centiinch setlinewidth
% draw surrounding crosses:
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0.5 centiinch setlinewidth
%-1.400 inch -1.200 inch moveto
-1.150 inch -1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch -1.200 inch moveto
0.950 inch -1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%-1.400 inch 1.200 inch moveto
-1.150 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch 1.200 inch moveto
0.950 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
stroke
grestore
% draw shifted surrounding crosses:
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0.5 centiinch setlinewidth
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0.950 inch 1.050 inch moveto
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theta1 rot add rotate
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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
xsave x sub
x % g1(x,y)
add xshift1 add
centiinch myrand rr mul sub
ysave y sub
y % 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
-1.01 inch -0.91 inch moveto
%(A) show
grestore
gsave
/Times-Roman findfont
12 scalefont setfont
-0.07 inch -1.15 inch moveto
((c)) show
grestore
grestore
% draw second dot screen:
25 srand % same seed for rand
/y dim2 neg def
gsave
2.5 inch 6.1 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
xsave x sub
alpha cos x mul alpha sin y mul sub % g3(x,y)
add xshift2 add
centiinch myrand rr mul sub
ysave y sub
alpha sin x mul alpha cos y mul add % 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
alpha rotate % rotate the letter B
-1.01 inch -0.95 inch moveto
(B) show
grestore
% ****************************************** Fig. (d):
/alpha 6 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 0.5 p1 mul def % x phase shift for first dot screen (e.g. 0.5)
/yshift1 0.5 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
% draw first (reference) dot screen:
25 srand % seed for rand
/y dim2 neg def
gsave
5 inch 6.1 inch translate
% draw cross:
gsave
newpath
2.5 centiinch setlinewidth
0.1 inch 0 inch moveto
-0.2 inch 0 inch rlineto
0 inch 0.1 inch moveto
0 inch -0.2 inch rlineto
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% draw surrounding crosses:
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0.5 centiinch setlinewidth
%-1.400 inch -1.200 inch moveto
-1.150 inch -1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch -1.200 inch moveto
0.950 inch -1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%-1.400 inch 1.200 inch moveto
-1.150 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch 1.200 inch moveto
0.950 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
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% draw shifted surrounding crosses:
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1.5 centiinch 1.5 centiinch translate
0.5 centiinch setlinewidth
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0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch -1.200 inch moveto
0.950 inch -1.050 inch moveto
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-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%-1.400 inch 1.200 inch moveto
-1.150 inch 1.050 inch moveto
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-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
%1.000 inch 1.200 inch moveto
0.950 inch 1.050 inch moveto
0.2 inch 0 inch rlineto
-0.1 inch -0.1 inch rmoveto
0 inch 0.2 inch rlineto
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theta1 rot add rotate
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{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
xsave x sub
x % g1(x,y)
add xshift1 add
centiinch myrand rr mul sub
ysave y sub
y % 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
-1.01 inch -0.91 inch moveto
%(A) show
grestore
gsave
/Times-Roman findfont
12 scalefont setfont
-0.07 inch -1.15 inch moveto
((d)) show
grestore
grestore
% draw second dot screen:
25 srand % same seed for rand
/y dim2 neg def
gsave
5 inch 6.1 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
xsave x sub
alpha cos x mul alpha sin y mul sub % g3(x,y)
add xshift2 add
centiinch myrand rr mul sub
ysave y sub
alpha sin x mul alpha cos y mul add % 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
alpha rotate % rotate the letter B
-1.01 inch -0.95 inch moveto
(B) show
grestore
gsave
1.35 inch 1.4 inch translate
0 inch 0 inch moveto
/Times-Bold findfont
12 scalefont setfont
(Figure 3.2(a)-(d)) show
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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
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( by I. Amidror, published by Springer, 2007.) show
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((Second layer only.)) show
grestore
showpage