woody@chinacat.Unicom.COM (Woody Baker @ Eagle Signal) (04/10/90)
Here is a cute little bit of PS that I cooked up the other day.
Postscript lends itself well to drawing optical illusions. How about
y'all posting some. Does anyone have any Escher? (sic)
Somewhere, I have seen an impossible nut. I can't find a copy of it (it
was just a drawing). It was shown in an exploded diagram for the 3
pronged impossible "fork".
Cheers
Woody
%
% Optical illusion
% written by Woody Baker
% Rt.1 Box I
% Manor, Tx. 78653
%
% hereby placed in the public domain. Would appreciate the header
% remaining in-tact.
%
%
% do 1/4th of the drawing
%
/onequarter
{
60 160 moveto
20 160 lineto
20 80 lineto
160 80 lineto
60 180 moveto
0 180 lineto
0 60 lineto
160 60 lineto
40 160 moveto
40 100 lineto
160 100 lineto
60 200 moveto
20 200 lineto
0 180 lineto
40 100 moveto
20 80 lineto
} def
%
% draw the illusion and label it
%
/optical
{
0 0 moveto onequarter
gsave
-90 rotate -260 0 translate onequarter
-90 rotate -260 0 translate onequarter
-90 rotate -260 0 translate onequarter
stroke
grestore
/Helvetica findfont 20 scalefont setfont
-10 -25 moveto
(Brought to you By Woody Baker) show
} def
%
% application code. Positions and scales and draws the actual
% illusion.
%
/xcoord 140 def
/ycoord 240 def
gsave
xcoord ycoord translate
1 1 scale
optical
grestore
showpagersmith@well.sf.ca.us (Ross Smith) (04/11/90)
In article <1144@chinacat.Unicom.COM>, woody@chinacat.Unicom.COM (Woody Baker @ Eagle Signal) writes: > y'all posting some. Does anyone have any Escher? (sic) Here's an Escher drawing that I like. Setting Maxlevel to 3 takes 25 minutes on a LaserWriter so be patient. %! %Just in case anyone has an idle printer I am posting a close replication of %"Square-limit" by M.C.Escher. I have called it "Square-recursion" because it %builds the image by recursion, following the triangle subdivision used by %Escher. % %I have used Postscript graphics to the full, using transformations and curves %freely. However it takes a long time to run as a result. The version posted %has a variable "Maxlevel", which defaults to 0, and takes 2 minutes to %produce a core picture. Try that first, and check that all is well, then %if you wish the full gory detail set Maxlevel to 3, and wait 25 minutes (on %an Apple laser writer) % %> 2 min 10 seconds on a RIPS at 400 dpi %> comment added 7/89 by Ross Smith, PC Publishing. % %Any tips on improving the run time would be welcome. Have fun. % %John M Pratt, %European Computer-industry Research Centre, %Arabellastrasse 17, %D 8000 Munich 81, %West Germany. % %email- harry%ecrcvax.UUCP@Germany.CSNET % %-----------Cut Here---------------------- %!PS-Adobe-1.0 %%Title:Square-recursion %%DocumentFonts: (atend) %%Creator: John Pratt and M.C.Escher %%CreationDate:25 November 1987 %%Pages: (atend) %%EndComments %%EndProlog %%Page: 1 1 /Helvetica-Bold findfont 0.5 scalefont setfont /level 0 def %control variable for recursion /maxlevel 0 def %Limit of recursion, 3 takes 25 min. /Down { /level level 1 add def }def /Up {/level level 1 sub def} def /Colour 0 def %base colour variable /Parity 0 def /Swap {/Parity 0.5 Parity sub def} def /Odd-colour {/Colour Parity def} def /Even-Colour {/Colour 0.5 Parity sub def} def /White {/Colour 1 def} def /Comp {Colour 1 ne {1 setgray} {0 setgray} ifelse} def /cm {28.35 mul} def /Root2 2 sqrt def /Invr2 0.5 sqrt def /HeadMatrix matrix %create matrix for head triangle 45 matrix rotate matrix concatmatrix Invr2 neg Invr2 matrix scale matrix concatmatrix 0 10 matrix translate matrix concatmatrix def %cf 0 10 translate Invr2 neg Invr2 scale 45 rotate /UpheadMatrix HeadMatrix matrix invertmatrix def % cf -45 rotate Root2 neg Root2 scale 0 -10 translate /TailMatrix matrix %create matrix for tail triangle -45 matrix rotate matrix concatmatrix Invr2 neg Invr2 matrix scale matrix concatmatrix 0 10 matrix translate matrix concatmatrix def %cf {0 10 translate Invr2 neg Invr2 scale -45 rotate} /UptailMatrix TailMatrix matrix invertmatrix def % cf 45 rotate Root2 neg Root2 scale 0 -10 translate /Op1 matrix %matrix for duple opposite 0 -10 matrix translate matrix concatmatrix 180 matrix rotate matrix concatmatrix 0 10 matrix translate matrix concatmatrix def /Downhead {HeadMatrix concat} def %apply to CTM /Uphead {UpheadMatrix concat} def %apply to CTM /Downtail {TailMatrix concat} def %apply to CTM /Uptail {UptailMatrix concat} def %apply to CTM /Op {Op1 concat} def %apply to CTM /DwnR {HeadMatrix transform} def %applies Head matrix to point /UpR {UpheadMatrix transform} def %applies UpHead matrix to point /DwnL {TailMatrix transform} def %applies Tail matrix to point /UpL {UptailMatrix transform} def %applies UpTail matrix to point /Opp {Op1 transform} def %applies opposite matrix to point /Qflip {exch neg exch} def %Flip by X, X/Y point 180 /Qrot90 {exch neg} def %rotate X/Y point -90 /Qrotm90 {neg exch } def %rotate X/Y point 90 /Qxtran {3 -1 roll add exch} def %adds top to 3rd, X /A {10 10} def /A1 {9 8} def /A2 {7.5 6.2} def /Ah {A -1 Qxtran -0.5 add } def /B {6 5.6} def /B1 {4.8 5} def /B2 {2.2 4.5} def /C {0 5} def /C1 {-1.1 5.3} def /C2 {-4.2 6} def /D {B Qrotm90} def /D1 {A1 Qrotm90} def /D2 {A2 Qrotm90} def /E {A Qrotm90} def /E1 {A1 DwnL} def /E2 {A2 DwnL} def /Eh {Ah Qflip} def /F {B DwnL} def /F1 {F 2 Qxtran 2 sub} def /F2 {-2 7} def /G {0 7.6} def /G1 {2 8.2} def /G2 {3.2 9.5 } def /Gt {G UpL} def /H {5.1 10} def /H1 {6.5 10.5} def /H2 {8 10.5} def /I1 {0 4} def /I2 {0 2} def /J {0 0} def /J1 {3 0} def /J2 {3 0} def /K {C Qrot90} def /L {C DwnR} def /L1 {C1 DwnR }def /L2 {4.7 11} def /N {0 10.7} def /N1 {I1 DwnR} def /N2 {I2 DwnR} def /Nt {N UpL} def /P {L Qflip} def /Q1 {4.1 12.4} def /Q2 {2 13.1} def /a {A1 A2 B} def /b {B1 B2 C} def /c {C1 C2 D} def /d {D2 D1 E} def /e {E1 E2 F} def /f {F1 F2 G} def /fr {F2 UpL F1 UpL F UpL} def /g {G1 G2 H} def /h {H1 H2 A} def /hr {H2 H1 H} def /i {I1 I2 J } def /j {J1 J2 K} def /k {C1 Qrot90 C2 Qrot90 B} def % c with 90 rotate about O /l {L2 L1 L} def /lr {L1 L2 H} def %l reversed /n {N1 N2 N } def /ns {I1 I2 N UpR} def /nm (J M P) def /o {G} def /ot {Gt} def % straight line /p {I2 Qrot90 I1 Qrot90 C Qrot90} def %ie of tailfish /pr {I1 I2 Nt } def /q {Q1 Q2 G Opp} def /s {Comp nm Pup} def /Fr1 { %Fish righthand (convex side) A moveto a curveto b curveto c curveto d curveto } def /Fr2 { %Fish righthand for 45 deg angle A moveto a curveto b curveto Uphead %always used in head half lr curveto h curveto Downhead } def /Fl1 { %Fish lefthand (concave side) e curveto f curveto g curveto h curveto } def /Fl2 { %Fish lefthand for duple Op %using opposite fish points hr curveto q curveto Op %cancelling Op g curveto h curveto } def /Fc1 { %Fishcentre inside Ah moveto C C -0.6 Qxtran Eh curveto } def /Fc2 { %Fish centre outside and blunt ends Eh -0.05 add lineto C -0.25 add -0.6 Qxtran C -0.25 add Ah -0.05 add curveto Ah lineto } def /Tailrib1 {newpath -6 9 moveto -5 8 -4 7.3 -2.4 6.9 curveto stroke} def /Tailrib2 {newpath -5.5 6.7 moveto -4.5 6.3 -3.5 6.2 -2.3 6 curveto stroke} def /Tailrib3 {newpath -2.2 7.1 moveto -2.4 6.7 -2.4 6.2 -2.2 5.8 curveto stroke} def /Tailribs {Tailrib1 Tailrib2 Tailrib3} def /EyeshapeL {newpath -0.4 0.8 moveto 0.7 1.3 1.5 1.2 2.5 0.8 curveto 1.9 0 1.1 -0.4 0.1 -0.9 curveto 0 -0.2 -0.1 0.3 -0.4 0.8 curveto closepath} def /EyeL {gsave 5.6 8.9 translate EyeshapeL Colour 1 ne {fill}{stroke} ifelse grestore} def /EyePupL { gsave 5.8 9 translate 0.4 0.4 scale EyeshapeL fill grestore } def /EyeshapeR { newpath 0 0.8 moveto 1.4 1.6 1.9 1.6 2.6 1.5 curveto 2.4 0.8 1.6 0 0.1 -0.8 curveto 0.1 -0.3 0.1 0.3 0 0.8 curveto closepath } def /EyeR {gsave 5.9 6.7 translate EyeshapeR Colour 1 ne {fill}{stroke} ifelse grestore} def /EyePupR { gsave 6.1 6.7 translate 0.4 0.4 scale EyeshapeR fill grestore} def /Pupcol {Colour 1 ne {Colour setgray } if } def /Pup {-3 0 moveto show} def /FishMain { Comp %compliment colour newpath Fc1 Fc2 closepath gsave fill grestore Tailribs 0.01 setlinewidth EyeR EyeL Pupcol EyePupR EyePupL } def /Fish { Colour setgray newpath Fr1 Fl1 closepath gsave fill grestore FishMain } def /Fishd { Colour setgray newpath Fr1 Fl2 closepath gsave fill grestore FishMain} def /Fish45r {Colour setgray newpath Fr2 Fl1 closepath gsave fill grestore FishMain } def /Fish45d { Colour setgray newpath Fr2 Fl2 closepath gsave fill grestore FishMain} def /Ribl {newpath H moveto l curveto stroke } def /Ribk {newpath K moveto k curveto stroke }def /Ribf {newpath Gt moveto fr curveto stroke } def /Ribb {newpath B moveto b curveto stroke } def /Ribg {newpath G moveto g curveto stroke} def /Wingribs %stack SideRib WingRib Translate-offset Translate-inc Y-Scale-inc {4 copy 4 copy %copy parameters given for 3 ribs Comp 0.15 setlinewidth 0 1 2 {gsave %stack --Wr To Ti Sy Loopv dup dup 0.25 mul 0.75 exch sub %stack ----Sy Lv Lv Sx exch 4 -1 roll mul 0.95 exch sub %stack ---To Ti Lv Sx Sy scale %stack --To Ti Lv mul add 0 exch translate %stack --Wr cvx exec %execute WingRibxx grestore } for %stack Sr cvx exec } def %execute Sideribxx /QuadWing { Colour setgray newpath %wing for quad C moveto i curveto j curveto k curveto b curveto closepath fill /Ribb /Ribk 0.5 0 0 Wingribs } def /TriWing1 { Colour setgray newpath %wing on Hypoteneuse for triple G moveto g curveto l curveto n curveto o lineto closepath fill /Ribg /Ribl -0.5 0 0.04 Wingribs } def /TriWing2 { Colour setgray newpath %wing on head side for triple C moveto ns curveto p curveto k curveto b curveto closepath fill /Ribb /Ribk 0.5 0.1 0 Wingribs } def /TriWing3 { Colour setgray newpath %wing on tail side for triple C moveto pr curveto ot lineto fr curveto b curveto closepath fill /Ribb /Ribf 0.8 0.6 0.03 Wingribs }def /DupleWing { Colour setgray newpath %wing for duple G moveto g curveto q curveto o lineto closepath fill /Ribg /Ribl -0.5 0 0.04 Wingribs }def /Wings0 {QuadWing TriWing1} def /Wings1 {TriWing2 TriWing1} def /Wings2 {TriWing3 TriWing1} def /Wings3 {TriWing2 DupleWing} def /Wings4 {TriWing3 DupleWing} def /Wings5 {QuadWing DupleWing} def /Headpair {Downhead Odd-colour Wings1 Fish45r %fish Hh Down Sextet Up % recurse to smaller level -90 rotate %Uphead Downtail Even-Colour Wings4 Fishd Uptail %fish Ht } def /Tailpair {Downhead White Wings3 Fish45d %fish Th -90 rotate %Uphead Downtail Odd-colour Wings2 Fish %fish Tt Down Sextet Up Uptail } def /Sextet {level maxlevel le { Downhead White Wings1 Fish45r %fish H Headpair -90 rotate %Uphead+downtail Even-Colour Wings2 Fish %fish T Tailpair Uptail }if} def /RCorner {level maxlevel le { 20 0 translate Downtail Downhead White Wings5 Fish45d %fish Th with S wing -90 rotate %Uphead Downtail Odd-colour Wings0 Fish %fish Tt Down Sextet RCorner Up Uptail Uptail -20 0 translate }if } def /LCorner {level maxlevel le { -20 0 translate Downhead Downtail Even-Colour Wings5 Fishd %fish Ht with S wing 90 rotate %Uptail Downhead Odd-colour Wings0 Fish Down Sextet LCorner Up Uphead Uphead 20 0 translate }if } def /Centre {Odd-colour Wings0 Fish} def gsave 10 cm 15 cm translate 0.3 cm 0.3 cm scale 0.05 setlinewidth 1 setflat 1 setlinecap %% 133 45 {0.5 mul add} setscreen 60 40 {dup mul exch dup mul add 1.0 exch sub} setscreen 4 {Centre Sextet RCorner LCorner Swap -90 rotate} repeat s grestore showpage %%Trailer %%Pages: 1 %%DocumentFonts: Helvetica-Bold -- Ross Smith rsmith@well.sf.ca.us {apple,pacbell,hplabs,ucbvax}!well!rsmith
shaw@paralogics.UUCP (Guy Shaw) (04/13/90)
In article <1144@chinacat.Unicom.COM>, woody@chinacat.Unicom.COM (Woody Baker @ Eagle Signal) writes: > . . . How about y'all posting some. Does anyone have any Escher? (sic) I don't have an impossible nut, but here is an impossible triangle. %! % M. C. Escher style impossible triangle % written by Guy Shaw % Things that are easy to play with: % Position on paper, overall size, and linewidth /inch { 72 mul } bind def 2 inch dup translate 3 inch dup scale 1 3 inch div setlinewidth % Thickness parameter: % /Thick is the thickness of the structural members of the triange, % as a fraction of the height of the triangle. % Reasonable looking impossible triangles can be obtained with Thick <= 1/6. % right at /Thick == 1/6, there is no space left inside the triangle. % /Thick > 1/6 yields bizarre, but not very interesting results. % /Thick < 1/20 is less interesting, because the "impossibility" % is not so striking when the structural members are that thin. % A good "standard" value is 1/8. /Thick 1 8 div def % You would not normally want to change anything that follows. /Tall 1 def /HalfThick Thick .5 mul def newpath HalfThick Thick moveto Thick 0 lineto 1 Thick sub 0 lineto 1 HalfThick sub Thick lineto .5 HalfThick add Tall Thick sub lineto 1 Thick sub 0 moveto .5 HalfThick add Tall 3 Thick mul sub lineto Thick 3 mul Thick 2 mul lineto 1 Thick 2.5 mul sub Thick moveto .5 Tall Thick 4 mul sub lineto stroke newpath HalfThick Thick moveto 1 Thick 2.5 mul sub Thick lineto HalfThick neg Thick rlineto Thick Thick add Thick Thick add lineto .5 HalfThick add Tall Thick sub lineto Thick neg 0 rlineto closepath fill showpage -- Guy Shaw Paralogics paralogics!shaw@uunet.uu.net or uunet!paralogics!shaw