.PS # EscherSVG.m4 # https://tex.stackexchange.com/questions/129274/showcase-of-optical-illusions-made-with-tex-latex-luatex-context threeD_init [ u=1/2.54 # unit size; could use scale for this define(`treadcolor',`0.8,0.75,0.7') define(`darkgrn',`.1,.1,0') define(`lightgrn',`.7,.7,.6') define(`northsteps',3) define(`eaststeps',8) define(`southsteps',7) define(`weststeps',4) define(`baselayers',10) define(`eb',eval(baselayers+eaststeps)) define(`ebs',eval(eb+southsteps)) define(`under',7) azimuth = -45 # view angles elevation = 25 setview(azimuth,elevation,0) # projected unit vectors UX: Project(u,0,0) UY: Project(0,-u,0) UZ: Project(0,0,u) # layer thickness in units of u f= -(eaststeps*UX.y + southsteps*UY.y - weststeps*UX.y - northsteps*UY.y)/dnl ((eaststeps+southsteps+weststeps+northsteps)*UZ.y) # XY projection of 3D coords in units of u define proj {UX*($1)+UY*($2)+UZ*($3)} define tread {line from UY/2 \ to UY then to UY+UX then to UX then to (0,0) \ then to UY/2 shaded rgbstring(treadcolor) \ with .start at proj($1,$2,$3)+UY/2 } define wrect {line invis from (0,0) to UX*($4) \ then to UX*($4)+UZ*($5) \ then to UZ*($5) then to (0,0) with .start at proj($1,$2,$3) \ shaded rgbstring(r,g,b)} define srect {line invis from (0,0) to UY*($4) then to UY*($4)+UZ*($5) \ then to UZ*($5) then to (0,0) with .start at proj($1,$2,$3) \ shaded rgbstring(r,g,b) } # color blending define(`blendwht',`between3D(`$1',`$2',`$3',`$4',1,1,1)') define makergb { r = $1; g = $2; b = $3 } define dorgb { gg = $2 if $1==0 then { makergb(blendwht(gg,lightgrn)) } \ else { makergb(blendwht(gg,darkgrn)) } } # East for i=-under to baselayers do { dorgb((i%2),0.2) wrect(1,1,i*f,eaststeps-2,-f) } for i=0 to eaststeps do { dorgb((i%2),0.2) wrect(i,1,(baselayers+i)*f,(eaststeps+1-i),-f) tread(i,0,(baselayers+i)*f) line from proj(i,1,(baselayers+i)*f) \ to proj(i,1,(baselayers-1+i)*f) } # South for i=0 to eb do { dorgb((i%2),0.4) srect(eaststeps+1,0,i*f,southsteps+1,-f) } for i=1 to southsteps do { dorgb((i%2),0.4) srect(eaststeps+1,i,(eb+i)*f,(southsteps+1-i),-f) tread(eaststeps,i,(eb+i)*f) line from proj(eaststeps+1,i,(eb+i)*f) \ to proj(eaststeps+1,i,(eb+i-1)*f) } # North for i=-under to baselayers-northsteps-1 do { dorgb((i%2),0.1) srect(1,1,i*f,northsteps-1,-f) } for i=1 to northsteps do { dorgb((i%2),0.1) srect(1,1,(baselayers-i)*f,i,-f) wrect(0,1+i,(baselayers-i)*f,1,-f) line from proj(0,1+i,(baselayers-i)*f) \ to proj(0,1+i,(baselayers-i-1)*f) line from proj(1,1+i,(baselayers-i)*f) \ to proj(1,1+i,(baselayers-i-1)*f) tread(0,i,(baselayers-i)*f) } # West for i=0 to ebs do { dorgb((i%2),0.4) wrect(eaststeps+1,southsteps+1,i*f,-(weststeps+1),-f) } for i=0 to weststeps-1 do { dorgb((i%2),0.4) wrect(eaststeps-i,southsteps+1,(ebs+i+1)*f,-(weststeps-i),-f,) srect(eaststeps-i,southsteps,(ebs+i+1)*f,1,-f) if i!=weststeps-1 then { line from proj(eaststeps-i,southsteps,(ebs+i+1)*f) \ to proj(eaststeps-i,southsteps,(ebs+i)*f) } line from proj(eaststeps-i,southsteps+1,(ebs+i+1)*f) \ to proj(eaststeps-i,southsteps+1,(ebs+i)*f) tread(eaststeps-(i+1),southsteps,(ebs+i+1)*f) } # Corner lines define(`dgreen',`outlined rgbstring(blendwht(0.2,darkgrn))') line dgreen from proj(1,1,(baselayers-1)*f) to proj(1,1,-under*f) line dgreen from proj(eaststeps+1,southsteps+1,ebs*f) \ to proj(eaststeps+1,southsteps+1,-f) line dgreen from proj(0,northsteps+1,(baselayers-northsteps)*f) \ to last line.end-UX*(weststeps+1) then to last line.end \ then to proj(eaststeps+1,0,-f) then to proj(eaststeps+1,0,eb*f) ] ifelse(1,1,` [ setview(-45,20) bwid = 2.8 bh = 1.5 bdp = 1.8 bth = 0.3 A: Project(0,0,0) AA: A+Project(bth,bth,-bth) B: Project(0,bwid,0) BB: B+Project(bth,-bth,-bth) C: Project(bdp,bwid,0) D: Project(bdp,0,0) E: Project(0,0,-bh) F: Project(bdp,0,-bh) G: Project(bdp,bwid,-bh) H: B + Project(0,0,-bh) line from A to B then to C then to D then to A then to E then to F \ then to G then to H then to E line from C to G line from A+Project(bth,bth,0) to B+Project(bth,-bth,0) \ then to C+Project(-bth,-bth,0) L1: line to D+Project(-bth,bth,0) L2: line to A+Project(bth,bth,0) L4: line from E+Project(bth,bth,0) to H+Project(bth,-bth,0) L3: line to C+Project(-bth,-bth,-bh) line to F+Project(-bth,bth,0) then to A+Project(bth,bth,-bh) L5: line from D+Project(-bth,0,-bth) to A+Project(bth,0,-bth) line to E+Project(bth,0,bth) L6: line to Here+Project(0,bwid-2*bth,0) L7: line from D+Project(0,bth,-bth) to C+Project(0,-bth,-bth) line to G+Project(0,-bth,bth) L8: line to Here+Project(-bdp+2*bth,0,0) Tmp: line invis from L8.start+Project(-bth,0,0) up bh line from Tmp.start to Intersect_(Tmp,L7) Tmp: line invis from L8.end up bh line from L8.end to Intersect_(Tmp,L7) line from Intersect_(Tmp,L1) to BB+Project(bth,0,0) Tmp: line invis to Here+Project(bdp,0,0) line from Tmp.start to Intersect_(Tmp,L1) Tmp: line invis from H up bh line from H to Intersect_(Tmp,L7) line from Intersect_(Tmp,L1) to B+Project(bth,-bth,0) Tmp: line invis from AA to AA+Project(0,bwid,0) Tmp2: line invis up bh from L6.end line from Intersect_(Tmp,L2) to Intersect_(Tmp2,Tmp) \ then to Intersect_(Tmp2,L1) line from L6.end to Intersect_(Tmp2,L7) Tmp: line invis down bh from AA line from Intersect_(Tmp,L6) to Intersect_(Tmp,L5) Tmp: line invis down bh from D line from D to Intersect_(Tmp,L6) line from Intersect_(Tmp,L4) to F+Project(-bth,bth,0) Tmp: line invis from L5.start to L5.start+Project(0,0,-bh) move to E+Project(0,2*bth,0) Tmp2: line invis to Here+Project(bdp,0,0) line from L5.start to Intersect_(Tmp,L6) line from Intersect_(Tmp,L4) to Intersect_(Tmp,Tmp2) \ then to Intersect_(Tmp2,L4) Tmp: line invis from L7.start to L7.start+Project(0,0,-(bh-bth)) line from L7.start to Intersect_(Tmp,L6) move to G+Project(-2*bth,0,0) Tmp2: line invis to Here+Project(0,-bwid,0) line from Intersect_(Tmp2,L3) to Intersect_(Tmp,Tmp2) line from Intersect_(Tmp,L4) to Intersect_(Tmp2,Tmp) ] with .sw at last [].se+(0.2,0) ') .PE