##+##########################################################################
 #
 # poly.tcl -- Draws polyhedron nets that you can print out, cut out, fold and
 # join tabs to construct your own polyhedra. See http://www.korthalsaltes.com
 # by Keith Vetter, March 5, 2003
 #
 
 package require Tk
 set S(bwidget) [expr {! [catch {package require BWidget}]}] ;# For combobox
 set S(title) "Polyhedron Nets"
 
 # Info for each polyhedron:
 #   name,I => {<# faces> <tab size>}
 #   name,# {<face polygon type> <where> <sides w/ tabs> <color>}
 #     where => EITHER <angle for side 0> OR {<neighbor face #> <attach side>}
 array set POLY {
   Tetrahedron,I {4 .1}
   Tetrahedron,0 {t 60 {0 2} blue} Tetrahedron,1 {t {0 1} {} yellow}
   Tetrahedron,2 {t {1 1} {} red}  Tetrahedron,3 {t {2 2} {2} green}
 
   Cube,I {6 .2}
   Cube,0 {s 0 {} yellow}     Cube,1 {s {0 1} {} blue}
   Cube,2 {s {0 2} {1 3} red} Cube,3 {s {2 2} {1 2} yellow}
   Cube,4 {s {0 3} {2} blue}  Cube,5 {s {0 0} {1 3} red}
 
   Octahedron,I {8 .2}
   Octahedron,0 {t 60 {} red}          Octahedron,1 {t {0 1} {} yellow}
   Octahedron,2 {t {1 1} {} cyan}      Octahedron,3 {t {2 2} {} blue}
   Octahedron,4 {t {3 1} {} green}     Octahedron,5 {t {0 2} {2} violet}
   Octahedron,6 {t {1 2} {1 2} orange} Octahedron,7 {t {2 1} {1 2} purple}
 
   Icosahedron,I {20 .2}
   Icosahedron,0 {t 60 {1} red}         Icosahedron,1 {t {0 0} {} blue}
   Icosahedron,2 {t {1 2} {1} cyan}     Icosahedron,3 {t {1 1} {1} green}
   Icosahedron,4 {t {2 2} {1} green}    Icosahedron,5 {t {4 2} {} yellow} 
   Icosahedron,6 {t {5 1} {} blue}      Icosahedron,7 {t {6 1} {2} cyan} 
   Icosahedron,8 {t {7 1} {2} red}      Icosahedron,9 {t {3 2} {1} red}
   Icosahedron,10 {t {9  2} {} yellow}  Icosahedron,11 {t {10 1} {} blue}
   Icosahedron,12 {t {11 1} {2} green}  Icosahedron,13 {t {12 1} {2} cyan}
   Icosahedron,14 {t {0 2} {1} cyan}    Icosahedron,15 {t {14 2} {} yellow}
   Icosahedron,16 {t {15 1} {} blue}    Icosahedron,17 {t {16 1} {} red}
   Icosahedron,18 {t {17 1} {2} green}  Icosahedron,19 {t {17 2} {} yellow}
 
   Dodecahedron,I {12 .2}
   Dodecahedron,0 {p 108 {} yellow}        Dodecahedron,1 {p {0 0} {4} blue}
   Dodecahedron,2 {p {0 1} {4} red}        Dodecahedron,3 {p {0 2} {4} blue}
   Dodecahedron,4 {p {0 3} {4} green}      Dodecahedron,5 {p {0 4} {4} red}
   Dodecahedron,6 {p {1 3} {2 3 4} yellow} Dodecahedron,7 {p {2 3} {3 4} green}
   Dodecahedron,8 {p {4 3} {2 3 4} yellow} Dodecahedron,9 {p {3 3} {2 3 4} red}
   Dodecahedron,10 {p {5 3} {2 3 4} green} Dodecahedron,11 {p {7 2} {} blue}
 
   Cubeoctahedron,I {14 .2}
   Cubeoctahedron,0 {s 90 {} yellow}     Cubeoctahedron,1 {t {0 2} {} blue}
   Cubeoctahedron,2 {s {1 2} {3} yellow} Cubeoctahedron,3 {t {2 2} {1 2} blue}
   Cubeoctahedron,4 {t {0 1} {} blue}    Cubeoctahedron,5 {s {4 2} {3} yellow}
   Cubeoctahedron,6 {t {5 2} {1 2} blue} Cubeoctahedron,7 {t {0 0} {} blue}
   Cubeoctahedron,8 {s {7 2} {3} yellow} Cubeoctahedron,9 {t {8 2} {1 2} blue}
   Cubeoctahedron,10 {t {0 3} {} blue}  Cubeoctahedron,11 {s {10 2} {3} yellow}
   Cubeoctahedron,12 {t {11 2} {2} blue} Cubeoctahedron,13 {s {12 1} {} yellow}
 
   Truncated\ Tetrahedron,I {8 .2}
   Truncated\ Tetrahedron,0 {h 120 {} green}
   Truncated\ Tetrahedron,1 {h {0 0} {3 4 5} blue}
   Truncated\ Tetrahedron,2 {t {0 1} {2} yellow}
   Truncated\ Tetrahedron,3 {h {0 2} {4 5} cyan}
   Truncated\ Tetrahedron,4 {t {3 3} {} yellow}
   Truncated\ Tetrahedron,5 {t {0 3} {2} yellow}
   Truncated\ Tetrahedron,6 {h {0 4} {3 4 5} red}
   Truncated\ Tetrahedron,7 {t {0 5} {2} yellow}
 
   Rhombicuboctahedron,I {26 .2}
   Rhombicuboctahedron,0 {s 180 {0} green}
   Rhombicuboctahedron,1 {t {0 1} {1} blue}
   Rhombicuboctahedron,2 {t {0 3} {2} blue}
   Rhombicuboctahedron,3 {s {0 2} {} red}
   Rhombicuboctahedron,4 {s {3 1} {1 2} green}
   Rhombicuboctahedron,5 {s {3 3} {2 3} green}
   Rhombicuboctahedron,6 {s {3 2} {} green}
   Rhombicuboctahedron,7 {t {6 1} {1} blue}
   Rhombicuboctahedron,8 {t {6 3} {2} blue}
   Rhombicuboctahedron,9 {s {6 2} {} red}
   Rhombicuboctahedron,10 {s {9 1} {1} green}
   Rhombicuboctahedron,11 {s {9 3} {3} green}
   Rhombicuboctahedron,12 {s {10 2} {} red}
   Rhombicuboctahedron,13 {s {11 2} {} red}
   Rhombicuboctahedron,14 {s {9 2} {} green}
   Rhombicuboctahedron,15 {t {14 1} {1} blue}
   Rhombicuboctahedron,16 {t {14 3} {2} blue}
   Rhombicuboctahedron,17 {s {14 2} {} red}
   Rhombicuboctahedron,18 {s {17 1} {1 2} green}
   Rhombicuboctahedron,19 {s {17 3} {2 3} green}
   Rhombicuboctahedron,20 {s {17 2} {} green}
   Rhombicuboctahedron,21 {t {20 1} {1} blue}
   Rhombicuboctahedron,22 {t {20 3} {2} blue}
   Rhombicuboctahedron,23 {s {20 2} {} red}
   Rhombicuboctahedron,24 {s {23 1} {1 2} green}
   Rhombicuboctahedron,25 {s {23 3} {2 3} green}
 
   Truncated\ Octahedron,I {14 .2}
   Truncated\ Octahedron,0 {h 180 {1 5} green}
   Truncated\ Octahedron,1 {h {0 3} {} cyan}
   Truncated\ Octahedron,2 {s {0 0} {} yellow}
   Truncated\ Octahedron,3 {s {1 1} {1 2} yellow}
   Truncated\ Octahedron,4 {s {1 3} {2} yellow}
   Truncated\ Octahedron,5 {s {1 5} {2 3} yellow}
   Truncated\ Octahedron,6 {h {1 2} {1 2 3 4 5} blue}
   Truncated\ Octahedron,7 {h {1 4} {1 2 3 4 5} red}
   Truncated\ Octahedron,8 {h {2 2} {} cyan}
   Truncated\ Octahedron,9 {s {8 2} {1} yellow}
   Truncated\ Octahedron,10 {s {8 4} {3} yellow}
   Truncated\ Octahedron,11 {h {8 1} {1} blue}
   Truncated\ Octahedron,12 {h {8 3} {1 5} green}
   Truncated\ Octahedron,13 {h {8 5} {} red}
 
   Truncated\ Cube,I {14 .4}
   Truncated\ Cube,0 {o 180 {0 1 5 6 7} yellow}
   Truncated\ Cube,1 {t {0 2} {} red}
   Truncated\ Cube,2 {t {0 4} {} red}
   Truncated\ Cube,3 {o {1 1} {} cyan}
   Truncated\ Cube,4 {t {3 2} {} red}
   Truncated\ Cube,5 {t {3 4} {} red}
   Truncated\ Cube,6 {t {3 6} {} red}
   Truncated\ Cube,7 {o {2 2} {} cyan}
   Truncated\ Cube,8 {o {0 3} {1 2 3 6 7} green}
   Truncated\ Cube,9 {o {8 4} {1 2 3 6 7} yellow}
   Truncated\ Cube,10 {o {9 4} {1 3 6 7} green}
   Truncated\ Cube,11 {t {8 5} {2} red}
   Truncated\ Cube,12 {t {9 5} {2} red}
   Truncated\ Cube,13 {t {10 5} {2} red}
 
   Truncated\ Cubeoctahedron,I {22 .4}
   Truncated\ Cubeoctahedron,0 {o 180 {0 1 7} cyan}
   Truncated\ Cubeoctahedron,1 {s {0 2} {1} yellow}
   Truncated\ Cubeoctahedron,2 {o {1 2} {} cyan}
   Truncated\ Cubeoctahedron,3 {s {0 6} {3} yellow}
   Truncated\ Cubeoctahedron,4 {o {3 2} {} cyan}
   Truncated\ Cubeoctahedron,5 {s {0 4} {} yellow}
   Truncated\ Cubeoctahedron,6 {h {5 1} {1 2 3} red}
   Truncated\ Cubeoctahedron,7 {h {5 3} {3 4 5} red}
   Truncated\ Cubeoctahedron,8 {o {5 2} {1 7} cyan}
   Truncated\ Cubeoctahedron,9 {s {8 2} {1 2} yellow}
   Truncated\ Cubeoctahedron,10 {s {8 6} {2 3} yellow}
   Truncated\ Cubeoctahedron,11 {s {8 4} {} yellow}
   Truncated\ Cubeoctahedron,12 {h {11 1} {1 2 3} red}
   Truncated\ Cubeoctahedron,13 {h {11 3} {3 4 5} red}
   Truncated\ Cubeoctahedron,14 {o {11 2} {1 7} cyan}
   Truncated\ Cubeoctahedron,15 {s {14 2} {1 2} yellow}
   Truncated\ Cubeoctahedron,16 {s {14 6} {2 3} yellow}
   Truncated\ Cubeoctahedron,17 {s {14 4} {} yellow}
   Truncated\ Cubeoctahedron,18 {h {17 1} {1 2 3} red}
   Truncated\ Cubeoctahedron,19 {h {17 3} {3 4 5} red}
   Truncated\ Cubeoctahedron,20 {o {17 2} {1 7} cyan}
   Truncated\ Cubeoctahedron,21 {s {20 2} {1 2} yellow}
   Truncated\ Cubeoctahedron,22 {s {20 6} {2 3} yellow}
 }
 #set len [llength [array names POLY "Truncated\ Cubeoctahedron,*"]]
 #set POLY(Truncated\ Cubeoctahedron,I) [list [incr len -1] .3]
 
 ;# Exterior angle and sides for various polygons
 array set polygon {t {120 3} s {90 4} p {72 5} h {60 6} o {45 8}}
 
 proc DoDisplay {} {
   wm title . $::S(title)
   pack [frame .ctrl -relief ridge -bd 2 -padx 5 -pady 5] \
       -side right -fill both -ipady 5
   pack [frame .top -relief raised -bd 2] -side top -fill x
   pack [frame .screen -bd 2 -relief raised] -side top -fill both -expand 1
 
   canvas .c -relief raised -borderwidth 0 -height 500 -width 500 \
       -highlightthickness 0
   label .msg -bg [.c cget -bg] -bd 2 -highlightthickness 0 \
       -textvariable S(type) -font {{Times Roman} 18 bold}
   pack .msg -in .screen -side top -fill x -expand 0
   pack .c -in .screen -side top -fill both -expand 1
 
   set ::S(color) blue
   set colors {red orange yellow green darkblue blue cyan purple violet white}
   lappend colors [lindex [.c config -bg] 3] black
   foreach color $colors {
       radiobutton .top.b$color -width 1 -padx 0 -pady 0 -bg $color \
           -variable ::S(color) -value $color
   }
   eval pack [winfo children .top] -side left -fill y
   bind .c <Configure> {CanvasCenter %W %h %w}
   bind all <Alt-c> {console show}
 
   DoCtrlFrame
   update
 }
 proc DoCtrlFrame {} {
   global S
 
   label .ltype -text "Polyhedron Type"
   .ltype configure -width 15 \
       -font "[font actual [.ltype cget -font]] -weight bold"
   if {$S(bwidget)} {
       ComboBox .type -textvariable S(type) -editable 0 -values [GetPTypes] \
           -exportselection 0 -justify center -takefocus 0
       grid .ltype - -in .ctrl -row 1 -sticky ew
       grid .type - -in .ctrl -row 2 -sticky ew
   } else {
       eval tk_optionMenu .type S(type) [GetPTypes]
       .type configure -width 20 -font [.ltype cget -font]
       grid .type - -in .ctrl -row 1 -sticky ew
   }
   trace add variable S(type) write DrawNet
 
   button .next -text Next -command {NextPoly 1}
   button .prev -text Prev -command {NextPoly -1}
   set txt "Print on heavy paper.\nFold all lines backwards."
   append txt "\nAttach the white tabs."
   label .instr -text $txt -font [.ltype cget -font] -justify left -anchor w
   button .post -text PostScript -command PrintIt
   button .about -text About -command About
 
   grid .prev .next -in .ctrl -sticky ew
   grid rowconfigure .ctrl 20 -minsize 100
   grid .instr - -in .ctrl -row 21
   grid rowconfigure .ctrl 50 -weight 1
   grid .post - -in .ctrl -row 100 -sticky ew
   grid .about - -in .ctrl -row 101 -sticky ew
 }
 proc GetPTypes {} {
   set ptypes {Tetrahedron Cube Octahedron Icosahedron Dodecahedron}
   foreach a [lsort -dictionary [array names ::POLY *,I]] {
       set type [lindex [split $a ","] 0]
       if {[lsearch $ptypes $type] > -1} continue ;# No duplicates
       lappend ptypes $type
   }
   return $ptypes
 }
 proc CanvasCenter {W h w} {
   foreach h [expr {$h / 2.0}] w [expr {$w / 2.0}] break
   $W config -scrollregion [list -$w -$h $w $h]
   ScaleIt
 }
 # DrawNet -- draws the net for the current polyhedron
 proc DrawNet {args} {
   global POLY V S
 
   .c delete all
   catch {unset V}
   foreach {faces S(tabsize)} $POLY($S(type),I) break
   set S(len) 100
   for {set face 0} {$face < $faces} {incr face} {
       foreach {type where} $POLY($S(type),$face) break
       GetVertices $type $where $face
   }
   CenterNet                                   ;# Shift to center net image
   DrawFaces $S(type)
   DrawTabs $S(type)
   ScaleIt
 }
 proc DrawFaces {ptype} {
   global POLY V
 
   set faces [lindex $POLY($ptype,I) 0]        ;# How many faces
   for {set face 0} {$face < $faces} {incr face} {
       set xy [GetFaceXY $face]
       set color [lindex $POLY($ptype,$face) 3]
       .c create poly $xy -tag [list poly f$face] -fill $color -outline black
       .c bind f$face <1> {.c itemconfig current -fill $S(color)}
   }
 }
 proc DrawTabs {ptype} {
   global POLY S
 
   set faces [lindex $POLY($ptype,I) 0]        ;# How many faces
   for {set face 0} {$face < $faces} {incr face} {
       set tabs [lindex $POLY($ptype,$face) 2]
       foreach tab $tabs {
           foreach {p0 p1} [GetSideXY $face $tab] break
           set v1 [RotateAdd $p1 $p0 120 $S(tabsize)]
           set v2 [RotateAdd $p0 $p1 -120 $S(tabsize)]
           set xy [concat $p0 $v1 $v2 $p1]
           .c create poly $xy -tag [list poly tab] -fill white -outline black
       }
   }
   .c lower tab
 }
 proc GetFaceXY {face} {
   global V
 
   set num [llength [array names V $face,*]]
   set xy {}
   for {set i 0} {$i < $num} {incr i} {
       set xy [concat $xy $V($face,$i)]
   }
   return $xy
 }
 proc GetSideXY {face n} {
   global V
 
   set n2 [expr {$n + 1}]
   if {! [info exists V($face,$n2)]} {set n2 0}
   return [list $V($face,$n) $V($face,$n2)]
 }
 # GetVertices -- populates V with all vertex info for every face
 proc GetVertices {type where face} {
   global S V polygon
 
   foreach {angle num} $polygon($type) break
   if {[llength $where] == 1} {                ;# First polygon
       set V($face,0) {0 0}
       set V($face,1) [RotateC [list $S(len) 0] -$where]
   } else {                                    ;# Polygon attached to another
       foreach {prev side} $where break
       foreach [list V($face,1) V($face,0)] [GetSideXY $prev $side] break
   }
   set p0 $V($face,0)
   set p1 $V($face,1)
   for {set i 2} {$i < $num} {incr i} {
       set V($face,$i) [RotateAdd $p0 $p1 $angle]
       set p0 $p1
       set p1 $V($face,$i)
   }
 }
 proc CenterNet {} {
   global V
 
   set an [array names V]                      ;# All the vertices
   set a1 [lindex $an 0]                       ;# First vertex
   set x0 [set x1 [lindex $V($a1) 0]]          ;# Initial min/max values
   set y0 [set y1 [lindex $V($a1) 1]]
 
   foreach a $an {
       foreach {x y} $V($a) break
       if {$x < $x0} {set x0 $x} elseif {$x > $x1} {set x1 $x}
       if {$y < $y0} {set y0 $y} elseif {$y > $y1} {set y1 $y}
   }
   set midx [expr {($x0 + $x1)/2}]             ;# This should be the center
   set midy [expr {($y0 + $y1)/2}]
 
   foreach a $an {
       foreach {x y} $V($a) break
       set V($a) [list [expr {$x - $midx}] [expr {$y - $midy}]]
   }
 }
 proc GetVector {p0 p1 {sc 1}} {
   foreach {x0 y0} $p0 {x1 y1} $p1 break
   return [list [expr {$sc * ($x1-$x0)}] [expr {$sc * ($y1-$y0)}]]
 }
 proc AddVector {v0 v1} {
   foreach {x0 y0} $v0 {x1 y1} $v1 break
   return [list [expr {$x1+$x0}] [expr {$y1+$y0}]]
 }
 proc RotateAdd {p0 p1 angle {sc 1}} {
   set v [GetVector $p0 $p1 $sc]
   set v [RotateC $v $angle]
   return [AddVector $p1 $v]
 }
 # RotateC -- rotates vector v by beta degrees clockwise
 proc RotateC {v beta} {
   foreach {x y} $v break
   set beta [expr {$beta * atan(1) * 4 / 180.0}]
   set xx [expr {$x * cos($beta) - $y * sin($beta)}]
   set yy [expr {$x * sin($beta) + $y * cos($beta)}]
   return [list $xx $yy]
 }
 # ScaleIt -- scales everything to just fit on the canvas
 proc ScaleIt {} {
   set bbox [.c bbox poly]
   if {[llength $bbox] == 0} return
   foreach {x0 y0 x1 y1} [.c bbox poly] break
   foreach w [winfo width .c] h [winfo height .c] break
 
   set s [GetZoom $bbox $w $h 20]
   if {$s == 0} return
   .c scale poly 0 0 $s $s
 }
 proc GetZoom {bbox w h margin} {
   foreach {x0 y0 x1 y1} [.c bbox poly] break
   set pw [expr {$x1 - $x0}]
   set ph [expr {$y1 - $y0}]
   set sw [expr {double($w - $margin) / $pw}]
   set sh [expr {double($h - $margin) / $ph}]
   if {$sh < $sw} {set s $sh} else {set s $sw}
   return $s
 }
 proc NextPoly {{dir 1}} {
   global S
   set ptypes [GetPTypes]
   set len [llength $ptypes]
 
   set n [lsearch $ptypes $S(type)]
   set n [expr {($n + $dir) % $len}]
   set S(type) [lindex $ptypes $n]
 }
 proc PrintIt {{zoom 1}} {
   set height 1350
   set width 975
   set pageheight 9.0i
   set pagewidth 6.5i
   set fname [file join [pwd] polyhedron.ps]
 
   set bbox [.c bbox all]
   set zoom [GetZoom $bbox $width $height 0]
   set width [expr {$width / $zoom}]
   set height [expr {$height / $zoom}]
   foreach {x0 y0 x1 y1} $bbox break
   set x [expr {($x0 + $x1 - $width) / 2}]     ;# Upper left corner
   set y [expr {($y0 + $y1 - $height) / 2}]
 
   set err [.c postscript -file $fname -rotate false -colormode color \
                -x $x -y $y -width $width -height $height \
                -pageheight $pageheight -pagewidth $pagewidth]
   if {$err == ""} {
       set msg "Created postscript version of the map in\n$fname"
   } else {
       set msg "Postscript creation error:\n$err"
   }
   tk_messageBox -title "Print" -message $msg
 }
 proc About {} {
   set msg "$::S(title)\nby Keith Vetter, March 2003\n\n"
   append msg "A polyhedron net is the planar unfolding of a polyhedron,\n"
   append msg "with each polygon represents a face of the polyhedron.\n"
   append msg "Included here are all five Platonic solids and several\n"
   append msg "of the thirteen Archimedean solids.\n\n"
   append msg "You can make a 3-D model of a polyhedron by printing\n"
   append msg "out a net, cutting it out, folding along the lines and\n"
   append msg "attaching the tabs. You can change the color of any\n"
   append msg "face by selecting a color and clicking on the polygon.\n\n"
   append msg "You cannot print directly from this program, but you can\n"
   append msg "create a color postscript version the net which you can\n"
   append msg "print using other tools."
   tk_messageBox -title "About $::S(title)" -message $msg
 }
 
 DoDisplay
 set S(type) [lindex [GetPTypes] [expr {int(rand() * [llength [GetPTypes]])}]]