##+##########################################################################
#
# 7div.tcl -- Animation to test for divisibility by 7
# by Keith Vetter 2013-08-07

package require Tk

set PTS(0) {at 270 circle 0}
set PTS(1) {at 0 circle 0}
set PTS(2) {at 90 circle 0}
set PTS(3) {at 70 circle 1}
set PTS(4) {at 110 circle 1}
set PTS(5) {at 290 circle 1}
set PTS(6) {at 180 circle 0}

set ARCS(0,black) {circle 0 to 1}
set ARCS(0,white) {circle 2 to 0}
set ARCS(1,black) {circle 0 to 2}
set ARCS(1,white) {circle 1 to 3}
set ARCS(2,black) {line 10 to 3}
set ARCS(2,white) {circle 0 to 6}
set ARCS(3,black) {circle 1 to 4}
set ARCS(3,white) {line 10 to 2}
set ARCS(4,black) {line 11 to 5}
set ARCS(4,white) {line 11 to 5}
set ARCS(5,black) {circle 1 to 6}
set ARCS(5,white) {circle 1 to 1}
set ARCS(6,black) {circle 0 to 0}
set ARCS(6,white) {circle 1 to 4}

set ARROW(0) {black_delta 8 15 white_delta 0 -20}
set ARROW(1) {black_delta 20 -5 white_delta -20 0}
set ARROW(2) {black_delta -15 10 white_delta -10 -15}
set ARROW(3) {black_delta -20 -18 white_delta 10 -15}
set ARROW(4) {black_delta -15 15 white_delta 30 10}
set ARROW(5) {black_delta -20 -12 white_delta 10 -18}
set ARROW(6) {black_delta -15 5 white_delta 22 -5}

set S(rad,0,a) 350
set S(rad,0,b) 300
set S(rad,0,y) 0
set S(rad,1,a) 350
set S(rad,1,b) 150
set S(rad,1,y) 0
set d [expr {($S(rad,0,b) - $S(rad,1,b))}]
set r [expr {$d * 5 / 12.0}]
set S(rad,2,a) $r
set S(rad,2,b) $r
set S(rad,2,y) [expr {$S(rad,0,b) - $r}]
set S(cross,10) {2 3}
set S(cross,11) {4 5}
set S(animate,stepSize) 5
set S(animate,delay) 20
set S(animate,extraDelay) 1000
set S(number,candidate) 315
set S(box) 10
set S(digits,font) {Times 48 bold}
set S(breadcrumbs) 1

set S(w) [expr {2*$S(rad,0,a) + 150}]
set S(h) [expr {2*$S(rad,0,b) + 150}]
set S(state) unstarted

proc DoDisplay {} {
    global S

    wm title . "Divisible by 7"
    
    frame .digits -bd 2 -relief solid -pady 3m
    pack .digits -side bottom -fill x
    ShowNumber $S(number,candidate)
    
    canvas .c -width $S(w) -height $S(h) -bd 0 -highlightthickness 0 -bg green4
    bind .c <Configure> {CenterCanvas %W %w %h}
    pack .c -side top -fill both -expand 1
    DrawOval 0 -width 5
    DrawOval 1 -width 5
    DrawOval 2 -width 5
    DrawPoints
    DrawCrossing 10 -width 5
    DrawCrossing 11 -width 5
    DrawArrows -width 10
    .c create oval [Box {*}$S(0,xy) 30] -tag animate -fill {} -width 10 -outline red

    ::ttk::frame .ctrl -padding 1m
    ::ttk::frame .ctrl.top
    ::ttk::label .ctrl.l -text "Number to test:"
    ::ttk::entry .ctrl.e -textvariable ::S(number,candidate) -width 5
    bind .ctrl.e <Key-Return> {.ctrl.test invoke}
    ::ttk::button .ctrl.test -text "Start" -command Start
    ::ttk::button .ctrl.about -text "About" -command About
    grid .ctrl.l .ctrl.e -sticky ew -in .ctrl.top
    grid columnconfigure .ctrl.top 1 -weight 1
    pack .ctrl.top -fill x
    pack .ctrl.test .ctrl.about -expand 1 -side left
    place .ctrl -in .c -relx 1 -rely 0 -x -10 -y 10 -anchor ne
    
}
proc ShowNumber {number} {
    destroy {*}[winfo child .digits]
    set digits " "
    if {[string is integer -strict $number]} {
        set ::S(msg) "Testing if $number is divisible by 7"
        set digits $number
    } elseif {[string trim $number] eq ""} {
        set ::S(msg) ""
    } else {
        set ::S(msg) "$number is not an integer"
    }
    for {set i 0} {$i < [string length $digits]} {incr i} {
        set digit [string index $digits $i]
        label .digits.d$i -text $digit -font $::S(digits,font)
        pack .digits.d$i -side left
    }
    frame .digits.bar -bg black -padx 1
    label .digits.msg -textvariable ::S(msg) -font $::S(digits,font)
    pack .digits.bar -side left -fill y
    pack .digits.msg -side left -fill both -expand 1
}

proc HighlightDigit {how digits subIdx idx} {
    global S
    set w .digits.d$idx
    if {$how eq "over"} {
        if {$idx == 0} {
            set S(msg) "$digits is divisible by 7"
        } else {
            set S(msg) "$digits is not divisible by 7"
        }
    } elseif {$how eq "done"} {
        $w config -bd 0 -bg [lindex [$w config -bg] 3]
    } elseif {$how eq "begin"} {
        set digit [string index $digits $idx]
        $w config -bd 2 -relief raised -bg black -fg magenta
        .c itemconfig breadcrumbs -fill cyan -tag breadcrumbs,old
        set S(msg) "Processing digit '$digit'"
        return $S(animate,extraDelay)
    } elseif {$how eq "black"} {
        set digit [string index $digits $idx]
        incr subIdx
        set S(msg) "Black step #$subIdx for '$digit'"
    } elseif {$how eq "white"} {
        set digit [string index $digits $idx]
        $w config -bg white
        set S(msg) "White step for '$digit'"
    } else {
        error "unknown how: $how"
    }
    return 1
}


proc ArcCoords {from color} {
    global S PTS ARCS

    lassign $ARCS($from,$color) type which . to
    if {$type eq "line"} {
        set xy [concat $S($from,xy) $S($to,xy)]
    } else {
        set startAngle [lindex $PTS($from) 1]
        set endAngle [lindex $PTS($to) 1]
        set xy [OvalCoords $which $startAngle $endAngle 5]
    }
    return $xy
}
proc ArrowCoords {from color distance} {
    global S ARCS

    set xy [ArcCoords $from $color]
    set axy {}
    
    set soFar 0
    lassign $xy x0 y0
    foreach {x1 y1} $xy {
        set leg [expr {hypot($x1-$x0, $y1-$y0)}]
        if {$soFar + $leg < $distance} {
            lappend axy $x1 $y1
            set soFar [expr {$soFar + $leg}]
        } else {
            set short [expr {$distance - $soFar}]
            lassign [ResizeLine $x0 $y0 $x1 $y1 $short] x y
            lappend axy $x $y
            break
        }
        lassign [list $x1 $y1] x0 y0
    }
    return $axy
}
proc LineLength {xy} {
    set total 0
    lassign $xy x0 y0
    foreach {x1 y1} $xy {
        set leg [expr {hypot($x1-$x0, $y1-$y0)}]
        set total [expr {$total + $leg}]
        lassign [list $x1 $y1] x0 y0
    }
    return $total
}
proc SegmentLine {xy maxLen} {
    set segments {}
    
    lassign $xy x0 y0
    set segment [list $x0 $y0]
    set segmentLength 0
    for {set idx 2} {$idx < [llength $xy]} {incr idx 2} {
        lassign [lrange $xy $idx $idx+1] x1 y1
        set leg [expr {hypot($x1-$x0, $y1-$y0)}]
        while {$segmentLength + $leg > $maxLen} {
            set short [expr {$maxLen - $segmentLength}]
            lassign [ResizeLine $x0 $y0 $x1 $y1 $short] x y
            lappend segments [concat $segment $x $y]
            set segment [list $x $y]
            set segmentLength 0

            lassign [list $x $y] x0 y0
            set leg [expr {hypot($x1-$x0, $y1-$y0)}]
        }
        lappend segment $x1 $y1
        set segmentLength [expr {$segmentLength + $leg}]
        lassign [list $x1 $y1] x0 y0
    }
    if {$segmentLength > 0} {
        lappend segments $segment
    }
    return $segments
}

proc ResizeLine {x0 y0 x1 y1 newLength} {
    set leg [expr {hypot($x1-$x0, $y1-$y0)}]
    set dx [expr {$x1 - $x0}]
    set dy [expr {$y1 - $y0}]

    set x [expr {$x0 + $dx * $newLength / $leg}]
    set y [expr {$y0 + $dy * $newLength / $leg}]

    return [list $x $y]
}
proc CenterCanvas {W w h} {
    set w [expr {$w / 2}]
    set h [expr {$h / 2}]
    $W config -scrollregion [list -$w -$h $w $h]
}
proc DrawOval {who args} {
    global S

    set xy [OvalCoords $who 0 360 5]
    .c create line $xy -tag oval$who {*}$args
    return "oval$who"
}
proc OvalCoords {who start end {delta 5}} {
    global S
    
    set a $S(rad,$who,a)
    set b $S(rad,$who,b)
    set y0 [expr {[info exist S(rad,$who,y)] ? $S(rad,$who,y) : 0}]
    set xy {}

    # Which direction
    set clockwise [expr {($end - $start) % 360}]
    set anticlockwise [expr {($start - $end) % 360}]
    set dir [expr {$clockwise <= $anticlockwise ? "clockwise" : "anticlockwise"}]
    if {$dir eq "anticlockwise"} {
        lassign [list $start $end] end start
    }
    if {$end <= $start} { incr end 360 }
    
    for {set deg $start} {$deg <= $end} {incr deg $delta} {
        set rad [expr {acos(-1) * $deg / 180}]

        set x [expr {$a * cos($rad)}]
        set y [expr {$y0 - $b * sin($rad)}]
        set x [format %.2f $x]
        set y [format %.2f $y]
        if {$dir eq "anticlockwise"} {
            set xy [concat $x $y $xy]
        } else {
            lappend xy $x $y
        }
    }
    return $xy
}
proc DrawArrows {args} {
    global S

    for {set who 0} {$who < 7} {incr who} {
        set dx0 0 ; set dy0 0 ; set dx1 0 ; set dy1 0
        lassign $::ARROW($who) . dx0 dy0 . dx1 dy1
        set xy [ArrowCoords $who black 40]
        set id [.c create line $xy -tag arrow,$who,black -fill black -arrow last -arrowshape {12 12 7} {*}$args]
        .c move $id $dx0 $dy0

        set xy [ArrowCoords $who white 40]
        set id [.c create line $xy -tag arrow,$who,white -fill white -arrow last -arrowshape {12 12 7} {*}$args]
        .c move $id $dx1 $dy1
    }
}
proc DrawPoints {} {
    global S
    for {set i 0} {$i < 7} {incr i} {
        #lassign $S($i) who degree
        lassign $::PTS($i) . degree . whichOval
        set a $S(rad,$whichOval,a)
        set b $S(rad,$whichOval,b)
        set S($i,xy) [PointOnEllipse $degree $a $b]

        .c create oval [Box {*}$S($i,xy) $S(box)] -fill black -tag [list points p$i]
    }
    set id [.c create poly [MakeStar {*}$S(0,xy) $S(box)] -fill green1 -tag {points p0}]
    .c move $id 1 0
}
proc DrawCrossing {who args} {
    set xy [CrossingCoords $who]
    .c create line $xy {*}$args
}
proc CrossingCoords {who} {
    global S
    lassign $S(cross,$who) node1 node2
    return [concat $S($node1,xy) $S($node2,xy)]
}
proc Box {x y r} {
    return [list [expr {$x-$r}] [expr {$y-$r}] [expr {$x+$r}] [expr {$y+$r}]]
}
proc PointOnEllipse {degree a b} {
    set rad [expr {acos(-1) * $degree / 180}]

    set x [expr {$a * cos($rad)}]
    set y [expr {-$b * sin($rad)}]
    set x [expr {round($x)}] ; set y [expr {round($y)}]
    return [list $x $y]
}

proc MakeStar {x y delta} {
    set pi [expr {acos(-1)}]

    # Compute distance to inner corner
    #set x1 [expr {$delta * cos(54 * $pi/180)}]  ;# Unit vector to inner point
    set y1 [expr {sin(54 * $pi/180)}]
    set y2 [expr {$delta * sin(18 * $pi/180)}]  ;# Y value to match
    set delta2 [expr {$y2 / $y1}]

    # Now get all coordinates of the 5 outer and 5 inner points
    for {set i 0} {$i < 10} {incr i} {
        set d [expr {($i % 2) == 0 ? $delta : $delta2}]
        set theta [expr {(90 + 36 * $i) * $pi / 180}]
        set x1 [expr {$x + $d * cos($theta)}]
        set y1 [expr {$y - $d * sin($theta)}]

        lappend coords $x1 $y1
    }
    return $coords
}

proc About {} {
    set msg "7 Graphical Divisibility Test\nby Keith Vetter -- April, 2016\n\n"
    append msg "Here's a simple, graphical way to test for divisibility by seven.\n\n"
    append msg "Start at the starred node at the bottom. Now take each digit in turn "
    append msg "from left to right in your number. For each digit, follow that many "
    append msg "black arrows in a row, and then add one white arrow. If you finish at "
    append msg "the bottom, then your number is divisible by 7.\n\n"
    append msg "How does it work? Here's a hint: the white arrows correspond to 10x mod 7."

    tk_messageBox -message $msg
}

namespace eval ::Animate {}

proc ::Animate::StepsForLeg {whichNode idx digits} {
    global ARCS

    set digit [string index $digits $idx]
    
    set steps {}
    lappend steps "begin" [list - $idx]
    for {set i 0} {$i < $digit} {incr i} {
        lappend steps "black" [list $i $idx]
        lappend steps {*}[::Animate::Xy2Steps [ArcCoords $whichNode black]]
        set whichNode [lindex $ARCS($whichNode,black) 3]
    }
    lappend steps "white" [list - $idx]
    lappend steps {*}[::Animate::Xy2Steps [ArcCoords $whichNode white]]
    lappend steps "done" [list - $idx]
    
    set whichNode [lindex $ARCS($whichNode,white) 3]
    return [list $whichNode $steps]
}
proc ::Animate::Xy2Steps {xy} {
    global S

    set segments [SegmentLine $xy $S(animate,stepSize)]
    set steps [lrange [lindex $segments 0] 0 1]
    set steps {}
    foreach segment $segments {
        lappend steps {*}[lrange $segment end-1 end]
    }
    return $steps
}
proc Start {} {
    global S
    
    set S(number,candidate) [string trim $S(number,candidate)]
    if {$S(state) eq "unstarted"} {
        ResetAnimation
        set S(state) started
        7Test $S(number,candidate)
    } else {
        set S(state) unstarted
    }
}
proc 7Test {digits} {
    ShowNumber $digits
    if {[string is integer -strict $digits]} {
        DoAnimation $digits 0 {} 0
    } else {
        set ::S(state) "unstarted"
    }
}
proc ResetAnimation {} {
    .c delete breadcrumbs breadcrumbs,old
    .c coords animate [Box {*}$::S(0,xy) 30]
}
proc DoAnimation {digits idx steps where} {
    global S
    
    if {$S(state) ne "started"} return
    if {$steps eq {} && $idx >= [string length $digits]} {
        HighlightDigit "over" $digits - $where
        set S(state) "unstarted"
        return
    }
    
    set nextWhere $where
    if {$steps eq {}} {
        set digit [string index $digits $idx]
        lassign [::Animate::StepsForLeg $where $idx $digits] nextWhere steps
        incr idx
    }

    set extraDelay 1
    if {$steps ne {}} {
        set nextSteps [lassign $steps newX newY]
        if {$newX in {"begin" "black" "white" "done"}} {
            set extraDelay [HighlightDigit $newX $digits {*}$newY]
        } else {
            lassign [.c bbox animate] x0 y0 x1 y1
            set x [expr {($x1 + $x0)/2}] ; set y [expr {($y1 + $y0)/2}]
            set dx [expr {$newX - $x}] ; set dy [expr {$newY - $y}]
            if {$S(breadcrumbs)} {
                set xy [.c coords breadcrumbs]
                if {$xy eq {}} {
                    .c create line $x $y $x $y -tag breadcrumbs -fill red -width 4
                    .c raise points
                    .c raise animate
                } else {
                    lappend xy $x $y
                    .c coords breadcrumbs $xy
                }   
            }
            .c move animate $dx $dy
        }
        set delay $S(animate,delay)
        if {$extraDelay > 1} {
            set delay $extraDelay
        }
        after $delay [list DoAnimation $digits $idx $nextSteps $nextWhere]
    }
    return
}


DoDisplay
return

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