##+##########################################################################
 # 
 # triags -- Draws nested triangles and displays the total number of
 # triangles there are and also shows how many triangles of each size.
 # 
 # Keith Vetter Jun 24, 1998 - initial revision
 #
 
 ##+##########################################################################
 # 
 # DoDisplay -- puts up our interface
 # 
 proc DoDisplay {} {
    global w h
    
    canvas .c -width $w -height $h -bd 2 -relief ridge
    frame .bottom
    scale .s -orient h -from 1 -to 50 -command DrawTriangles -showvalue 0 \
        -variable S(n) -highlightthickness 0
    set ::S(n) 3
    focus .s
    label .lcntU -text "Up triangles: "
    label .lcntD -text "Down triangles: "
    label .lcntT -text "Total triangles: "
    label .cntU -textvariable S(up)
    label .cntD -textvariable S(down)
    label .cntT -textvariable S(total)
    catch {image create photo ::img::blank -width 1 -height 1}
    button .about -image ::img::blank -highlightthickness 0 -command {
        tk_messageBox -title "About" -message "by Keith Vetter\nJanuary, 2003"}
    pack .c -side top -fill both -expand 1
    place .s -in .c -x 10 -y 5 -anchor nw
    pack .bottom -side bottom -fill x
 
    grid .lcntU .cntU -in .bottom
    grid .lcntD .cntD -in .bottom
    grid .lcntT .cntT -in .bottom
    grid configure .lcntU .lcntD .lcntT -sticky e
    grid configure .cntU  .cntD  .cntT  -sticky w
    grid columnconfigure .bottom 1 -weight 1
    place .about -in .c -relx 1 -rely 1 -anchor se
    update
    bind . <Configure> {triag $S(n)}
 }
 ##+##########################################################################
 # 
 # DrawTriangles -- called when the number of sides changes.
 # 
 proc DrawTriangles {n} {
    global S CNT
    
    .s config -label "Sides: $n"
    triag $n
    set S(up) [CountUp $n]
    set S(down) [CountDown $n]
    set S(total) [expr {$CNT(up) + $CNT(down)}]
 }
 ##+##########################################################################
 # 
 # triag -- draws an N sided triangle
 # 
 proc triag {n} {
    global w h alt len
 
    set w [winfo width .c]
    set h [winfo height .c]
    
    set alt [expr {($h - 20.0) / $n}]           ;# Scale to fit window
    set len [expr {($w - 20.0) / $n}]
    
    .c delete all
    set b [GetBottom $n]                       ;# Bottom coords
    set l [GetLeft $n]                         ;# Left side coords
    set r [GetRight $n]                        ;# Right side coords
    
    foreach {x1 y1} $l {x2 y2} $r {             ;# Parallel to bottom
        .c create line $x1 $y1 $x2 $y2 -width 2
    }
    foreach {x1 y1} $b {x2 y2} $r {             ;# Parallel to left side
        .c create line $x1 $y1 $x2 $y2 -width 2
    }
    foreach {x1 y1} [reverse $b] {x2 y2} $l {   ;# Parallel to right side
        .c create line $x1 $y1 $x2 $y2 -width 2
    }
 }    
 ##+##########################################################################
 # 
 # GetXY -- returns x,y coordinates for this triangle
 # 
 proc GetXY {row col} {
    global w len alt
 
    set y [expr {round(10 + $row * $alt)}]
    set x [expr {round($w/2.0 + $len * ($col - $row / 2.0))}]
    return [list $x $y]
 }
 ##+##########################################################################
 # 
 # GetBottom -- returns coordinates of all bottom side vertices
 # 
 proc GetBottom {n} {
    for {set c 0} {$c <= $n} {incr c} {
        eval lappend result [GetXY $n $c]
    }
    return $result
 }
 ##+##########################################################################
 # 
 # GetLeft -- returns coordinates of all left side vertices
 # 
 proc GetLeft {n} {
    for {set r 0} {$r <= $n} {incr r} {
        eval lappend result [GetXY $r 0]
    }
    return $result
 }
 ##+##########################################################################
 # 
 # GetRight -- returns coordinates of all right side vertices
 #
 proc GetRight {n} {
    for {set r 0} {$r <= $n} {incr r} {
        eval lappend result [GetXY $r $r]
    }
    return $result
 }
 ##+##########################################################################
 # 
 # reverse -- reverses a list (by pairs)
 # 
 proc reverse {l} {
    set r ""
    foreach {x y} $l {
        set r "$x $y $r"
    }
    return $r
 }
 ##+##########################################################################
 # 
 # CountUp -- counts how many upright triangles there are.
 # 
 proc CountUp {n} {
    global CNT
 
    set CNT(up) 0                               ;# Reset all values to zero
    for {set i 1} {$i <= $n} {incr i} {
        set CNT(up,$i) 0
    }
    
    for {set row 0} {$row < $n} {incr row} {
        set size 1
        set num [expr {$n - $row}]              ;# How many size 1 triangles
        while {$num > 0} {
            incr CNT(up,$size) $num
            incr CNT(up) $num
            incr num -1                         ;# One less triangle at size+1
            incr size
        }
    }
    set v "$CNT(up): "
    for {set i 1} {$i <= $n && $CNT(up,$i) > 0} {incr i} {
        append v "$CNT(up,$i) "
    }
    return $v
 }
 ##+##########################################################################
 # 
 # CountDown -- same as count but for upside down triangles
 # 
 proc CountDown {n} {
    global CNT
 
    set CNT(down) 0                             ;# Reset all values to zero
    for {set i 1} {$i <= $n} {incr i} {
        set CNT(down,$i) 0
    }
 
    for {set row 0} {$row < $n-1} {incr row} {
        set size 1
        set num [expr {$n - $row - 1}]          ;# How many size 1 triangles
        while {$num > 0} {
            incr CNT(down,$size) $num
            incr CNT(down) $num
            incr num -2                         ;# Two less triangles at size+1
            incr size
        }
    }
    set v "$CNT(down): "
    for {set i 1} {$i <= $n && $CNT(down,$i) > 0} {incr i} {
        append v "$CNT(down,$i) "
    }
    return $v
 
 }
 
 set w 276
 set h 276
 DoDisplay
 update
 wm geom . [wm geom .]                           ;# Keeps window from growing
 .c config -width 0 -height 0                    ;# Better resizing behavior