Arbitrary Rectangle Selection

Keith Vetter 2007-10-12 : I'd thought I'd share some new techniques I've created while adding a new feature to my KLIMB bike mapping program which lets you plan bike routes interactively on topo maps [1 ].

The new feature is another way of printing out bike routes by collecting multiple, smaller map segments and laying them out on a page. The key problem, however, is that the smaller map segments, in order to better cover the bike route, can be at any angle.

I'm still working on this new feature, and would like feedback on it, especially on the user interaction in specifying the map segment--it's tricky because the user can move, rotate and resize the selection.

A selection box is drawn on the map. The user can grab and move it anywhere. Grabbing the SE corner or by using the 3rd button, the user can rotate the box. Grabbing either of two resize controls lets you change the size.

The second aspect of this problem is laying out the results, and I haven't really done much with that yet. The third aspect is printing the result--that's going to be real fun to solve.

I included demo code, including a sample map image (compressed to death jpeg so it doesn't look great).


Some technical details.

The hardest/funnest part was extracting an angled rectangle area off a canvas. Initially I used TclMagick to do it, but because of poor documentation (I ended up using the php doc) and a few programming snags, I realized that that was overkill. Instead I used xphoto from Enhanced photo image copy command.

I use Img to grab the whole window, then crop that image to the bounding box of the selection. Next, I use xphoto to rotate the image. Then, after some simple trig, I use Img again to crop down to the selected area.


 ##+##########################################################################
 #
 # Clipbox -- grabs rectangular region of an image at any angle or size
 # by Keith Vetter, Sep, 2007
 #
 
 package require Tk
 package require Img
 
 set hasXPhoto 1
 if {[catch {load xphoto.dll}]} {
     wm withdraw .
     set msg "ERROR: missing xphoto.dll\n\n"
     append msg "This program requires the xphoto extension, which\n"
     append msg "can be downloaded from https://wiki.tcl-lang.org/11924\n\n"
     append msg "You can still run the program and interact with\n"
     append msg "the map but you cannot take snapshots."
     tk_messageBox -icon error -message $msg
     set hasXPhoto 0
     wm deiconify .
 }
 
 namespace eval ::ClipBox {
     variable P                                  ;# Box position
     variable M                                  ;# Mousing info
 
     unset -nocomplain P
     set P(clr,1) cyan
     set P(clr,0) red
     array set M {
         xy {} minWidth 200 minHeight 200 mousing 0 resizeSize 8 cornerSize 15
         cursor,corner exchange cursor,strip hand2 cursor,width fleur
         cursor,height fleur
     }
 }
 
 ##+##########################################################################
 #
 # Go -- creates the initial instance of our clipping box
 #
 proc ::ClipBox::Go {W p0 angle width height} {
     variable P
     set P(0) $p0
     set P(a,deg) $angle
     set P(w) $width
     set P(h) $height
 
     $W delete BOX
     $W create poly -tag {BOX clip} -fill cyan -stipple gray50 -width 2 \
         -outline black -dash -
     $W create poly -tag {BOX corner} -outline black -fill {} -width 2
     $W create poly -tag {BOX width} -fill black
     $W create poly -tag {BOX height} -fill black
     $W create text -100 -100 -text "N" -font {Helvetica 20 bold} -fill red \
         -anchor s -tag {BOX north northText}
     $W create line -100 -100 -200 -200 -width 5 -tag {BOX north northLine} \
         -fill red -arrow first -arrowshape {25 25 6}
 
     foreach tag {clip corner width height} {
         $W bind $tag <1> [list ::ClipBox::MouseDown %W $tag %x %y]
         $W bind $tag <B1-Motion> [list ::ClipBox::MouseMove %W $tag %x %y]
         $W bind $tag <ButtonRelease-1>  [list ::ClipBox::MouseUp %W]
         $W bind $tag <Enter> [list ::ClipBox::MouseEnter %W $tag]
         $W bind $tag <Leave> [list ::ClipBox::MouseLeave %W $tag]
 
         $W bind $tag <3> [list ::ClipBox::MouseDown %W corner %x %y]
         $W bind $tag <B3-Motion> [list ::ClipBox::MouseMove %W corner %x %y]
         $W bind $tag <ButtonRelease-3>  [list ::ClipBox::MouseUp %W]
     }
     ::ClipBox::DrawClipBox $W
 }
 ##+##########################################################################
 #
 # DrawClipBox -- repositions all elements of our clipbox
 #
 proc ::ClipBox::DrawClipBox {W} {
     set xy [::ClipBox::GetBoxCoords]
     foreach {bxy wxy hxy} [::ClipBox::GetSmallBoxCoords] break
     foreach {top bot} [::ClipBox::NorthArrow] break
     $W coords clip $xy
     $W coords corner $bxy
     $W coords width $wxy
     $W coords height $hxy
     $W coords northText $top
     $W coords northLine [concat $top $bot]
 }
 ##+##########################################################################
 #
 # GetBoxCoords -- given topleft corner, width, height and angle
 # returns coordinates of the box
 #
 proc ::ClipBox::GetBoxCoords {} {
     variable P
 
     set w $P(w)
     set h $P(h)
     set a $P(a,deg)
 
     set a [expr {$a * acos(-1) / 180}]          ;# Radians
 
     foreach {x0 y0} $P(0) break
     set x1 [expr {$x0 + $w*cos($a)}]
     set y1 [expr {$y0 + $w*sin($a)}]
     set P(1) [list $x1 $y1]
 
     set top [::Data::VSub $P(1) $P(0)]
     set left [::Data::VNormalTo $top $h]
     set P(3) [::Data::VAdd $P(0) $left]
     set P(2) [::Data::VAdd $P(3) $top]
 
     set xy [concat $P(0) $P(1) $P(2) $P(3)]
 
     return $xy
 }
 ##+##########################################################################
 #
 # GetSmallBoxCoords -- returns coords for rotate box and two sizing boxes
 #
 proc ::ClipBox::GetSmallBoxCoords {} {
     variable P
     variable M
 
     # Assumes P(0-3) are correct
     set top  [::Data::VSub $P(1) $P(0)]
     set left [::Data::VSub $P(3) $P(0)]
     set nTop  [::Data::VReScale $top 1]
     set nLeft [::Data::VReScale $left 1]
 
     set c2 $P(2)
     set c1 [::Data::VAdd $c2 $nLeft -$M(cornerSize)]
     set c0 [::Data::VAdd $c1 $nTop -$M(cornerSize)]
     set c3 [::Data::VAdd $c0 $nLeft $M(cornerSize)]
     set cxy [concat $c0 $c1 $c2 $c3]
 
     # Width adjust box
     set w [::Data::VAdd $P(1) $left .5]
     set rSize2 [expr {$M(resizeSize)/2.0}]
     set w1 [::Data::VAdd $w $nLeft -$rSize2]
     set w0 [::Data::VAdd $w1 $nTop -$M(resizeSize)]
     set w3 [::Data::VAdd $w0 $nLeft $M(resizeSize)]
     set w2 [::Data::VAdd $w3 $nTop $M(resizeSize)]
     set wxy [concat $w0 $w1 $w2 $w3]
 
     # Height adjust box
     set h [::Data::VAdd $P(3) $top .5]
     set h2 [::Data::VAdd $h $nTop $rSize2]
     set h1 [::Data::VAdd $h2 $nLeft -$M(resizeSize)]
     set h0 [::Data::VAdd $h1 $nTop -$M(resizeSize)]
     set h3 [::Data::VAdd $h0 $nLeft $M(resizeSize)]
     set hxy [concat $h0 $h1 $h2 $h3]
 
     return [list $cxy $wxy $hxy]
 }
 ##+##########################################################################
 #
 # NorthArrow -- computes where north compass arrow should be positioned
 #
 proc ::ClipBox::NorthArrow {} {
     variable P
 
     set cornerOffset 35
     set fudgeFactor {0 15}
     set arrowLength {0 150}
 
     set dir [expr {$P(a,deg) >= 0 ? 1 : -1}]
     if {($P(a,deg) >= 0 && $P(a,deg) <= 90) || $P(a,deg) < -90} {
         set bisect [::Data::VBisect $P(1) $P(0) $P(3)]
         set pt $P(0)
     } else {
         set bisect [::Data::VBisect $P(2) $P(3) $P(0)]
         set pt $P(3)
     }
     set pt1 [::Data::VAdd $pt $bisect $cornerOffset]
     set top [::Data::VAdd $pt1 $fudgeFactor]
     set bot [::Data::VAdd $top $arrowLength $dir]
     if {$dir == -1} {foreach {top bot} [list $bot $top] break}
     return [list $top $bot]
 }
 
 proc ::ClipBox::MouseEnter {W who} {
     variable M
     if {[info exists M(cursor,$who)]} {
         $W config -cursor $M(cursor,$who)
     }
 }
 proc ::ClipBox::MouseLeave {W who} {
     variable M
     if {$M(mousing)} return                     ;# Mouse down, don't change
     $W config -cursor {}
 }
 proc ::ClipBox::MouseDown {W who x y} {
     variable M
     variable P
 
     set M(xy) [list [$W canvasx $x] [$W canvasy $y]]
     set M(mousing) 1
     if {$who eq "corner"} {
         $W config -cursor $M(cursor,corner)
         ::ClipBox::FourCorners $W
 
         # Create pivot
         foreach {X Y} $P(0) break
         set xy [list [expr {$X-10}] [expr {$Y-10}] [expr {$X+10}] [expr {$Y+10}]]
         $W create oval $xy -tag {BOX pivot} -fill black
         ::ClipBox::MouseMove $W $who $x $y
     }
 }
 proc ::ClipBox::MouseUp {W} {
     variable M
     set M(mousing) 0
     $W delete pivot
     $W config -cursor {}
 }
 proc ::ClipBox::MouseMove {W who x y} {
     variable M
 
     set x [$W canvasx $x]
     set y [$W canvasy $y]
     if {$who eq "corner"} {
         ::ClipBox::MouseSpin $W $who $x $y
     } elseif {$who eq "width" || $who eq "height"} {
         ::ClipBox::MouseResize $W $who $x $y
     } else {
         foreach {bx by} $M(xy) break
         set M(xy) [list $x $y]
         set dx [expr {$x - $bx}]
         set dy [expr {$y - $by}]
         $W move BOX $dx $dy
         ::ClipBox::Onscreen $W
     }
 }
 ##+##########################################################################
 #
 # MouseSpin -- rotates clipbox to keep mouse point on the main diagonal
 #
 proc ::ClipBox::MouseSpin {W who x y} {
     variable P
 
     set v [::Data::VReScale [::Data::VSub [list $x $y] $P(0)] 1]
     set n [::Data::VDot [list 1 0] $v]
     set a1 [expr {acos($n)}]
     if {[lindex $v 1] < 0} { set a1 [expr {-$a1}] } ;# Quadrant check
     set a2 [expr {atan2($P(h), $P(w))}]
     set a3 [expr {$a1 - $a2}]
     set P(a,deg) [expr {$a3 * 180 / acos(-1)}]
     ::ClipBox::DrawClipBox $W
     ::ClipBox::Onscreen $W
 }
 ##+##########################################################################
 #
 # MouseResize -- resizes clipbox vertically or horizontally
 #
 proc ::ClipBox::MouseResize {W who x y} {
     variable P
     variable M
 
     ::ClipBox::FourCorners $W
     set top  [::Data::VSub $P(1) $P(0)]
     set left [::Data::VSub $P(3) $P(0)]
     set nTop  [::Data::VReScale $top 1]
     set nLeft [::Data::VReScale $left 1]
 
     if {$who eq "width"} {
         set p0 [::Data::VAdd $P(0) $left .5]
         set v [::Data::VSub [list $x $y] $p0]
         set w [::Data::VDot $nTop $v]
 
         if {$w < $M(minWidth)} return
         set P(w) $w
     } else {
         set p0 [::Data::VAdd $P(0) $top .5]
         set v [::Data::VSub [list $x $y] $p0]
         set h [::Data::VDot $nLeft $v]
 
         if {$h < $M(minHeight)} return
         set P(h) $h
     }
     ::ClipBox::DrawClipBox $W
     ::ClipBox::Onscreen $W
 }
 ##+##########################################################################
 #
 # Onscreen -- figures out if clipbox is off the screen at all
 #
 proc ::ClipBox::Onscreen {W} {
     variable P
 
     foreach {x0 y0 x1 y1 x2 y2 x3 y3} [$W coords clip] break
     set l [expr {round([::Data::Min $x0 $x1 $x2 $x3])}]
     set r [expr {round([::Data::Max $x0 $x1 $x2 $x3])}]
     set t [expr {round([::Data::Min $y0 $y1 $y2 $y3])}]
     set b [expr {round([::Data::Max $y0 $y1 $y2 $y3])}]
 
     set cx0 [$W canvasx 0]
     set cy0 [$W canvasy 0]
     set cx1 [expr {$cx0 + [winfo width $W]}]
     set cy1 [expr {$cy0 + [winfo height $W]}]
 
     set onscreen 1
     if {$l < $cx0 || $t < $cy0 || $r > $cx1 || $b > $cy1} {
         set onscreen 0
     }
     $W itemconfig clip -fill $P(clr,$onscreen)
     return $onscreen
 }
 proc ::ClipBox::PointOnscreen {W pt} {
     foreach {x y} $pt break
     set cx0 [$W canvasx 0]
     set cy0 [$W canvasy 0]
     set cx1 [expr {$cx0 + [winfo width $W]}]
     set cy1 [expr {$cy0 + [winfo height $W]}]
 
     return [expr {$x >= $cx0 && $x <= $cx1 && $y >= $cy0 && $y <= $cy1}]
 }
 ##+##########################################################################
 #
 # FourCorners -- fills in our data structures with clipbox's corners
 #
 proc ::ClipBox::FourCorners {W} {
     variable P
     foreach idx {0 1 2 3} {x y} [$W coords clip] {
         set P($idx) [list $x $y]
     }
 }
 ##+##########################################################################
 #
 # GetClipBoxSizes -- computes parameters needed to crop, rotate
 # and crop again the image
 #
 proc ::ClipBox::GetClipBoxSizes {W} {
     variable P
 
     ::ClipBox::FourCorners $W
     foreach {x0 y0} $P(0) {x1 y1} $P(1) {x2 y2} $P(2) {x3 y3} $P(3) break
     set l [expr {round([::Data::Min $x0 $x1 $x2 $x3])}]
     set r [expr {round([::Data::Max $x0 $x1 $x2 $x3])}]
     set t [expr {round([::Data::Min $y0 $y1 $y2 $y3])}]
     set b [expr {round([::Data::Max $y0 $y1 $y2 $y3])}]
     #set P(bbox) [list $l $t $r $b]
     set P(bbox) [::ClipBox::World2Canvas $W $l $t $r $b]
 
     set dy [expr {$y1 - $y0}]
     set dx [expr {$x1 - $x0}]
     set dx2 [expr {$x3 - $x0}]
     set dy2 [expr {$y3 - $y0}]
 
     # Question: use values from p or recompute from coordinates???
 
     set P(a,rad) [expr {atan2($dy,$dx)}]
     set P(a,deg) [expr {$P(a,rad)*180/acos(-1)}]
     set P(w) [expr {round(hypot($dx,$dy))}]
     set P(h) [expr {round(hypot($dx2,$dy2))}]
 
     # R0 is topleft corner in the rotated image
     # R1 is bottomright corner in the rotated image
     set P(rx0) [expr {abs(round($dy2 * sin($P(a,rad))))}]
     set P(ry0) [expr {abs(round($dx * sin($P(a,rad))))}]
     set P(rx1) [expr {$P(rx0) + $P(w)}]
     set P(ry1) [expr {$P(ry0) + $P(h)}]
 }
 ##+##########################################################################
 #
 # World2Canvas -- translates world coordinates into canvas ones
 #
 proc ::ClipBox::World2Canvas {W args} {
     set x0 [$W canvasx 0]
     set y0 [$W canvasy 0]
     set result {}
     foreach {x y} $args {
         set x [expr {round($x - $x0)}]
         set y [expr {round($y - $y0)}]
         lappend result $x $y
     }
     return $result
 }
 ##+##########################################################################
 #
 # Snapshot -- extracts content of the clipbox, with the proper
 # cropping and rotating.
 #
 proc ::ClipBox::Snapshot {W} {
     variable P
 
     # Hide everything except compass north
     raise [winfo toplevel $W]
     $W lower BOX ; $W raise north
     update idletasks
 
     ::ClipBox::GetClipBoxSizes $W
     set snap [image create photo -data $W]
     set rot [image create photo]
     set chop [image create photo]
     $W raise BOX ; $W raise north
 
     set crop [eval ::ClipBox::SafeCrop $snap $P(bbox)]
     $rot copy $crop -rotate $P(a,deg)
     $chop copy $rot -from $P(rx0) $P(ry0) $P(rx1) $P(ry1)
 
     image delete $snap
     image delete $crop
     image delete $rot
 
     if {[::ClipBox::PointOnscreen $W $P(1)]} {  ;# Move clipbox forward
         set P(0) $P(1)
         ::ClipBox::DrawClipBox $W
     }
     return $chop
 }
 ##+##########################################################################
 #
 # SafeCrop -- crops image handling off image coordinates
 #
 proc ::ClipBox::SafeCrop {cimg left top right bottom} {
     set w [image width $cimg]
     set h [image height $cimg]
 
     set pad(l) [expr {$left < 0 ? -$left : 0}]
     set left [::Data::Max $left 0]
     set pad(t) [expr {$top < 0 ? -$top : 0}]
     set top [::Data::Max $top 0]
     set pad(r) [expr {$right > $w ? $right-$w : 0}]
     set right [::Data::Min $right $w]
     set pad(b) [expr {$bottom > $h ? $bottom-$h : 0}]
     set bottom [::Data::Min $bottom $h]
 
     set crop [image create photo]
     $crop copy $cimg -from $left $top $right $bottom
     set pimg [::ClipBox::PadImage $crop $pad(l) $pad(t) $pad(r) $pad(b)]
 
     return $pimg
 }
 ##+##########################################################################
 #
 # PadImage -- adds requested borders to the image
 #
 proc ::ClipBox::PadImage {img left top right bottom} {
     if {$left == 0 && $top == 0 && $right == 0 && $bottom == 0} {return $img}
 
     set w [expr {[image width $img] + $left + $right}]
     set h [expr {[image height $img] + $top + $bottom}]
 
     set tmp [image create photo -width $w -height $h]
     $tmp put yellow -to 0 0 $w $h
     $tmp copy $img -to $left $top
     image delete $img
     return $tmp
 }
 
 namespace eval ::ShowPics {
     variable S
     unset -nocomplain S
     image create bitmap ::bmp::up -data {
         #define up_width 11
         #define up_height 11
         static char up_bits = {
             0x00, 0x00, 0x20, 0x00, 0x70, 0x00, 0xf8, 0x00, 0xfc, 0x01, 0xfe,
             0x03, 0x70, 0x00, 0x70, 0x00, 0x70, 0x00, 0x00, 0x00, 0x00, 0x00
         }
     }
     image create bitmap ::bmp::down -data {
         #define down_width 11
         #define down_height 11
         static char down_bits = {
             0x00, 0x00, 0x00, 0x00, 0x70, 0x00, 0x70, 0x00, 0x70, 0x00, 0xfe,
             0x03, 0xfc, 0x01, 0xf8, 0x00, 0x70, 0x00, 0x20, 0x00, 0x00, 0x00
         }
     }
     image create bitmap ::bmp::x -foreground white -data {
         #define X_width 11
         #define X_height 11
         static char X_bits = {
             0x04, 0x01, 0x8e, 0x03, 0xdf, 0x07, 0xfe, 0x03, 0xfc, 0x01, 0xf8,
             0x00, 0xfc, 0x01, 0xfe, 0x03, 0xdf, 0x07, 0x8e, 0x03, 0x04, 0x01
         }
     }
 }
 
 proc ::ShowPics::ShowImg {W} {
     variable S
     global I
 
     set img [::ClipBox::Snapshot $W]
     if {! [winfo exists .show]} {
         toplevel .show
         wm protocol .show WM_DELETE_WINDOW ::ShowPics::Cleanup
         wm title .show "Snap Shot Gallery"
         RightWindow .show $W
         #wm transient .show [winfo toplevel $W]
         unset -nocomplain S
     }
     set id [expr {1 + [llength [grid slaves .show]]}]
     set w .show.$id
     frame $w
     grid $w -sticky w
     if {$id > 1} { grid config $w -pady {10 0}}
 
     button $w.up -image ::bmp::up -takefocus 0 \
         -command [list ::ShowPics::Swap up $id]
     button $w.x -image ::bmp::x -bg red -takefocus 0 \
         -command [list ::ShowPics::DeleteRow $id]
     button $w.down -image ::bmp::down -takefocus 0 \
         -command [list ::ShowPics::Swap down $id]
     frame $w.right -bd 2 -relief solid
     ::ShowPics::OneImage $w.right $img $id
 
     set S($id,img) $img
     set S($id,txt) "<description for this map>"
     ::ShowPics::DoButtons
 
     grid $w.up $w.right -sticky s
     grid $w.x ^ -pady 5
     grid $w.down ^ -sticky n -pady [list 0 [winfo reqheight $w.right.txt]]
 
     grid rowconfigure $w {0 2} -weight 1
     grid columnconfigure $w 0 -pad 10
     raise .show
 }
 proc ::ShowPics::Cleanup {} {
     variable S
 
     destroy .show
     foreach arr [array names S *,img] {
         image delete $S($arr)
     }
     unset -nocomplain S
 }
 proc ::ShowPics::OneImage {w img id} {
     variable S
 
     set S($id,w) $w.img
     label $w.img -image $img -bd 0
     label $w.id -text "MAP $id" -font {Helvetica 12 bold} -anchor e
     entry $w.txt -font {Helvetica 12 bold} -justify c -bd 0 \
         -textvariable ::ShowPics::S($id,txt)
     pack $w.img -side top -fill both -expand 1
     pack $w.id -side right
     pack $w.txt -side left -fill both -expand 1
 }
 proc ::ShowPics::SwapRows {row1 row2} {
     variable S
 
     set txt $S($row1,txt)
     set S($row1,txt) $S($row2,txt)
     set S($row2,txt) $txt
 
     set img $S($row1,img)
     set S($row1,img) $S($row2,img)
     set S($row2,img) $img
     $S($row1,w) config -image $S($row1,img)
     $S($row2,w) config -image $S($row2,img)
 }
 proc ::ShowPics::Swap {dir which} {
     set other [expr {$dir eq "up" ? $which-1 : $which+1}]
     ::ShowPics::SwapRows $which $other
 }
 proc ::ShowPics::DeleteRow {which} {
     variable S
 
     set len [llength [array names S *,img]]
     for {set row $which} {$row < $len} {incr row} {
         ::ShowPics::SwapRows $row [expr {$row+1}]
     }
     destroy .show.$len
     image delete $S($len,img)
     array unset S $len,*
     ::ShowPics::DoButtons
     if {$len == 1} ::ShowPics::Cleanup
 }
 proc ::ShowPics::DoButtons {} {
     variable S
 
     set len [llength [array names S *,img]]
     if {$len == 0} return
     for {set i 1} {$i <= $len} {incr i} {
         .show.$i.up config -state normal
         .show.$i.down config -state normal
     }
     .show.1.up config -state disabled
     .show.$len.down config -state disabled
 }
 
 ################################################################
 #
 # Utility routines
 #
 namespace eval ::Data {}
 proc ::Data::Max {a args} {
     foreach arg $args {if {$arg > $a} { set a $arg}}
     return $a
 }
 proc ::Data::Min {a args} {
     foreach arg $args {if {$arg < $a} { set a $arg}}
     return $a
 }
 proc ::Data::VAdd {v1 v2 {scaling 1}} {
     foreach {x1 y1} $v1 {x2 y2} $v2 break
     return [list [expr {$x1 + $scaling*$x2}] [expr {$y1 + $scaling*$y2}]]
 }
 proc ::Data::VSub {v1 v2} { return [::Data::VAdd $v1 $v2 -1] }
 proc ::Data::VReScale {v scaling} {
     foreach {x y} $v break
     set len [expr {hypot($x,$y)}]
     return [list [expr {$x * $scaling / $len}] [expr {$y * $scaling / $len}]]
 }
 proc ::Data::VNormalTo {vv length} {
     foreach {x y} $vv break
     set len [expr {hypot($x,$y)}]
     set xx [expr {-$y * $length / $len}]
     set yy [expr {$x * $length / $len}]
     return [list $xx $yy]
 }
 proc ::Data::VBisect {p1 p2 p3} {
     set v1 [::Data::VReScale [::Data::VSub $p1 $p2] 1]
     set v2 [::Data::VReScale [::Data::VSub $p3 $p2] 1]
     set v [::Data::VReScale [::Data::VAdd $v1 $v2] 1]
     return $v
 }
 proc ::Data::VDot {v1 v2} {
     foreach {x1 y1} $v1 {x2 y2} $v2 break
     return [expr {$x1*$x2 + $y1*$y2}]
 }
 
 proc RightWindow {w {W .}} {
     update idletasks
 
     set W [winfo toplevel $W]
     set y [expr {3 + [winfo y $W]}]              ;# Top of main window
     set x [expr {15 + [winfo x $W] + [winfo width $W]}] ;# Right side
     wm geom $w +$x+$y
 }
 
 ################################################################
 #
 # DEMO CODE BELOW
 #
 
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proc About {} {
    set msg "Route Map Selection\nby Keith Vetter\n\n"
    append msg "This demonstrates a package that lets\n"
    append msg "select arbitrary rectangular areas of\n"
    append msg "canvas and to extract exactly that area.\n\n"

    append msg "You can move the selection by dragging it,\n"
    append msg "you can resize the selection by dragging\n"
    append msg "a resize button, and you can rotate the\n"
    append msg "selection by dragging the resize control\n"
    append msg "or by dragging with the 3rd mouse button.\n"

    tk_messageBox -icon info -message $msg
}

 ################################################################
 #
 # Demo code
 
 proc DoDisplay {} {
     bind all <F2> {console show}
     wm title . "Clip Box Demo"
     canvas .c -highlightthickness 0 -bd 0 \
         -width [image width ::img::img] -height [image height ::img::img]
     .c create image 0 0 -image ::img::img -anchor nw
     .c config -scrollregion [.c bbox all]
     button .chop -text "Take Snap Shot" -command [list ::ShowPics::ShowImg .c]
     if {! $::hasXPhoto} { .chop config -state disabled }
     button .about -text About -command About
     pack .c -side top
     #pack .chop .about -side left -pady 10 -expand 1 -padx 10
     pack .about -side right -padx 10 -pady 10
     pack .chop -side bottom -pady 10
 
     bind .c <2>          [bind Text <2>]         ;# Enable dragging w/ <2>
     bind .c <B2-Motion>  [bind Text <B2-Motion>]
 }
 
 DoDisplay
 wm geom . +1+1
 ::ClipBox::Go .c {35 135} -7 700 200
 set W .c
 
 return