[http://mini.net/files/funplot.jpg]
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[Richard Suchenwirth] - My teenage daughter hates math. In order to
motivate her, I beefed up [A little function plotter] which before only
took one function, in strict Tcl (expr) notation, from the command line. Now
there's an entry widget, and the accepted language has also been
enriched: beyond ''expr''s rules, you can omit dollar and multiplication
signs, like ''2x+1'',
powers can be written as ''x3'' instead of ($x*$x*$x); in simple cases you
can omit parens round function arguments, like ''sin x2''. Hitting
<Return> in the entry widget displays the function's graph.

If you need some ideas, click on the "?" button to cycle through a set of demo
functions, from boring to bizarre (e.g. if ''rand()'' is used).
Besides default scaling, you can zoom in or out. Moving the
mouse pointer over the canvas displays x and y coordinates, and the
display changes to white if you're on a point on the curve.

The target was not reached: my daughter still hates math. But at least I had hours of Tcl (and function) fun again, surfing in the Cartesian
plane... hope you enjoy it too!
 proc main {} {
    canvas .c -bg white -borderwidth 0
      bind .c <Motion> {displayXY .info %x %y}
    frame  .f
      label  .f.1 -text "f(x) = "
      entry  .f.f -textvar ::function -width 40
        bind .f.f <Return> {plotf .c $::function}
      button .f.demo -text " ? " -pady 0 -command {demo .c}
      label  .f.2 -text " Zoom: "
      entry  .f.fac -textvar ::factor -width 4
        set                  ::factor 32
        bind .f.fac <Return>               {zoom .c 1.0}
      button .f.plus  -text " + " -pady 0 -command {zoom .c 2.0}
      button .f.minus -text " - " -pady 0 -command {zoom .c 0.5}
      eval pack [winfo children .f] -side left -fill both
    label  .info -textvar ::info -just left
    pack .info .f -fill x -side bottom
    pack .c -fill both -expand 1
    demo .c
 }
 set ::demos {
        "cos x3" 2 1-x 0.5x2 x3/5 "sin x" "sin x2" 1/x sqrt(x)
        "tan x/5" x+1/x x abs(x) "exp x" "log x" "log x2"
        round(x) "int x%2" "x-int x" "0.2tan x+1/tan x" x*(rand()-0.5)
        x2/5-1/(2x) "atan x" sqrt(1-x2) "abs(x-int(x*2))" (x-1)/(x+1)
        "sin x-tan x" "sin x-tan x2" "x-abs(int x)" 0.5x-1/x
        -0.5x3+x2+x-1 3*sin(2x) -0.05x4-0.2x3+1.5x2+2x-3 "9%int x"
        0.5x2/(x3-3x2+4) "abs x2-3 int x" "int x%3"
 }
 proc displayXY {w cx cy} {
        set x [expr {double($cx-$::dx)/$::factor}]
        set y [expr {double(-$cy+$::dy)/$::factor}]
        set ::info [format "x=%.2f y=%.2f" $x $y]
        catch {
        $w config -fg [expr {abs([expr $::fun]-$y)<0.01?"white":"black"}]
        } ;# may divide by zero, or other illegal things
 }
 proc zoom {w howmuch} {
    set ::factor [expr round($::factor*$howmuch)]
    plotf $w $::function
 }
 proc plotf {w function} {
    foreach {re subst} {
        {([a-z]) +(x[0-9]?)} {\1(\2)}   " " ""   {([0-9])([a-z])} {\1*\2}
        x2 x*x   x3 x*x*x    x4 x*x*x*x   x \$x   {e\$xp} exp
    } {regsub -all $re $function $subst function}
    set ::fun $function
    set ::info "Tcl: expr $::fun"
    set color [lpick {red blue purple brown green}]
    plotline $w [fun2points $::fun] -fill $color
 }
 proc lpick L {lindex $L [expr {int(rand()*[llength $L])}]}
 proc fun2points {fun args} {
    array set opt {-from -10.0 -to 10.0 -step .01}
    array set opt $args
    set res "{"
    for {set x $opt(-from)} {$x<= $opt(-to)} {set x [expr {$x+$opt(-step)}]} {
        if {![catch {expr $fun} y]} {
            if {[info exists lasty] && abs($y-$lasty)>100} {
                append res "\} \{" ;# incontinuity
            }
            append res " $x $y"
            set lasty $y
        } else {append res "\} \{"}
    }
    append res "}"
 }
 proc plotline {w points args} {
    $w delete all
    foreach i $points {
        if {[llength $i]>2} {eval $w create line $i $args -tags f}
    }
    set fac $::factor
    $w scale all 0 0 $fac -$fac
    $w create line -10000 0 10000 0      ;# X axis
    $w create line 0 -10000 0 10000      ;# Y axis
    $w create line $fac 0     $fac -3    ;# x=1 tick
    $w create line -3   -$fac 0    -$fac ;# y=1 tick
    set ::dx [expr {[$w cget -width]/2}]
    set ::dy [expr {[$w cget -height]/2}]
    $w move all $::dx $::dy
    $w raise f
 }
 proc demo {w} {
    set ::function [lindex $::demos 0] ;# cycle through...
    set ::demos [concat [lrange $::demos 1 end] [list $::function]]
    set ::factor 32
    plotf $w $::function
 }
 main
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[Arts and crafts of Tcl-Tk programming]
- [Category Mathematics]