[L1 ]
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 exprs 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
}
mainArts and crafts of Tcl-Tk programming - Category Mathematics