Bitmap/Bézier curves/Cubic: Difference between revisions

=={{header|Tcl}}==

This solution can be applied to any number of points

<lang tcl>package require Tcl 8.5

package require Tk

proc drawBezier {img colour args} {

# ensure the 3 points are increasing along the x-axis

set points [lsort -real -index 0 $args]

set xmin [x [lindex $points 0]]

set xmax [x [lindex $points end]]

set prev [lindex $points 0]

set increment 2

for {set x [expr {$xmin + $increment}]} {$x <= $xmax} {incr x $increment} {

set t [expr {1.0 * ($x - $xmin) / ($xmax - $xmin)}]

set this [list $x [::tcl::mathfunc::round [bezier $t $points]]]

drawLine $img $colour $prev $this

set prev $this

}

}

# the generalized n-degree Bezier summation

proc bezier {t points} {

set n [expr {[llength $points] - 1}]

set sum 0.0

for {set i 0} {$i <= $n} {incr i} {

set sum [expr {$sum + [C $n $i] * (1-$t)**($n - $i) * $t**$i * [y [lindex $points $i]]}]

}

return $sum

}

proc C {n i} {expr {[ifact $n] / ([ifact $i] * [ifact [expr {$n - $i}]])}}

proc ifact n {

for {set i $n; set sum 1} {$i >= 2} {incr i -1} {

set sum [expr {$sum * $i}]

}

return $sum

}

proc x p {lindex $p 0}

proc y p {lindex $p 1}

proc newbezier {n w} {

set size 400

set bezier [newImage $size $size]

fill $bezier white

for {set i 1} {$i <= $n} {incr i} {

set point [list [expr {int($size*rand())}] [expr {int($size*rand())}]]

lappend points $point

drawCircle $bezier red $point 3

}

puts $points

drawBezier $bezier blue {*}$points

$w configure -image $bezier

}

set degree 4 ;# cubic bezier -- for quadratic, use 3

label .img

button .new -command [list newbezier $degree .img] -text New

button .exit -command exit -text Exit

pack .new .img .exit -side top</lang>