Arjen Markus One page, two scripts: both concerned with the construction of geometrical curves.
The first will draw a parabola and the second will draw a cardioid.
You can (more or less) easily vary the parameters of the drawing process and get different curves each time.
# tangent.tcl --
# Draw tangent lines and try to determine the curve that they
# define
# tangentLine --
# Draw a tangent line
# Arguments:
# xcrd X-coordinate at which the line intersects the x-axis
# ycrd Y-coordinate at which the line intersects the y-axis
# Result:
# None
# Side effect:
# Line drawn
# Note:
# Assumes the x-axis to run from -200 to +200, ditto the y-axis
#
proc tangentLine { xcrd ycrd scale } {
if { $xcrd == 0.0 } { return }
#
# Parametrisation of the line:
# x = $xcrd - m*$xcrd
# y = 0 + m*$ycrd
#
set x1 -2000.0
set m [expr {-($x1-$xcrd)/$xcrd}]
set y1 [expr {$m*$ycrd}]
set x2 2000.0
set m [expr {-($x2-$xcrd)/$xcrd}]
set y2 [expr {$m*$ycrd}]
set x11 [expr {100.0+$x1/$scale}]
set x22 [expr {100.0+$x2/$scale}]
set y11 [expr {300.0-$y1/$scale}]
set y22 [expr {300.0-$y2/$scale}]
.c create line $x11 $y11 $x22 $y22 -fill black
}
#
# Main code
#
canvas .c -background white -width 400 -height 400
pack .c -fill both
set hlines 40
set scale 1.0
.c create line 0 300 400 300 -fill red -width 2
.c create line 100 0 100 400 -fill red -width 2
for { set i -$hlines } { $i < $hlines } { incr i } {
#tangentLine [expr {$i*10+0.01}] [expr {200.0-$i*10-0.01}] $scale
tangentLine [expr {$i*$scale*10}] [expr {200.0-$i*$scale*10}] $scale
#tangentLine [expr {$i*$scale*10}] [expr {200.0-$i*$i}] $scale
#tangentLine [expr {$i*$scale*10}] [expr {200.0-3.0*$i*$scale}] $scale
} # tangent.tcl --
# Draw tangent lines and try to determine the curve that they
# define
# tangentLine --
# Draw a tangent line
# Arguments:
# xcrd X-coordinate at which the line intersects the x-axis
# ycrd Y-coordinate at which the line intersects the y-axis
# Result:
# None
# Side effect:
# Line drawn
# Note:
# Assumes the x-axis to run from -200 to +200, ditto the y-axis
#
proc tangentLine { xcrd ycrd scale } {
if { $xcrd == 0.0 } { return }
#
# Parametrisation of the line:
# x = $xcrd - m*$xcrd
# y = 0 + m*$ycrd
#
set x1 -2000.0
set m [expr {-($x1-$xcrd)/$xcrd}]
set y1 [expr {$m*$ycrd}]
set x2 2000.0
set m [expr {-($x2-$xcrd)/$xcrd}]
set y2 [expr {$m*$ycrd}]
set x11 [expr {100.0+$x1/$scale}]
set x22 [expr {100.0+$x2/$scale}]
set y11 [expr {300.0-$y1/$scale}]
set y22 [expr {300.0-$y2/$scale}]
.c create line $x11 $y11 $x22 $y22 -fill black
}
#
# Main code
#
canvas .c -background white -width 400 -height 400
pack .c -fill both
set hlines 40
set scale 1.0
.c create line 0 300 400 300 -fill red -width 2
.c create line 100 0 100 400 -fill red -width 2
for { set i -$hlines } { $i < $hlines } { incr i } {
#tangentLine [expr {$i*10+0.01}] [expr {200.0-$i*10-0.01}] $scale
tangentLine [expr {$i*$scale*10}] [expr {200.0-$i*$scale*10}] $scale
#tangentLine [expr {$i*$scale*10}] [expr {200.0-$i*$i}] $scale
#tangentLine [expr {$i*$scale*10}] [expr {200.0-3.0*$i*$scale}] $scale
}]