# 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
} # cardioid.tcl --
# Draw a classical curve:
# - The "support" circle is at 200,300 with a radius of 100
# - The point that passes through all other circles is 100,300
# - The cardioid is the envelope of these circles
#
# From the book:
# E.H. Lockwood, A book of curves, Cambridge University Press, 1960
#
canvas .c -width 600 -height 600 -bg white
pack .c -fill both
.c create oval 100 200 300 400 -outline blue -width 2
set support_radius 100.0
for { set angle 0 } { $angle < 360 } { incr angle 18 } {
set rads [expr {$angle*3.1415926/180.0}]
set xc [expr {200+int($support_radius*cos($rads))}]
set yc [expr {300+int($support_radius*sin($rads))}]
set radius [expr {hypot($xc-100.0,$yc-300.0)}]
set xup [expr {$xc-$radius}]
set yup [expr {$yc-$radius}]
set xdown [expr {$xc+$radius}]
set ydown [expr {$yc+$radius}]
.c create oval $xup $yup $xdown $ydown -outline black
}AM Some magic with line segments that I felt is somwhat similar: Patterns with pentagons
