# 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
 }