[Arjen Markus] 2012-10-07: The discussion on [https://groups.google.com/forum/?hl=en&fromgroups=#!topic/comp.lang.tcl/V5ZkH9zL_eQ%|%comp.lang.tcl%|%]
inspired me to create the procedure below. The devil, as they say, is in the detail, which is why it took me longer than I thought to get correct. (I suspect
it can be simplified a bit)

The idea: given two points create a circular arc with an adjustable curvature.


** Screenshot **

[curve.png]


** Code **

======
# curve.tcl --
#     Draw a curve between two points
#     (Based on a dscussion in comp.lang.tcl)
#

# curve --
#     Draw a circle section between two points
#
# Arguments:
#     canvas         Canvas to draw it on
#     coords         Coordinates of the start and end points
#     angle          Angle determining the curvature (in degrees)

proc curve {canvas coords angle} {

    #
    # Preliminaries
    #
    set angle_rad [expr {$angle * acos(-1.0) / 180.0}]

    lassign $coords xb yb xe ye

    set xv [expr {$xe-$xb}]
    set yv [expr {$ye-$yb}]

    #
    # Determine the radius and the distance of the centre to the
    # line through the two points
    #
    set length   [expr {hypot($xv,$yv)}]
    set radius   [expr {$length / sqrt( 2.0 * (1.0-cos($angle_rad)) )}]
    set distance [expr {sqrt($radius**2-0.25*$length**2)}]
    if { $angle > 180.0 } {
        set distance [expr {-$distance}]
    }

    #
    # Coordinates of the centre
    #
    set xc [expr {0.5 * ($xb + $xe) - $distance * $yv / $length}]
    set yc [expr {0.5 * ($yb + $ye) + $distance * $xv / $length}]

    #
    # Start angle for the section (note the inversion for y)
    #
    set angle_start [expr {180.0 / acos(-1.0) * atan2($yc-$yb,$xb-$xc)}]

    #
    # Draw the circle section
    #
    $canvas create arc [expr {$xc-$radius}] [expr {$yc-$radius}] \
                       [expr {$xc+$radius}] [expr {$yc+$radius}] \
                       -start [expr {$angle_start-$angle}] -extent $angle -style arc
}

# main --
#     Test the algorithm
#
pack [canvas .c -width 400 -height 400]

.c create line 100 100 300 300 -width 3 -fill red
curve .c {100 100 300 300} 30
curve .c {100 100 300 300} 70
curve .c {100 100 300 300} 100
curve .c {100 100 300 300} 180
curve .c {100 100 300 300} 270
======
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