Circumcenter of three points

KPV See also Triangle Madness for a whizzlet showing the circumcenter of a triangle plus some other interesting points such as the incenter, centroid, orthocenter, etc.

 # circumcenter.tcl

 # Quick demo program about finding the circumcenter of three
 # points.  E.g. given three points, find the center of the
 # circle which passes through all three points.  Derived from
 # the book "A Programmer's Geometry".  --willdye, 2004-11-23

 set Kx  80.0 ; set Ky  50.0 ;# First  point
 set Lx 200.0 ; set Ly  20.0 ;# Second point
 set Mx 230.0 ; set My 100.0 ;# Third  point

 set LKx [expr { $Lx - $Kx }] ; set LKy [expr { $Ly - $Ky }]
 set MKx [expr { $Mx - $Kx }] ; set MKy [expr { $My - $Ky }]

 set faccuracy 0.00001 ;# Value depends on the application.
 set determinant [expr { $LKx * $MKy - $MKx * $LKy }]
 if {[expr { abs( $determinant ) < $faccuracy }]} {
     puts "Error: two or more points are coincident." ; exit}
 set d2 [expr { 0.5 / $determinant }]

 set LKr [expr {  $LKx * $LKx + $LKy * $LKy }]
 set MKr [expr {  $MKx * $MKx + $MKy * $MKy }]
 set Cx  [expr {( $LKr * $MKy - $MKr * $LKy ) * $d2 + $Kx }]
 set Cy  [expr {( $LKx * $MKr - $MKx * $LKr ) * $d2 + $Ky }]

 # We'll probably want the radius, also.  The straightforward
 # method should be good enough in this case, but of course in
 # general it is not very efficent, and has some accuracy issues.

 set rad [expr { sqrt( pow( ( $Cx - $Kx ), 2 ) +
                       pow( ( $Cy - $Ky ), 2 ) ) }]

 # Display the result.

 puts "Circumcenter, as X/Y/Radius: $Cx $Cy $rad"

 if {![package present Tk]} {exit}
 destroy .c ; canvas .c -background gray ; pack .c
 .c create polygon $Lx $Ly $Mx $My $Kx $Ky -fill white
 .c create oval $Cx $Cy $Cx $Cy -fill black
 .c create oval [expr { $Cx - $rad }] [expr { $Cy - $rad }] \
     [expr { $Cx + $rad }] [expr { $Cy + $rad }] -outline red

uniquename 2013aug18

Here is an image of what is drawn on the canvas, by the code above. (I replaced a 'puts' statement by a statement to put the x,y,radius data on the canvas, instead of to 'stdout'.)