Triangle minimum enclosing disk solution

turtles-own [name]
globals [Ix Iy radius ExtList wholist step pos slopes intercepts Ax Ay Bx By Cx Cy ABx ABy ABm ABb BCx BCy BCm BCb CAx CAy CAm CAb midx midy]

to doit
  if step = 0 [triangle]
  if step = 1 [midpoints]
  if step = 2 [bisect]
  if step = 3 [bi_intersect]
  set step step + 1
  if step > 4 [set step 0 ca clear-output]
end 

to triangle
  ;make color set
  set pos 0
  ;make points
  foreach ["A" "B" "C"][
     crt 1 [set shape "square" set size 2 set color 48 set name ? set label name set heading random 360 jump (10 + random 10 + (random 100) / 100)]
  ]
  set wholist []
  ask turtles[set wholist lput who wholist]
  set wholist sort wholist
  set pos 0
  repeat (length wholist - 1) [
   set pos pos + 1
   ask turtle (item pos wholist) [create-link-with turtle (item (pos - 1) wholist)]]
  ask turtle (last wholist) [create-link-with turtle (first wholist)]
  ask links [set thickness 0.5 set color 5]
end 

to midpoints
  set Ax [xcor] of one-of turtles with [name = "A"]
  set Ay [ycor] of one-of turtles with [name = "A"]
  set Bx [xcor] of one-of turtles with [name = "B"]
  set By [ycor] of one-of turtles with [name = "B"]
  set Cx [xcor] of one-of turtles with [name = "C"]
  set Cy [ycor] of one-of turtles with [name = "C"]
  set ABx first midpoint Ax Ay Bx By
  set ABy last midpoint Ax Ay Bx By
  crt 1 [set name "AB" set label name setxy ABx ABy set shape "triangle" set color yellow]
  set BCx first midpoint Bx By Cx Cy
  set BCy last midpoint Bx By Cx Cy
  crt 1 [set name "BC" set label name setxy BCx BCy set shape "triangle" set color yellow]
  set CAx first midpoint Cx Cy Ax Ay
  set CAy last midpoint Cx Cy Ax Ay
  crt 1 [set name "CA" set label name setxy CAx CAy set shape "triangle" set color yellow]
end 

to bisect
  set ABm -1 / (slope Ax Ay Bx By)
  set ABb intercept ABx ABy ABm
  set BCm -1 / (slope Bx By Cx Cy)
  set BCb intercept BCx BCy BCm
  set CAm -1 / (slope Cx Cy Ax Ay)
  set CAb intercept CAx CAy CAm
  ;draw them
  ;find the intercept with the world-height and world-width?
  ;extend the lines

  let scale 0.95
  set ExtList []
  ;set the x to the world left edge and see of the y value is within the range of the height.  If so keep the coordinates
  carefully [if abs ((ABm * ((world-width * scale) / -2.0)) + ABb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((ABm * ((world-width * scale) / -2.0)) + ABb))  ExtList]][]
  carefully [if abs ((ABm * ((world-width * scale) / 2.0)) + ABb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((ABm * ((world-width * scale) / 2.0)) + ABb))  ExtList]][]
  carefully [if abs ((((world-height * scale) / 2.0) - ABb) / ABm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - ABb) / ABm) ((world-height * scale) / 2.0))  ExtList]][]
  carefully [if abs ((((world-height * scale) / -2.0) - ABb) / ABm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - ABb) / ABm) ((world-height * scale) / -2.0))  ExtList]][]
  carefully [create-turtles 1 [set name "AB1" set xcor first first ExtList set ycor last first ExtList set color white set shape "dot"]][]
  carefully [create-turtles 1 [set name "AB2" set xcor first last ExtList set ycor last last ExtList set color white set shape "dot"]][]
  carefully [ask one-of turtles with [name = "AB1"] [create-link-with one-of turtles with [name = "AB2"]]][]
  carefully[ask link ([who] of one-of turtles with [name = "AB1"]) ([who] of one-of turtles with [name = "AB2"]) [set thickness 0.2 set color red]][]
  set ExtList []
  carefully [if abs ((BCm * ((world-width * scale) / -2.0)) + BCb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((BCm * ((world-width * scale) / -2.0)) + BCb))  ExtList]][]
  carefully [if abs ((BCm * ((world-width * scale) / 2.0)) + BCb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((BCm * ((world-width * scale) / 2.0)) + BCb))  ExtList]][]
  carefully [if abs ((((world-height * scale) / 2.0) - BCb) / BCm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - BCb) / BCm) ((world-height * scale) / 2.0))  ExtList]][]
  carefully [if abs ((((world-height * scale) / -2.0) - BCb) / BCm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - BCb) / BCm) ((world-height * scale) / -2.0))  ExtList]][]
  carefully [create-turtles 1 [set name "BC1" set xcor first first ExtList set ycor last first ExtList set color white set shape "dot"]][]
  carefully [create-turtles 1 [set name "BC2" set xcor first last ExtList set ycor last last ExtList set color white set shape "dot"]][]
  carefully [ask one-of turtles with [name = "BC1"] [create-link-with one-of turtles with [name = "BC2"]]][]
  carefully[ask link ([who] of one-of turtles with [name = "BC1"]) ([who] of one-of turtles with [name = "BC2"]) [set thickness 0.2 set color red]][]
  set ExtList []
  carefully [if abs ((CAm * ((world-width * scale) / -2.0)) + CAb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((CAm * ((world-width * scale) / -2.0)) + CAb))  ExtList]][]
  carefully [if abs ((CAm * ((world-width * scale) / 2.0)) + CAb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((CAm * ((world-width * scale) / 2.0)) + CAb))  ExtList]][]
  carefully [if abs ((((world-height * scale) / 2.0) - CAb) / CAm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - CAb) / CAm) ((world-height * scale) / 2.0))  ExtList]][]
  carefully [if abs ((((world-height * scale) / -2.0) - CAb) / CAm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - CAb) / CAm) ((world-height * scale) / -2.0))  ExtList]][]
  ;show ExtList
  carefully [create-turtles 1 [set name "CA1" set xcor first first ExtList set ycor last first ExtList set color white set shape "dot"]][]
  carefully [create-turtles 1 [set name "CA2" set xcor first last ExtList set ycor last last ExtList set color white set shape "dot"]][]
  carefully [ask one-of turtles with [name = "CA1"] [create-link-with one-of turtles with [name = "CA2"]]][]
  carefully[ask link ([who] of one-of turtles with [name = "CA1"]) ([who] of one-of turtles with [name = "CA2"]) [set thickness 0.2 set color red]][]
end 

to bi_intersect
  set Ix ((ABb - BCb) / (BCm - ABm))
  set Iy (ABm * Ix + ABb)
  ifelse abs Ix < world-width / 2 and abs Iy < world-height / 2
     [
     set radius (((Ix - Ax) ^ 2) + ((Iy - Ay) ^ 2)) ^ 0.5
     set pos 0
     carefully[
       repeat 179 [
         set pos pos + 2
         crt 1 [set name "circle" setxy Ix Iy set size 3 set shape "dot" set color white set size 1 set heading pos]
         ]
     ]
     []
     ][show "outside of view"]
     ask turtles with [name = "circle"] [carefully[jump radius set shape "line" set heading heading + 90][die]]
end 

to-report slope [x1 y1 x2 y2]
  report ((y1 - y2) / (x1 - x2))
end 

to-report intercept [x y m]
  report (y - (m * x))
end 

to-report midpoint [px py qx qy]
  set midx ((px + qx) / 2)
  set midy ((py + qy) / 2)
  ;show (list px py qx qy midx midy)
  report (list midx midy)
end