Point to line distance

turtles-own [name]
globals [p2l_dist nearestelement online1 Intersect step alt Area Above DPx DPy A1 A2 B1 B2 A1x A1y A2x A2y B1x B1y B2x B2y Ix Iy Am Ab Bm Bb D-Pointword A1word A2word B1word B2word Ixword Iyword Iword Intersection Disp ExtList]

to doit
  if step = 0 [line_1]
  if step = 1 [dpoint]
  if step = 2 [ipoint]
  if step = 3 [line_2]
  if step = 4 [altdist]
  set step step + 1
  if step > 5 [set step 0 ca clear-output]
end 

to line_1
    ask patches with [pxcor = 0] [set pcolor 1]
    ask patches with [pycor = 0] [set pcolor 1]
    create-turtles 1 [set name "A1" setxy random-xcor random-ycor set shape "circle" set color red set size 2 set label name set label-color white]
    set A1 one-of turtles with [name = "A1"]
    let A1who [who] of A1
    create-turtles 1 [set name "A2" setxy random-xcor random-ycor set shape "circle" set color red set size 2 set label name set label-color white]
    set A2 one-of turtles with [name = "A2"]
    let A2who [who] of A2
    ask A1 [create-link-with A2]
    ask link A1who A2who [set thickness 0.8 set color red]
    ;line A:  y=(m*x) + b  or x = (y - b) / m
    set A1x [xcor] of A1
    set A1y [ycor] of A1
    set A2x [xcor] of A2
    set A2y [ycor] of A2
    set Am (A1y - A2y) / (A1x - A2x)
    set Ab A1y - (Am * A1x)
    set A1word (word "(" substring (word A1x) 0 6 ", " substring (word A1y) 0 6 ")")
    set A2word (word "(" substring (word A2x) 0 6 ", " substring (word A2y) 0 6 ")")
    ;extend the line extension
    set ExtList []
    let scale 0.99
    if abs ((Am * ((world-width * scale) / -2.0)) + Ab) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((Am * ((world-width * scale) / -2.0)) + Ab))  ExtList]
    if abs ((Am * ((world-width * scale) / 2.0)) + Ab) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((Am * ((world-width * scale) / 2.0)) + Ab))  ExtList]
    if abs ((((world-height * scale) / 2.0) - Ab) / Am) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - Ab) / Am) ((world-height * scale) / 2.0))  ExtList]
    if abs ((((world-height * scale) / -2.0) - Ab) / Am) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - Ab) / Am) ((world-height * scale) / -2.0))  ExtList]
    show ExtList
    create-turtles 1 [set name "AE1" set xcor first first ExtList set ycor last first ExtList set color black]
    create-turtles 1 [set name "AE2" set xcor first last ExtList set ycor last last ExtList set color black]
    ask one-of turtles with [name = "AE1"] [create-link-with one-of turtles with [name = "AE2"]]
    ask link ([who] of one-of turtles with [name = "AE1"]) ([who] of one-of turtles with [name = "AE2"]) [set thickness 0.2 set color red]
end 

to dpoint
    create-turtles 1 [set name "D-Point" setxy random-xcor random-ycor set shape "circle" set color yellow set size 2 set label name set label-color white]
    set B1x [xcor] of one-of turtles with [name = "D-Point"]
    set B1y [ycor] of one-of turtles with [name = "D-Point"]
    set D-Pointword (word "(" substring (word B1x) 0 6 ", " substring (word B1y) 0 6 ")")
end 

to ipoint
        set Bm -1 / Am
        set Bb B1y - (Bm * B1x) ;get the y intercept
        set B2x 0
        set B2y Bb
        ;solve for point intersection at right angle
        set Ix ((Bb - Ab) / (Bm - Am)) * -1
        set Iy Bm * Ix + Bb
        set Intersect (word "(" substring (word Ix) 0 6 ", " substring (word Iy) 0 6 ")")
        ;set B2word (word "(" substring (word B2x) 0 6 ", " substring (word B2y) 0 6 ")")
        ;report the distance
        set alt (((B1x - Ix) ^ 2) + ((B1y - Iy) ^ 2)) ^ 0.5
        set Area ((((A1x - A2x) ^ 2 + (A1y - A2y) ^ 2) ^ 0.5)  + alt ) / 2
        ifelse B1y > Iy [set Above true][set Above false]
        ifelse (abs Ix > (world-width / 2.0)) or (abs Iy > (world-height / 2.0)) [set Disp "Outside display"][set Disp "YES" create-turtles 1 [set name "intersect" set label name setxy Ix Iy set shape "star" set color WHITE set size 3]]
end 

to line_2
  set ExtList []
  let scale 0.99
  if abs ((Bm * ((world-width * scale) / -2.0)) + Bb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((Bm * ((world-width * scale) / -2.0)) + Bb))  ExtList]
  if abs ((Bm * ((world-width * scale) / 2.0)) + Bb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((Bm * ((world-width * scale) / 2.0)) + Bb))  ExtList]
  if abs ((((world-height * scale) / 2.0) - Bb) / Bm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - Bb) / Bm) ((world-height * scale) / 2.0))  ExtList]
  if abs ((((world-height * scale) / -2.0) - Bb) / Bm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - Bb) / Bm) ((world-height * scale) / -2.0))  ExtList]
  show ExtList
  create-turtles 1 [set name "BE1" set xcor first first ExtList set ycor last first ExtList set color black]
  create-turtles 1 [set name "BE2" set xcor first last ExtList set ycor last last ExtList set color black]
  ask one-of turtles with [name = "BE1"] [create-link-with one-of turtles with [name = "BE2"]]
  ask link ([who] of one-of turtles with [name = "BE1"]) ([who] of one-of turtles with [name = "BE2"]) [set thickness 0.2 set color green]
  if Disp = "YES" [
    ask one-of turtles with [name = "intersect"] [create-link-with one-of turtles with [name = "D-Point"]]
    ask link ([who] of one-of turtles with [name = "intersect"]) ([who] of one-of turtles with [name = "D-Point"]) [set thickness 0.8 set color green]
  ]
end 

to altdist
  if Disp = "YES" [
    ;is the intersect point on ineAline 1?
    ifelse ((Ix < A1x and Ix > A2x) or (Ix < A2x and Ix > A1x)) and ((Iy < A1y and Iy > A2y) or (Iy < A2y and Iy > A1y)) [set online1 "YES" set nearestelement "along line"][set online1 "NO" set nearestelement "endpoint"]
    ifelse online1 = "YES"
      [ask link ([who] of one-of turtles with [name = "intersect"]) ([who] of one-of turtles with [name = "D-Point"]) [set thickness 0.8 set color yellow]
       ask one-of turtles with [name = "D-Point"] [set p2l_dist distancexy Ix Iy]]
      [ask link ([who] of one-of turtles with [name = "intersect"]) ([who] of one-of turtles with [name = "D-Point"]) [die]
       ask one-of turtles with [name = "D-Point"] [create-link-with one-of turtles with [name = [name] of min-one-of turtles with [name = "A1" or name = "A2"] [distance one-of turtles with [name = "D-Point"]]]]
       ask link ([who] of one-of turtles with [name = "D-Point"]) ([who] of one-of turtles with [name = [name] of min-one-of turtles with [name = "A1" or name = "A2"] [distance one-of turtles with [name = "D-Point"]]]) [set thickness 0.8 set color yellow ]]
    ]
end