' gd1lib.bas - jackord@kw.igs.net - revised 28 Feb 08 - Liberty Basic v4.02
' solution of Laplace's equation:
'   128 iterations at 4 pixel steps
'    16 iterations at 2 pixel steps
'     6 iterations at 1 pixel steps

  nomainwin
  button#1.b, "Plot", [plot], UL, 30, 170, 65, 20
'  textbox#1.tx, 110, 170, 65, 20
  WindowWidth=222     ' pixel scale 0-204
  WindowHeight=228    ' pixel scale 0-190
  UpperLeftX=100: UpperLeftY=50
  open "Laplace's Equation" for graphics_nsb as #1
  #1 "trapclose [quit]"
  dim p(4): dim q(4): dim c$(6): dim v(205, 169)
  p(1)=60: q(1)=108: p(2)=102: q(2)=36: p(3)=144: q(3)=108
  c$(0)="blue": c$(1)="cyan": c$(2)="red"
  c$(3)="yellow": c$(4)="darkpink": c$(5)="green"
  gosub [pin]

[waitHere]
  wait

[pin]
  #1 "backcolor white ; cls ; color black ; down"
  #1 "place 105 168": #1 "\\Pass/150"
  #1 "color blue ; place 0 0": #1 "box 204 168"
  #1 "color red ; backcolor red"
  for i=1 to 3
    #1 "place "; p(i); " "; q(i)
    #1 "circlefilled 6"
  next i
return

[plot]
  d=4: nplt=8
  for k=d to 168-d
    for j=d to 204-d
      v(j, k)=50
    next j
  next k
  for i=1 to 3
    for k=q(i)-6 to q(i)+6
      for j=p(i)-6 to p(i)+6
        r2=(p(i)-j)*(p(i)-j)+(q(i)-k)*(q(i)-k)
        if r2<=36 then v(j, k)=100
      next j
    next k
  next i
  for i=1 to 150
    #1 "color white ; backcolor white ; place 105 168 ; boxfilled 200 189 ; color black"
    #1 "\\Pass "; str$(i); "/150"
    for k=d to 168-d step d
      for j=d to 204-d step d
        if v(j, k)<100 then
          v(j, k)=(v(j, k-d)+v(j, k+d)+v(j+d, k)+v(j-d, k))/4
        end if
        if i=1 or i=nplt then
          plt=int(v(j, k)/7): plt=plt-6*int(plt/6)
          #1 "color "; c$(plt)
          if d<2 then
            #1 "line "; j-1; " "; k; " "; j; " "; k
          else
            #1 "place "; j-d/2; " "; k-d/2
            #1 "backcolor "; c$(plt)
            #1 "boxfilled "; j+d/2; " "; k+d/2
          end if
        end if
      next j
    next k
    if i=128 or i=144 then
      d=d/2
      for k=d to 168-d step 2*d
        for j=2*d to 204-2*d step 2*d
          if v(j, k)<100 then v(j, k)=(v(j, k-d)+v(j, k+d))/2
        next j
      next k
      for k=d to 168-d step d
        for j=d to 204-d step 2*d
          if v(j, k)<100 then v(j, k)=(v(j-d, k)+v(j+d, k))/2
        next j
      next k
    end if
    if i=nplt then nplt=nplt+2*d
    scan
  next i
  #1 "color white ; place 105 168 ; boxfilled 200 189 ; color black"
  #1 "\\Finished!"
goto [waitHere]

[quit]
  close#1
end