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'r'
maxb=30               ' maximum # of celestial bodies
gravity=.09           ' gravitational constant (in this sim)
col_sense=.2          ' sensitivity for collision ( 0>= x <=1)
deffn$="celest_test"  ' default data file
''
option base 1
dim mass(maxb),diam(maxb),vx(maxb),vy(maxb),xp(maxb),yp(maxb)
init_prog()
load_bodies()         ' starting system 
make_sprites()
do
  if rest=0 then gravity_calc(mass,diam,vx,vy,xp,yp,dt)
  show_sprites()
  user_action()
until forever
end

def load_bodies()  '  fill / change .nb and the data statements
'r'
.nb=3
''
mm=0
for i=1 to .nb
  read .mass(i),.diam(i), .xp(i),.yp(i),.vx(i),.vy(i)
  mm=max(mm,.mass(i)) ! .max_m=mm
  next i
'r'
data 100,8,-100,-100,0,0,   100,8,-100,200,.1,0
data 1,3,300,-100,-1,-.0058
''
end def

def init_prog()
graphics ! graphics clear .2,.2,.2
set orientation portrait ! set toolbar off
option sprite pos central
randomize
maxx=screen_width() ! maxy=screen_height() ! .xy=min(maxx,maxy)
fill color .7,.7,.7 ! fill rect 0,769 to .xy,maxy
.sc=.xy/2
.trail=1 ! .centron=0 ! .scale=1 ! .rest=1 ! .dt=0.05
set buttons custom
draw color 1,0,0 ! fill color 0,1,0 ! fill alpha .3
set buttons font size 30
switch "trail" state 1 at maxx-220,.xy+10
switch "collo" state 0 at maxx-220,.xy+60
switch "centr" state 0 at maxx-220,.xy+110
button "zoom+" text "+" at 20,.xy+10 size 60,40
button "zoom-" text "-" at 230,.xy+10 size 60,40
button "speed+" text "+" at 230,.xy+70 size 60,40
button "speed-" text "-" at 20,.xy+70 size 60,40
button "load" text "Load" at 20,.xy+130 size 120,40
button "save" text "Save" at 20,.xy+190 size 120,40
button "stop" text "Quit" at maxx-180,maxy-60 size 150,40
button "cent" text "Centre" at 170,.xy+130 size 120,40
button "rand" text "Random" at 170,.xy+190 size 120,40
button "start" text "Start" at 355,.xy+70 size 120,40
button "clear" text "Clear" at 355,.xy+190 size 120,40
field "fname" text .deffn$ at 310,.xy-130 size 200,60
field "fname" hide
draw color 0,0,0
draw text "<- Zoom ->" at 95,.xy+20
draw text "<- Speed ->" at 90,.xy+80
draw text "Trail on" at maxx-160,.xy+15
draw text "Collisions on" at maxx-160,.xy+65
draw text "Centre always" at maxx-160,.xy+115
fill alpha 1
sprite "nova" begin 56,56
  fill color 1,1,.8 ! fill circle 28,28 size 25
  sprite end
sprite "nova" hide
end def

def make_sprites()
for i=1 to .nb
  d=.diam(i) ! d2=2.2*d
  sprite i begin d2,d2
    set_fill_color(.mass(i))
    fill circle d2/2,d2/2 size d
  sprite end
next i
end def

def show_sprites()
for i= 1 to .nb
  xs=.sc+.scale*.xp(i) ! ys=.sc-.scale*.yp(i) ! d=.diam(i)
  sprite i at xs,ys
  if ys<.xy-2*d then
    sprite i show
    if .trail then draw pixel 2*(xs),2*(ys) color .4,.4,.4
    else ! sprite i hide
    end if
  next i
end def

def user_action()
if bp("start") then
  .rest=1-.rest
  if .rest then ! button "start" text "Start"
    else ! button "start" text "Pause"
    end if
  end if
if bp("zoom+") then .scale*=1.5
if bp("zoom-") then .scale/=1.5
if bp("speed+") then .dt*=1.5
if bp("speed-") then .dt/=1.5
if bp("cent") then centre()
if bp("rand") then
  .nb=rnd(15) ! .gravity=.1+rnd(.1)
  for i=1 to .nb
    .mass(i)=4+rnd(10) ! .diam(i)=2+rnd(7)
    .xp(i)=200-rnd(400) ! .yp(i)=200-rnd(400)
    .vx(i)=0 ! .vy(i)=0
    next i
  make_sprites()
  end if
if bp("load") then
  field "fname" show ! field "fname" select
  do until field_changed("fname")
  deffn$=field_text$("fname")
  if not file_exists(deffn$) then
    field "fname" hide ! return
    end if
  file deffn$ reset
  file deffn$ input .nb, .gravity, .dt
  for i=1 to .nb
    file deffn$ input .mass(i),.diam(i),.xp(i),.yp(i),.vx(i),.vy(i)
    next i
  field "fname" hide
  make_sprites()
  end if
if bp("save") then
  if .nb=0 then return
  field "fname" show ! field "fname" select
  do until field_changed("fname")
  deffn$=field_text$("fname")
  if file_exists(deffn$) then file deffn$ delete 
  file deffn$ print .nb, .gravity, .dt
  for i=1 to .nb
    file deffn$ print .mass(i),.diam(i),.xp(i),.yp(i),.vx(i),.vy(i)
    next i
  field "fname" hide
  end if
if switch_state("collo") then
  for i=1 to .nb-1 ! i$=i
    for j=i+1 to .nb ! j$=j
      if sprites_collide(i$,j$) then
        s=sqrt((.xp(i)-.xp(j))^2+(.yp(i)-.yp(j))^2)
        if s<.col_sense*(.diam(i)+.diam(j)) then merge(i,j)
        end if
      next j
    next i
  end if
.centron=switch_state("centr")
.trail=switch_state("trail")
if bp("clear") then
  fill color .2,.2,.2
  fill rect 0,0 to .xy,769

  end if
if bp("stop") then stop
end def

def centre()
mtot=0 ! zx=0 ! zy=0
for i=1 to .nb
  mtot+=.mass(i) ! zx+=.mass(i)*.xp(i) ! zy+=.mass(i)*.yp(i)
  next i
zx=zx/mtot ! zy=zy/mtot
for i=1 to .nb ! .xp(i)-=zx ! .yp(i)-=zy ! next i
end def

def merge (p,q)    ' collision !
super_nova(.xp(p),.yp(p))
mn=.mass(p)+.mass(q) ! .mass(p)=mn
.diam(p)=(.diam(p)^3+.diam(q)^3)^(1/3)
.xp(p)=(.xp(p)+.xp(q))/2 ! .yp(p)=(.yp(p)+.yp(q))/2
.vx(p)=(.mass(p)*.vx(p)+.mass(q)*.vx(q))/mn
.vy(p)=(.mass(p)*.vy(p)+.mass(q)*.vy(q))/mn
sprite p delete ! sprite q delete
d=.diam(p) ! d2=2.2*d
sprite p begin d2,d2
    set_fill_color(.mass(p))
    fill circle d2/2,d2/2 size d
  sprite end
.nb-=1
for i=q to .nb
  .mass(i)=.mass(i+1) ! .diam(i)=.diam(i+1)
  .xp(i)=.xp(i+1) ! .yp(i)=.yp(i+1)
  .vx(i)=.vx(i+1) ! .vy(i)=.vy(i+1)
  sprite str$(i+1) rename str$(i)
  next i
end def

def super_nova(x,y)
xs=.sc+.scale*x ! ys=.sc-.scale*y
sprite "nova" at xs,ys ! sprite "nova" show
for s=.5 to 2.5 step .1
  sprite "nova" at xs,ys scale s ! pause .01
  next s
for a=1 to .1 step -.1
  sprite "nova" alpha a ! pause .1
  next a
sprite "nova" hide
end def

def set_fill_color(m)
if m=.max_m then ! fill color .9,.9,.9
  else
  t=max(1,100*rnd(4)+rnd(40)-20) ! pal(t)
  fill color pal.r, pal.g, pal.b
  end if
end def

def gravity_calc(mass(),diam(),vx(),vy(),xp(),yp(),dt)
n=.maxb ! nb=.nb
dim dist(n,n),newt(n,n),gonio(n,n),f_x(n,n),f_y(n,n)
dim fx(n),fy(n)
for i=1 to nb-1           ' calculate dx and dy
  for j=i+1 to nb
    dist(i,j)=yp(j)-yp(i)
    dist(j,i)=xp(j)-xp(i)
    next j
  next i
for i=1 to nb-1           ' calculate (squared) distances and forces
  for j=i+1 to nb
    newt(i,j)=dist(i,j)*dist(i,j) + dist(j,i)*dist(j,i)
    newt(j,i)=.gravity*mass(i)*mass(j)/newt(i,j) ' Newton formula
    newt(i,j)=sqrt(newt(i,j))
    next j
  next i
for i=1 to nb-1           ' calculate angles (sin and cos)
  for j=i+1 to nb
    gonio(i,j)=dist(i,j)/newt(i,j)
    gonio(j,i)=dist(j,i)/newt(i,j)
    next j
  next i
for i=1 to nb-1           ' calculate force components
  for j=i+1 to nb
    f_x(j,i)=gonio(j,i)*newt(j,i) ! f_x(i,j)=-f_x(j,i)
    f_y(j,i)=gonio(i,j)*newt(j,i) ! f_y(i,j)=-f_y(j,i)
    next j
  next i
for j=1 to nb          ' calculate total forces per planet
  fx(j)=0 ! fy(j)=0
  for i=1 to nb ! fx(j)+=f_x(i,j) ! fy(j)+=f_y(i,j) ! next i
  next j
if dt=1 then
  for i=1 to nb         ' calculate accel, velocity and position
    acc=fx(i)/mass(i) ! vx(i)+=acc ! xp(i)+=vx(i)-acc/2
    acc=fy(i)/mass(i) ! vy(i)+=acc ! yp(i)+=vy(i)-acc/2
    next i
  else
  for i=1 to nb          ' calculate accel, velocity and position
    acc=fx(i)/mass(i) ! vx(i)+=acc*dt
    xp(i)+=vx(i)*dt-acc*dt*dt/2
    acc=fy(i)/mass(i) ! vy(i)+=acc*dt
    yp(i)+=vy(i)*dt-acc*dt*dt/2
    next i
  end if
if .centron then centre()
end def

def pal(t)
r=0 ! g=0 ! b=0
if t<120 or t>240 then r=palsub(abs(t-360*floor(t/240)))
if t<240 then g=palsub(abs(t-120))
if t>120 then b=palsub(abs(t-240))
end def
def palsub(e)
f=.5   ' 0<=f<=1 better balance between prim. and sec. colors
if e<60 then c=1 else ! x=(120-e)/60 ! c=x*(1+f-f*x) ! end if
return c
end def

'  atan for option degrees
'
def deg_atan(x,y)
if x=0 then return 90*(2-sign(y)) else ta=atan(y/x)
if x<0 then ! ta+=180 ! else ! if y<0 then ! ta+=360 ! end if ! end if
return ta
end def

def bp(a$) = button_pressed(a$)