3Dcl.lua

--3Dcl.lua
--cloth falls on a round table
--code by Siapran
--09.04.13

--USER VALUES
--you may modify these to fit your needs
local g=1/32 --gravity
local r=49/100 --elasticity (MUST BE UNDER 1/2)
local f=49/50 --friction
local t=5 --table radius
--end of user values

for a=1,4,1 do
 misc.contrast(-1)
end

local print=nbdraw.print
local cursor=nbdraw.cursor
local line=nbdraw.line
local pixel=nbdraw.pixel
local page=nbdraw.copypage
local wait=misc.wait

--REQUIRES module math for trigonometric functions.
--Module math defines cos(), sin(), pi, pisurdeux, pisurquatre.
--you may replace the following code with your own
--cos() and sin() functions, or a module that defines these functions.
clear nil
cursor(1,1)
print "loading module"
func,err=misc.modload("math")
if func==nil then
 clear nil
 print(err)
 repeat until key(36)
end
func()
--end of module loading section

clear nil
cursor(1,1)
print "preparing engine"

local coord={}
local clothx={}
local clothy={}
local clothz={}
local clothxm={}
local clothym={}
local clothzm={}

local mode=0
local az=pi-pisurquatre --replace with value if needed (corresponds to pi*3/4)
local ay=pisurquatre --replace with value if needed (corresponds to pi/8)
local p=0
local x=0
local xb=0
local xc=0
local y=0
local yb=0
local z=0
local zb=0
local crz=0
local srz=0
local cry=0
local sry=0
local count=0
local lm
local vtwo=sqrt(2)

p=0
for i=-7,7,1 do
 for j=-7,7,1 do
  p=p+1
  clothx[p]=i
  clothy[p]=j
  clothz[p]=3
  clothxm[p]=0
  clothym[p]=0
  clothzm[p]=0
 end
end

local function traction(ia,ja,ib,jb,l) --calculates the traction exerced by a plot on another relative to its relaxed length
 lm=nil --length measured
 coord[1]=clothx[ib+15*(jb-1)]-clothx[ia+15*(ja-1)] --get 3D vector AB
 coord[2]=clothy[ib+15*(jb-1)]-clothy[ia+15*(ja-1)]
 coord[3]=clothz[ib+15*(jb-1)]-clothz[ia+15*(ja-1)]
 lm=sqrt(coord[1]^2+coord[2]^2+coord[3]^2) --measure AB
 coord[1]=coord[1]*(lm-l)*r/lm --apply elasticity
 coord[2]=coord[2]*(lm-l)*r/lm
 coord[3]=coord[3]*(lm-l)*r/lm
 clothxm[ia+15*(ja-1)]=clothxm[ia+15*(ja-1)]+coord[1] --write out
 clothym[ia+15*(ja-1)]=clothym[ia+15*(ja-1)]+coord[2]
 clothzm[ia+15*(ja-1)]=clothzm[ia+15*(ja-1)]+coord[3]
end

count=0
clear nil

repeat
 if key(3)then az=az-(pi/16)end --replace with value if needed
 if key(1)then az=az+(pi/16)end
 if key(7)and ay>-pisurdeux then ay=ay-(pi/16)end --replace with value if needed (corresponds to pi/2)
 if key(2)and ay<pisurdeux then ay=ay+(pi/16)end
 if key(5) then
  if mode==0 then
   mode=1
  else
   mode=0
  end
  while key(5) do
   wait(1)
  end
 end
 crz=cos(az) --compute rotation matrix
 srz=sin(az)
 cry=cos(ay)
 sry=sin(ay)
 if mode==0 then --if mode==compute mode
  cursor(1,1)
  print(count) --show number of frames computed
  for a=1,15,1 do --compute new momentums
   for b=1,15,1 do
    if sqrt((a-8)^2+(b-8)^2)>t then --if the plot is not on the table
     for c=-1,1,1 do --explore adjacent plots
      for d=-1,1,1 do
       if c+a>0 and c+a<16 and d+b>0 and d+b<16 then --clipping
        if c%2~=d%2 then
         traction(a,b,a+c,b+d,1) --sides
        else
         if c~=0 and d~=0 then
          traction(a,b,a+c,b+d,vtwo) --diagonals
         end
        end
       end
      end
     end
    end
   end
  end
  for a=1,15,1 do --apply new momentums
   for b=1,15,1 do
    p=a+15*(b-1)
    if sqrt((a-8)^2+(b-8)^2)>t then --if plot is not on the table
     clothzm[p]=clothzm[p]-g --apply gravity
     clothxm[p]=clothxm[p]*f --apply friction
     clothym[p]=clothym[p]*f
     clothzm[p]=clothzm[p]*f
     clothx[p]=clothx[p]+clothxm[p] --update coordinates
     clothy[p]=clothy[p]+clothym[p]
     clothz[p]=clothz[p]+clothzm[p]
    end
    x=clothx[p]*crz-clothy[p]*srz --rotate plot
    y=clothx[p]*srz+clothy[p]*crz
    xc=x*cry-clothz[p]*sry
    z=x*sry+clothz[p]*cry
    x=xc
    pixel(y/(x+50)*250+64,64-(z/(x+50)*250+32),1,1) --draw plot
   end
  end
  count=count+1
  page(1,0)
  clear(1)
 else --if mode==wireframe mode
  clear(1)
  for a=1,15,1 do
   p=a
   xb=clothx[p]*crz-clothy[p]*srz
   yb=clothx[p]*srz+clothy[p]*crz
   xc=xb*cry-clothz[p]*sry
   zb=xb*sry+clothz[p]*cry
   xb=xc
   for b=2,15,1 do
    p=a+15*(b-1)
    x=clothx[p]*crz-clothy[p]*srz
    y=clothx[p]*srz+clothy[p]*crz
    xc=x*cry-clothz[p]*sry
    z=x*sry+clothz[p]*cry
    x=xc
    line(yb/(xb+50)*250+64,64-(zb/(xb+50)*250+32),y/(x+50)*250+64,64-(z/(x+50)*250+32),1)
    xb=x
    yb=y
    zb=z
   end
  end
  for b=1,15,1 do
   p=(b-1)*15+1
   xb=clothx[p]*crz-clothy[p]*srz
   yb=clothx[p]*srz+clothy[p]*crz
   xc=xb*cry-clothz[p]*sry
   zb=xb*sry+clothz[p]*cry
   xb=xc
   for a=2,15,1 do
    p=a+15*(b-1)
    x=clothx[p]*crz-clothy[p]*srz
    y=clothx[p]*srz+clothy[p]*crz
    xc=x*cry-clothz[p]*sry
    z=x*sry+clothz[p]*cry
    x=xc
    line(yb/(xb+50)*250+64,64-(zb/(xb+50)*250+32),y/(x+50)*250+64,64-(z/(x+50)*250+32),1)
    xb=x
    yb=y
    zb=z
   end
  end
  page(1,0)
 end
until key(36)