I Can't figure out this Nested Loop

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Pincho Paxton

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Posted: 5th Jul 2012 18:48 Edited at: 5th Jul 2012 18:58

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I've been trying to figure out how to automate this nested loop for months...

The first 6 balls of particles are 0.06 from centre, with 6 more balls 0.03 from centre. This creates 12 balls around a single 13th ball at the centre. Then I instance this object as a bunch of limbs.

Now I need to make the same shape again but from this instanced object, and because it is bigger the distances change to 0.09, and 0.06. This then just repeats but moving the origin over, and to the side 0.09, and 0.06, -0.09, and -0.06. To create a bigger version.

My problem has been repeating this shape infinitely in a loop determined by the user. It will be very large, at least 40,000 sphere objects.

The idea is to get a ball, where all of the sphere are a repeating pattern. So a nested loop should work. I just can't figure it out.

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Latch

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Posted: 5th Jul 2012 21:15 Edited at: 5th Jul 2012 21:23

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Perhaps you could use the formula for a sphere to build your ultimate sphere of particles.

1. Build your single molecule of 12 individual spheres.
2. get the radius of this individual molecule.
3a. Plug this radius*2*shell_layer into the sphere formula and build the next shell of molecules

3b. The first shell is at 2*radius*1 from the original center
The second shell is at 2*radius*2 from the original center and so on.

4. You have to determine the increase in molecules per shell. I'm not really sure what the calculation for this value is. But this should be proportional to the angles between molecules as the radius increases from center.

The pseudo code might look like

rem build the very center
make object sphere 1,1

rem number of shells
for shell=0 to maxshells

rem figure out number of muleculse in shell
   mcount=shell * some factor (the 0 shell layer will have no additional molecules)

Loop through molecule count
      rem build molecule by adding spheres around the center
      for build = 1 to 13
         add limb spheres around the center with one extra center lmb at the center
      next build
   endloop

rem calculate the displacement radius
   displace=radius*shell*2

rem figure out the angle increments based on the shell layer and displacement
   angchange1#=180.0/((rings-1)*1.0)
   angchange2#=360.0/((slices)*1.0)
   angy#=(angy#-angchange2#)
   angx#=180+angchange1#

rem start the loop for the sphere formula and plug in your displacement
   repeat
      use sphere formula with radius equal to displacement
      displace the CENTER LIMB of each 13 sphere cluster and all of it's children will move with it
   until positions in current shell are filled

onto the next shell of molecules
next shell

+ Code Snippet

rem build the very center
make object sphere 1,1

rem number of shells
for shell=0 to maxshells

   rem figure out number of muleculse in shell
   mcount=shell * some factor (the 0 shell layer will have no additional molecules)

   Loop through molecule count
      rem build molecule by adding spheres around the center
      for build = 1 to 13
         add limb spheres around the center with one extra center lmb at the center
      next build
   endloop

   rem calculate the displacement radius
   displace=radius*shell*2

   rem figure out the angle increments based on the shell layer and displacement
   angchange1#=180.0/((rings-1)*1.0)
   angchange2#=360.0/((slices)*1.0)
   angy#=(angy#-angchange2#)
   angx#=180+angchange1#

   rem start the loop for the sphere formula and plug in your displacement
   repeat
      use sphere formula with radius equal to displacement
      displace the CENTER LIMB of each 13 sphere cluster and all of it's children will move with it
   until positions in current shell are filled

   onto the next shell of molecules
next shell

My assumption is that you are creating a solid mass of multilayered molecules as opposed to a single shell of molecules on the outside of the sphere at some radius from the center.

Enjoy your day.

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Pincho Paxton

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Posted: 5th Jul 2012 21:46 Edited at: 5th Jul 2012 21:48

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Quote: "My assumption is that you are creating a solid mass of multilayered molecules as opposed to a single shell of molecules on the outside of the sphere at some radius from the center."

Yeah, the instanced object is 12 particles around 1, and that is the repeat pattern that I need to loop. The Radius is 1.8.... which is
3 * 0.6

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chromatic3d

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Posted: 5th Jul 2012 21:52 Edited at: 5th Jul 2012 21:53

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Not sure if I know enough to help but here is how I would do it.

You could use three mods and base it off of where in the x,y,z grid the first mole of each set is located to create a blend of +/- mods.
Not sure if helping.
How do you expand in the sphere?
Do you want to vary the sphere size or distance between sets based on total number of molecules?

+ Code Snippet


input = 40000/13
for i = 1 to input

  "magic formula" to establish next center point on curved line in sphere depending on how you want to progress from center.
  make center molecule
  
  for t 1 to 2
    if t = 1 then mod =1
    if t = 2 then mod =-1
    
    for c = 1 to 12
      
      make all 12 sub moles using x mod to make half negative.

      next c

  next t
next i

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Pincho Paxton

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Posted: 5th Jul 2012 22:20 Edited at: 5th Jul 2012 22:25

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Yeah that's sort of how it works. Each positive is followed by a negative from an origin which is reset to zero. All locations must be divisible by 3. So X can be 0.06, 0.6, 1.8, 6, 9, 12, 18. Same with Y, and Z. Every particle must fall on these exact locations. It's such a perfect shape that there might be a way to do it with an array.

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Pincho Paxton

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Posted: 6th Jul 2012 16:20

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Got the first part to loop through which is a start.

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Pincho Paxton

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Posted: 6th Jul 2012 21:29 Edited at: 6th Jul 2012 21:55

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It's no good, I've tried lots of ways to make this into a ball, and now it's currently spiky...

Here's the code so far. Can anyone make this into a ball where all of the sphere are on X/Y/Z coordinates divisible by 0.03 close together, and not overlapping? It can be a ball, or 3D hexagon stacking, that doesn't matter so long as the first shape is repeated...

Set Display Mode 1024,768,32
autocam off
backdrop off
sync on

set normalization on
set ambient light 20
hide mouse
load image "Background.png",1
load image "Blue.png",2
hide light 0
make light 1
set light range 1,300
wait 500
Origin# = 0.06
Glow = 12
Glow1 = 0
fov = 12
set camera fov fov

`I add an outer boundary to the universe because of my slow computer.
UniverseScale = 1000

Particles = 17
`I also need to Limit the maximun number of particles because of computer speed.
`limit = 18 is OK
`Limit 100 not easy to get right
limit = 100
`Total is just the first particle number, and it's 3 because of some fake boundary particles.
total = 3

`Setup routines, not part of main program...
set camera range 0.1,3000
make object sphere 1,3000,6,6

set object 1,1,1,0,1,1,1,1
Texture object 1,1
position camera 0,0,-5

set alpha mapping on 1,95
`Loop that jumps to Generates first shape
Gosub Generate

count = 0
Do
if  Particles < Limit and glow1 = 0

Origin# = PA#
`Clone the initial shape
gosub clone

Endif
If particles >= limit
glow1 = 1
Endif
if glow1 = 1

Gosub Animate

endif
`gosub animate
gosub PositionCamera
position object 1,camera position x(0),camera position y(0),camera position z(0)
position light 1,camera position x(0),camera position y(0),camera position z(0)

sync
Loop

Clone:
`The loop that shapes Spacetime

PA# = PA# + 0.06
NA# = PA# - (PA# * 2.0)
PB# = PA#/2.0
NB# = NA#/2.0
PC# = PB#/2.0
NC# = NB#/2.0

inc total,14
OriginX# = PA#-Origin#
OriginY# = NA# + Origin#
OriginZ# = PB# - (origin#/2.0)

inc particles
instance object particles,6
position object particles,NB#+OriginX#,PA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object Particles, PB#+OriginX#,NA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,NA#+OriginX#,0+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,PA#+OriginX#,0+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,NB#+OriginX#,NA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,PB#+OriginX#,PA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,PC#+OriginX#,PB#+OriginY#,PA#+OriginZ#

inc particles
instance object particles,6
position object particles,NC#+OriginX#,NB#+OriginY#,NA#+OriginZ#

inc particles
instance object particles,6
position object particles,NB#+OriginX#,0+OriginY#,PA#+OriginZ#

inc particles
instance object particles,6
position object particles,PB#+OriginX#,0+OriginY#,NA#+OriginZ#

inc particles
instance object particles,6
position object particles,PC#+OriginX#,NB#+OriginY#,PA#+OriginZ#

inc particles
instance object particles,6
position object particles,NC#+OriginX#,PB#+OriginY#,NA#+OriginZ#

Return

Generate:
`The loop that creates the Universe. How small can I get it?
`Add as many particles as a computer can allow based on the speed of the computer
`This setup is currently far more Hard Coded than I want it to be
`I want the maths to be naturally occuring in the universe, so everything uses the number 6
`The Number 6 in this case 0.6 is divided to represent Hexidecimal in Decimal
PA# = 0.06
NA# = PA# - (PA# * 2.0)
PB# = PA#/2.0
NB# = NA#/2.0
PC# = PB#/2.0
NC# = NB#/2.0

inc total,14
OriginX# = PA#-Origin#
OriginY# = NA# + Origin#
OriginZ# = PB# - (origin#/2.0)
make OBJECT sphere total,0.06,6,6
make OBJECT sphere total-13,0.21

make OBJECT sphere 6, 0.06,6,6

set object 6,1,1,1,1,1,1,0

color object 6,rgb(10,10,90)
position mouse screen width()/2,screen height()/2

position object total-13,0+OriginX#,0+OriginY#,0+OriginZ#
make mesh from object 1, total

`These Hard Coded positions look like they can be reduced to a single loop

add limb 6,1,1
add limb 6,2,1
add limb 6,3,1
add limb 6,4,1
add limb 6,5,1
add limb 6,6,1
add limb 6,7,1
add limb 6,8,1
add limb 6,9,1
add limb 6,10,1
add limb 6,11,1
add limb 6,12,1
add limb 6,13,1

offset limb 6,1,NB#+OriginX#,PA#+OriginY#,0+OriginZ#
offset limb 6,2,PB#+OriginX#,NA#+OriginY#,0+OriginZ#
offset limb 6,3,NA#+OriginX#,0+OriginY#,0+OriginZ#
offset limb 6,4,PA#+OriginX#,0+OriginY#,0+OriginZ#
offset limb 6,5,NB#+OriginX#,NA#+OriginY#,0+OriginZ#
offset limb 6,6,PB#+OriginX#,PA#+OriginY#,0+OriginZ#
offset limb 6,7,PC#+OriginX#,PB#+OriginY#,PA#+OriginZ#
offset limb 6,8,NC#+OriginX#,NB#+OriginY#,NA#+OriginZ#
offset limb 6,9,NB#+OriginX#,0+OriginY#,PA#+OriginZ#
offset limb 6,10,PB#+OriginX#,0+OriginY#,NA#+OriginZ#
offset limb 6,11,PC#+OriginX#,NB#+OriginY#,PA#+OriginZ#
offset limb 6,12,NC#+OriginX#,PB#+OriginY#,NA#+OriginZ#
color limb 6,13,rgb(0,0,0)

for n = 1 to 12
color limb 6,n,rgb(0,0,50)
next n

set alpha mapping on 6,10
SET OBJECT TRANSPARENCY 6,6

delete object total
delete object total-13

hide object 6

Return

Animate:
`GlowTest just illuminates the path of energy

if t <= timer()
t = timer() + 50
if on = 0

color limb 6,glow,rgb(200,200,255)
On = 1
Endif

if on = 2

color limb 6,glow,rgb(0,0,90)
set alpha mapping on 6,10
SET OBJECT TRANSPARENCY 6,6

Dec Glow
If Glow = 0

inc total,14
glow = 12
if total = particles+14 then total = 17

endif

On = 0
Endif
if on = 1 then on = 2
endif
Return

positionCamera:
control camera using arrowkeys 0,0.00001*((200-fov)/2),0.0001*((200-fov)/2)

if leftkey() then move camera left 0.000001*((200-fov)/2)
if rightkey() then move camera right 0.000001*((200-fov)/2)

if keystate(17) = 1
      if smoothcamera = 0
         smoothcamera = 1
      else
         smoothcamera = 0
      endif
      repeat until keystate(17) = 0
   endif

smoothcamx# = ( smoothcamx# + mousemovey() )
      smoothcamy# = ( smoothcamy# + mousemovex() )
      xrotate camera ( camera angle x() + ( smoothcamx# - camera angle x() ) / 50.0 )
      yrotate camera ( camera angle y() + ( smoothcamy#/50 - camera angle y() ) / 150.0 )

return

+ Code Snippet

Set Display Mode 1024,768,32
autocam off
backdrop off
sync on

set normalization on
set ambient light 20
hide mouse
load image "Background.png",1
load image "Blue.png",2
hide light 0
make light 1
set light range 1,300
wait 500
Origin# = 0.06
Glow = 12
Glow1 = 0
fov = 12
set camera fov fov


`I add an outer boundary to the universe because of my slow computer.
UniverseScale = 1000

Particles = 17
`I also need to Limit the maximun number of particles because of computer speed.
`limit = 18 is OK
`Limit 100 not easy to get right
limit = 100
`Total is just the first particle number, and it's 3 because of some fake boundary particles.
total = 3

`Setup routines, not part of main program...
set camera range 0.1,3000
make object sphere 1,3000,6,6

set object 1,1,1,0,1,1,1,1
Texture object 1,1
position camera 0,0,-5


set alpha mapping on 1,95
`Loop that jumps to Generates first shape
Gosub Generate


count = 0
Do
if  Particles < Limit and glow1 = 0

Origin# = PA#
`Clone the initial shape
gosub clone


Endif
If particles >= limit
glow1 = 1
Endif
if glow1 = 1

Gosub Animate

endif
`gosub animate
gosub PositionCamera
position object 1,camera position x(0),camera position y(0),camera position z(0)
position light 1,camera position x(0),camera position y(0),camera position z(0)

sync
Loop


Clone:
`The loop that shapes Spacetime


PA# = PA# + 0.06
NA# = PA# - (PA# * 2.0)
PB# = PA#/2.0
NB# = NA#/2.0
PC# = PB#/2.0
NC# = NB#/2.0

inc total,14
OriginX# = PA#-Origin#
OriginY# = NA# + Origin#
OriginZ# = PB# - (origin#/2.0)






inc particles
instance object particles,6
position object particles,NB#+OriginX#,PA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object Particles, PB#+OriginX#,NA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,NA#+OriginX#,0+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,PA#+OriginX#,0+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,NB#+OriginX#,NA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,PB#+OriginX#,PA#+OriginY#,0+OriginZ#

inc particles
instance object particles,6
position object particles,PC#+OriginX#,PB#+OriginY#,PA#+OriginZ#

inc particles
instance object particles,6
position object particles,NC#+OriginX#,NB#+OriginY#,NA#+OriginZ#

inc particles
instance object particles,6
position object particles,NB#+OriginX#,0+OriginY#,PA#+OriginZ#

inc particles
instance object particles,6
position object particles,PB#+OriginX#,0+OriginY#,NA#+OriginZ#

inc particles
instance object particles,6
position object particles,PC#+OriginX#,NB#+OriginY#,PA#+OriginZ#

inc particles
instance object particles,6
position object particles,NC#+OriginX#,PB#+OriginY#,NA#+OriginZ#



Return

Generate:
`The loop that creates the Universe. How small can I get it?
`Add as many particles as a computer can allow based on the speed of the computer
`This setup is currently far more Hard Coded than I want it to be
`I want the maths to be naturally occuring in the universe, so everything uses the number 6
`The Number 6 in this case 0.6 is divided to represent Hexidecimal in Decimal
PA# = 0.06
NA# = PA# - (PA# * 2.0)
PB# = PA#/2.0
NB# = NA#/2.0
PC# = PB#/2.0
NC# = NB#/2.0

inc total,14
OriginX# = PA#-Origin#
OriginY# = NA# + Origin#
OriginZ# = PB# - (origin#/2.0)
make OBJECT sphere total,0.06,6,6
make OBJECT sphere total-13,0.21

make OBJECT sphere 6, 0.06,6,6


set object 6,1,1,1,1,1,1,0

color object 6,rgb(10,10,90)
position mouse screen width()/2,screen height()/2



position object total-13,0+OriginX#,0+OriginY#,0+OriginZ#
make mesh from object 1, total

`These Hard Coded positions look like they can be reduced to a single loop


add limb 6,1,1
add limb 6,2,1
add limb 6,3,1
add limb 6,4,1
add limb 6,5,1
add limb 6,6,1
add limb 6,7,1
add limb 6,8,1
add limb 6,9,1
add limb 6,10,1
add limb 6,11,1
add limb 6,12,1
add limb 6,13,1

offset limb 6,1,NB#+OriginX#,PA#+OriginY#,0+OriginZ#
offset limb 6,2,PB#+OriginX#,NA#+OriginY#,0+OriginZ#
offset limb 6,3,NA#+OriginX#,0+OriginY#,0+OriginZ#
offset limb 6,4,PA#+OriginX#,0+OriginY#,0+OriginZ#
offset limb 6,5,NB#+OriginX#,NA#+OriginY#,0+OriginZ#
offset limb 6,6,PB#+OriginX#,PA#+OriginY#,0+OriginZ#
offset limb 6,7,PC#+OriginX#,PB#+OriginY#,PA#+OriginZ#
offset limb 6,8,NC#+OriginX#,NB#+OriginY#,NA#+OriginZ#
offset limb 6,9,NB#+OriginX#,0+OriginY#,PA#+OriginZ#
offset limb 6,10,PB#+OriginX#,0+OriginY#,NA#+OriginZ#
offset limb 6,11,PC#+OriginX#,NB#+OriginY#,PA#+OriginZ#
offset limb 6,12,NC#+OriginX#,PB#+OriginY#,NA#+OriginZ#
color limb 6,13,rgb(0,0,0)


for n = 1 to 12
color limb 6,n,rgb(0,0,50)
next n

set alpha mapping on 6,10
SET OBJECT TRANSPARENCY 6,6

delete object total
delete object total-13

hide object 6

Return

Animate:
`GlowTest just illuminates the path of energy


if t <= timer()
t = timer() + 50
if on = 0

color limb 6,glow,rgb(200,200,255)
On = 1
Endif

if on = 2

color limb 6,glow,rgb(0,0,90)
set alpha mapping on 6,10
SET OBJECT TRANSPARENCY 6,6

Dec Glow
If Glow = 0

inc total,14
glow = 12
if total = particles+14 then total = 17

endif

On = 0
Endif
if on = 1 then on = 2
endif
Return

positionCamera:
control camera using arrowkeys 0,0.00001*((200-fov)/2),0.0001*((200-fov)/2)

if leftkey() then move camera left 0.000001*((200-fov)/2)
if rightkey() then move camera right 0.000001*((200-fov)/2)

 if keystate(17) = 1
      if smoothcamera = 0
         smoothcamera = 1
      else
         smoothcamera = 0
      endif
      repeat until keystate(17) = 0
   endif


      smoothcamx# = ( smoothcamx# + mousemovey() )
      smoothcamy# = ( smoothcamy# + mousemovex() )
      xrotate camera ( camera angle x() + ( smoothcamx# - camera angle x() ) / 50.0 )
      yrotate camera ( camera angle y() + ( smoothcamy#/50 - camera angle y() ) / 150.0 )


return

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Latch

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Posted: 7th Jul 2012 23:40 Edited at: 7th Jul 2012 23:42

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I tried the shell building suggestion I made using the sphere formula. It works - but it needs the proper modifiers to expand each layer the correct amount. It also showed something interesting. Here's a screeny, but it might be a bit hard to understand what you are seeing:

There are three sphere layers in this example: red at the center, green in the middle, and yellow on the outside. Each sphere is made up of individual cubes spaced at about 10 times the radius of an individual cube from the center (so I could see the layers). Each layer is the radius times the current shell number from the center so each layer should be the same distance from the previous layer.

What is interesting is, though the sphere formula works, as we approach the polar caps, the distance between particles decreases, and as we approach the equator, the distance between particles increases. Each shell layer has more particles than the previous one, which stands to reason because it's a larger surface area so that's a compensation to a degree. The problem is that a standard sphere formula won't give you the equidistant particles that you want. I don't know if there is a way to maintain the same proportions and maintain a sphere shape. Maybe instead of the standard sphere formula, you could use an icosahedron of some sort.

Enjoy your day.

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Pincho Paxton

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Posted: 8th Jul 2012 02:28 Edited at: 8th Jul 2012 02:47

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It's very important to get the exact 0.03 multiple distribution. The problem it's more of a nested loop problem. If I could figure out a few layers thick, and take the X/Y/Z distribution, then I might figure out by how much the loop is growing. It's really annoying, because after this is made, the rest of the program is a lot more exciting.

You see this second shape could be copied, and pasted with the exact same rules as the first shape. Then 13 of those would also have the same rules. But I found that Instancing instanced objects repeatedly isn't easy.

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DarkBASIC Professional Discussion / I Can't figure out this Nested Loop