matrix 3d problem

General FreeBASIC programming questions.
bluatigro
Posts: 651
Joined: Apr 25, 2012 10:35
Location: netherlands

matrix 3d problem

Postby bluatigro » May 04, 2012 9:26

i m also trying graphics whit matrix's

i have a bug / typo somewere ?

Code: Select all

type matrix
  dim as single m( 3 , 3 )
end type
operator * ( a as matrix , b as matrix ) as matrix
  dim as integer i , j , k
  dim uit as matrix
  for i = 0 to 3
    for j = 0 to 3
''      uit.m( i , j ) = 0
      for k = 0 to 3
''        uit.m( i , j ) += a.m( i , k ) * b.m( k , j )
        uit.m( j , k ) += a.m( j , i ) * b.m( i , k )
      next k
    next j
  next i
  return uit
end operator
dim shared as matrix v( 20 )
v( 0 ).m( 0 , 0 ) = 1
v( 0 ).m( 1 , 1 ) = 1
v( 0 ).m( 2 , 2 ) = 1
v( 0 ).m( 3 , 3 ) = 1
dim shared as single sk( 64 , 2 )
declare sub link( no as integer , x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , ax as integer , p as integer )
declare sub child( no as integer , x as single , y as single , z as single _
, lim as integer , ax as integer , p as integer )
declare sub spot( byref x as single , byref y as single , byref z as single )
declare sub rotate( byref k as single , byref l as single , deg as single )
declare function rad( x as single ) as single
dim shared as integer number
const as single pi = atn( 1 ) * 4
dim shared as single cam( 6 )
declare sub camara( x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , zoom as single )
declare function pend( f as single , a as single ) as single
declare sub skelet( no as integer , x as single , y as single , z as single )

const as integer xyz = 0
const as integer xzy = 1
const as integer yxz = 2
const as integer yzx = 3
const as integer zxy = 4
const as integer zyx = 5


''  graphics

''primary colors
const as integer black   = &h000000
const as integer red     = &hff0000
const as integer green   = &h00ff00
const as integer yellow  = &hffff00
const as integer blue    = &h0000ff
const as integer magenta = &hff00ff
const as integer cyan    = &h00ffff
const as integer white   = &hffffff
''mix colors
const as integer orange  = &hff7f00
const as integer gray    = &h7f7f7f
const as integer pink    = &hff7f7f
const as integer purple  = &h7f007f

''  lijn world

declare sub lijn( x1 as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
declare sub cube( x1 as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
declare sub dodeca( x as single , y as single , z as single _
, d as single , dik as integer )
declare sub lijnman( kl as integer )
const as integer arm = 0
const as integer elbow = 1
const as integer wrist = 2
const as integer leg = 3
const as integer knee = 4
const as integer enkle = 5
const as integer neck = 6
const as integer head = 7
const as integer eye = 8
const as integer lr = 10

screen 20 , 32 , 2
dim frame as single
do
  cls
 
  ''  test 3d engine

  skelet leg , pend( frame * 5 , 30 ) , 0 , 0
  skelet knee , pend( frame * 5 - 90 , 30 ) + 30  , 0 , 0
  skelet leg + lr , pend( frame * 5 + 180 , 30 ) , 0 , 0
  skelet knee + lr , pend( frame * 5 + 90 , 30 ) + 30 , 0 , 0
  skelet arm , pend( frame * 5 + 180 , 30 ) , 0 , 0
  skelet elbow , -30 , 0 , 0
  skelet arm + lr , pend( frame * 5 , 30 ) , 0 , 0
  skelet elbow + lr , -30 , 0 , 0
 
    ''  test lijn world
 
  link 1 , -250,0,0 , frame,frame,0 , 0 , 0
    dodeca 0,0,0 , 100 , cyan
   
  link 1 , 0,0,0 , frame,0,0 , 0 , 0
    lijnman yellow
   
  link 1 , 250,0,0 , -frame,0,0 , 0 , 0
    lijnman magenta

  frame = frame + 1
  sleep 40
  flip
loop while inkey = ""
end

''                                                  lijn world

sub lijnman( kl as integer )
    lijn 30,0,0 ,-30,0,0 , kl
    lijn 0,0,0 , 0,120,0 , kl
    lijn 50,100,0 , -50,100,0 , kl
    cube 0,140,0 , 15,15,15 , kl
    child 2 , 30,0,0 , leg , yzx , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , knee , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
        lijn 0,-70,0 , 0,-70,20 , kl
    child 2 , -30,0,0 , leg + lr , yzx , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , knee + lr , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
        lijn 0,-70,0 , 0,-70,20 , kl
    child 2 , 50,100,0 , arm , xzy , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , elbow , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
    child 2 , -50,100,0 , arm + lr , xzy ,  1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , elbow + lr , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
end sub
sub dodeca( x as single , y as single , z as single , d as single , dik as integer )
  dim f as single
  f = ( sqr( 5 ) - 1 ) / 2
  ''(±1, ±1, ±1)
  ''(0, ±1/f, ±f)
  ''(±1/f, ±f, 0)
  ''(±f, 0, ±1/f)
  lijn x + d , y + d , z + d , x , y + 1/f*d , z + f*d ,dik
  lijn x + d , y + d , z + d , x + 1/f*d , y + f*d , z ,dik
  lijn x + d , y + d , z + d , x + f*d , y , z + 1/f*d ,dik
  lijn x - d , y - d , z - d , x , y - 1/f*d , z - f*d ,dik
  lijn x - d , y - d , z - d , x - 1/f*d , y - f*d , z ,dik
  lijn x - d , y - d , z - d , x - f*d , y , z - 1/f*d ,dik
  lijn x+1/f*d,y+f*d,z,x+1/f*d,y-f*d,z,dik
  lijn x-1/f*d,y-f*d,z,x-1/f*d,y+f*d,z,dik
  lijn x,y+1/f*d,z+f*d,x,y+1/f*d,z-f*d,dik
  lijn x,y-1/f*d,z-f*d,x,y-1/f*d,z+f*d,dik
  lijn x-f*d,y,z-1/f*d,x+f*d,y,z-1/f*d,dik
  lijn x+f*d,y,z+1/f*d,x-f*d,y,z+1/f*d,dik
  lijn x+1/f*d,y+f*d,z,x+d,y+d,z-d,dik
  lijn x-1/f*d,y-f*d,z,x-d,y-d,z+d,dik
  lijn x+f*d,y,z+1/f*d,x-f*d,y,z+1/f*d,dik
  lijn x-f*d,y,z-1/f*d,x+f*d,y,z-1/f*d,dik
  lijn x-f*d,y,z+1/f*d,x-d,y+d,z+d,dik
  lijn x+f*d,y,z-1/f*d,x+d,y-d,z-d,dik
  lijn x+f*d,y,z-1/f*d,x+d,y+d,z-d,dik
  lijn x-f*d,y,z+1/f*d,x-d,y-d,z+d,dik
  lijn x-d,y+d,z+d,x,y+1/f*d,z+f*d,dik
  lijn x+d,y-d,z-d,x,y-1/f*d,z-f*d,dik
  lijn x-d,y+d,z+d,x-1/f*d,y+f*d,z,dik
  lijn x+d,y-d,z-d,x+1/f*d,y-f*d,z,dik
  lijn x+f*d,y,z+1/f*d,x+d,y-d,z+d,dik
  lijn x-f*d,y,z-1/f*d,x-d,y+d,z-d,dik
  lijn x+d,y-d,z+d,x,y-1/f*d,z+f*d,dik
  lijn x-d,y+d,z-d,x,y+1/f*d,z-f*d,dik
  lijn x+d,y+d,z-d,x,y+1/f*d,z-f*d,dik
  lijn x-d,y-d,z+d,x,y-1/f*d,z+f*d,dik
  lijn x+d,y-d,z+d,x+1/f*d,y-f*d,z,dik
  lijn x-d,y+d,z-d,x-1/f*d,y+f*d,z,dik
end sub
sub cube( x as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )

  lijn x + x2 , y + y2 , z + z2 , x - x2 , y + y2 , z + z2 , kl
  lijn x + x2 , y + y2 , z - z2 , x - x2 , y + y2 , z - z2 , kl
  lijn x + x2 , y - y2 , z + z2 , x - x2 , y - y2 , z + z2 , kl
  lijn x + x2 , y - y2 , z - z2 , x - x2 , y - y2 , z - z2 , kl
 
  lijn x + x2 , y + y2 , z + z2 , x + x2 , y - y2 , z + z2 , kl
  lijn x + x2 , y + y2 , z - z2 , x + x2 , y - y2 , z - z2 , kl
  lijn x - x2 , y + y2 , z + z2 , x - x2 , y - y2 , z + z2 , kl
  lijn x - x2 , y + y2 , z - z2 , x - x2 , y - y2 , z - z2 , kl
 
  lijn x + x2 , y + y2 , z + z2 , x + x2 , y + y2 , z - z2 , kl
  lijn x + x2 , y - y2 , z + z2 , x + x2 , y - y2 , z - z2 , kl
  lijn x - x2 , y + y2 , z + z2 , x - x2 , y + y2 , z - z2 , kl
  lijn x - x2 , y - y2 , z + z2 , x - x2 , y - y2 , z - z2 , kl
end sub
sub lijn( x1 as single , y1 as single , z1 as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
  spot x1 , y1 , z1
  spot x2 , y2 , z2
  dim as single a1 , b1 , a2 , b2
  a1 = 1024 / 2 + x1 / ( z1 + 1000 ) * 1000
  b1 = 768 / 2 - y1 / ( z1 + 1000 ) * 1000
  a2 = 1024 / 2 + x2 / ( z2 + 1000 ) * 1000
  b2 = 768 / 2 - y2 / ( z2 + 1000 ) * 1000
  line ( a1 , b1 ) - ( a2 , b2 ) , kl
end sub

''                                                               3d engine

function pend( f as single , a as single ) as single
  return sin( rad( f ) ) * a
end function
sub skelet( lim as integer , x as single , y as single , z as single )
  if lim < 0 or lim > 64 then exit sub
  sk( lim , 0 ) = x
  sk( lim , 1 ) = y
  sk( lim , 2 ) = z
end sub
sub camara( x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , zoom as single )
  cam( 0 ) = x
  cam( 1 ) = y
  cam( 2 ) = z
  cam( 3 ) = pan
  cam( 4 ) = tilt
  cam( 5 ) = rol
  cam( 6 ) = zoom
end sub
sub link( no as integer , x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , ax as integer , p as integer )
  if no < 1 or no > 20 then exit sub
  if p < 0 or p > 20 then exit sub
  if p = no then exit sub
  dim as matrix mp , rotx , roty , rotz , translate
  mp = v( p )
  rotx = v( 0 )
  roty = v( 0 )
  rotz = v( 0 )
  translate = v( 0 )
  roty.m( 0 , 0 ) = cos( rad( rol ) )
  roty.m( 0 , 1 ) = -sin( rad( rol ) )
  roty.m( 1 , 0 ) = sin( rad( rol ) )
  roty.m( 1 , 1 ) = cos( rad( rol ) )
  roty.m( 0 , 0 ) = cos( rad( pan ) )
  roty.m( 0 , 2 ) = -sin( rad( pan ) )
  roty.m( 2 , 0 ) = sin( rad( pan ) )
  roty.m( 2 , 2 ) = cos( rad( pan ) )
  roty.m( 1 , 1 ) = cos( rad( tilt ) )
  roty.m( 1 , 2 ) = -sin( rad( tilt ) )
  roty.m( 2 , 1 ) = sin( rad( tilt ) )
  roty.m( 2 , 2 ) = cos( rad( tilt ) )
  translate.m( 3 , 0 ) = x
  translate.m( 3 , 1 ) = y
  translate.m( 3 , 2 ) = z
  select case ax
  case xyz
    v( no ) = mp * rotx * roty * rotz * translate
  case xzy
    v( no ) = mp * rotx * rotz * roty * translate
  case yxz
    v( no ) = mp * roty * rotx * rotz * translate
  case yzx
    v( no ) = mp * roty * rotz * rotx * translate
  case zxy
    v( no ) = mp * rotz * rotx * roty * translate
  case zyx
    v( no ) = mp * rotz * roty * rotx * translate
  case else
  end select
  number = no
end sub
sub child( no as integer , x as single , y as single , z as single _
, lim as integer , ax as integer , p as integer )
  if lim < 0 or lim > 64 then exit sub
  link no , x , y , z , sk( lim , 1 ) , sk( lim , 0 ) , sk( lim , 2 ), ax , p
end sub
sub spot( byref x as single , byref y as single , byref z as single )
  dim as single hx , hy , hz
  dim as integer i
  i = number
  hx = x * v( i ).m( 0 , 0 ) + y * v( i ).m( 1 , 0 ) _
  + z * v( i ).m( 2 , 0 ) + v( i ).m( 3 , 0 )
  hy = x * v( i ).m( 0 , 1 ) + y * v( i ).m( 1 , 1 ) _
  + z * v( i ).m( 2 , 1 ) + v( i ).m( 3 , 1 )
  hz = x * v( i ).m( 0 , 2 ) + y * v( i ).m( 1 , 2 ) _
  + z * v( i ).m( 2 , 2 ) + v( i ).m( 3 , 2 )
  x = hx
  y = hy
  z = hz
  x += - cam( 0 )
  y += - cam( 1 )
  z += - cam( 2 )
  rotate x , z , -cam( 3 )
  rotate y , z , -cam( 4 )
  rotate x , y , -cam( 5 )
end sub
sub rotate( byref k as single , byref l as single , deg as single )
  dim as single hk , hl , s , c
  s = sin( rad( deg ) )
  c = cos( rad( deg ) )
  hk = k * c - l * s
  hl = k * s + l * c
  k = hk
  l = hl
end sub
function rad( x as single ) as single
  return x * pi / 180
end function

pestery
Posts: 493
Joined: Jun 16, 2007 2:00
Location: Australia

Re: matrix 3d problem

Postby pestery » May 04, 2012 12:32

AAH!! Too much maths in a confined space :-)
What is the bug? I guess that the limbs of the body don't join, or is it that the perspective looks a bit warped. Also, could you add a few comments to the code so it not just one big page of pure maths. It looks very familiar but its hard to figure out what part of the code does what, which makes tracking the bug difficult :-)

Just out of curiosity, are you looking into skeletal animation? Interesting stuff, I had a mess around with it a couple of years ago.
bluatigro
Posts: 651
Joined: Apr 25, 2012 10:35
Location: netherlands

Re: matrix 3d problem

Postby bluatigro » May 06, 2012 18:17

error :
-the dodeca shoot be sphere like al the time
-the lim's dont join up

i shal ad comments so you can folow the flow

i know that this shoot work because i made this earlyer in vb2008

i m looking in for skeletal animations
so i can store the animations seperately in code
TJF
Posts: 3596
Joined: Dec 06, 2009 22:27
Location: N47°, E15°
Contact:

Re: matrix 3d problem

Postby TJF » May 07, 2012 7:04

@bluatigro

FB isn't vb2008. You can use lots of libraries here.

  • A common physics library for your purpose is ODE.
  • To visualize the results you can use OpenGL.
  • To test your code there's a FB tool called OpenGl_Player.
pestery
Posts: 493
Joined: Jun 16, 2007 2:00
Location: Australia

Re: matrix 3d problem

Postby pestery » May 07, 2012 10:09

I had another look at your code and I've found the source of the distortion problem. In the link() function you messed up the rotation matrix (rotx, roty, rotz). You may want to check it, but this seems to work:

Code: Select all

rotz.m( 0, 0 ) = Cos( rad( rol ))
rotz.m( 0, 1 ) = -Sin( rad( rol ))
rotz.m( 1, 0 ) = Sin( rad( rol ))
rotz.m( 1, 1 ) = Cos( rad( rol ))
roty.m( 0, 0 ) = Cos( rad( pan ))
roty.m( 0, 2 ) = Sin( rad( pan ))
roty.m( 2, 0 ) = -Sin( rad( pan ))
roty.m( 2, 2 ) = Cos( rad( pan ))
rotx.m( 1, 1 ) = Cos( rad( tilt ))
rotx.m( 1, 2 ) = -Sin( rad( tilt ))
rotx.m( 2, 1 ) = Sin( rad( tilt ))
rotx.m( 2, 2 ) = Cos( rad( tilt ))

Now that I've worked out how your code works I'll see if I can find out why the bones/limbs don't join. No guarantees though :-)

On a side note, you may want to have a quick look at the maths library I wrote a while ago. It's designed to work with OpenGL, but you might find it useful with FBGFX, or maybe not. Either way here is the link to the topic, link.
pestery
Posts: 493
Joined: Jun 16, 2007 2:00
Location: Australia

Re: matrix 3d problem

Postby pestery » May 07, 2012 10:57

I just found the source of the bone/limbs not joining. You just needed to re-order your matrix multiplication equations. I moved the value 'mp' from the beginning of the equation to the end and presto, it worked. Although the feet are on backward :-)

Anyway, here is the entire link() function with the changes.

Code: Select all

Sub link( no As Integer, x As Single, y As Single, z As Single, pan As Single, tilt As Single, rol As Single, ax As Integer, p As Integer )
   If no < 1 Or no > 20 Then Exit Sub
   If p < 0 Or p > 20 Then Exit Sub
   If p = no Then Exit Sub
   Dim As matrix mp, rotx, roty, rotz, translate
   mp = v( p )
   rotx = v( 0 )
   roty = v( 0 )
   rotz = v( 0 )
   translate = v( 0 )
   rotz.m( 0, 0 ) = Cos( rad( rol ))
   rotz.m( 0, 1 ) = -Sin( rad( rol ))
   rotz.m( 1, 0 ) = Sin( rad( rol ))
   rotz.m( 1, 1 ) = Cos( rad( rol ))
   roty.m( 0, 0 ) = Cos( rad( pan ))
   roty.m( 0, 2 ) = Sin( rad( pan ))
   roty.m( 2, 0 ) = -Sin( rad( pan ))
   roty.m( 2, 2 ) = Cos( rad( pan ))
   rotx.m( 1, 1 ) = Cos( rad( tilt ))
   rotx.m( 1, 2 ) = -Sin( rad( tilt ))
   rotx.m( 2, 1 ) = Sin( rad( tilt ))
   rotx.m( 2, 2 ) = Cos( rad( tilt ))
   translate.m( 3, 0 ) = x
   translate.m( 3, 1 ) = y
   translate.m( 3, 2 ) = z
   Select Case ax
      Case xyz
         v( no ) = rotx * roty * rotz * translate * mp
      Case xzy
         v( no ) = rotx * rotz * roty * translate * mp
      Case yxz
         v( no ) = roty * rotx * rotz * translate * mp
      Case yzx
         v( no ) = roty * rotz * rotx * translate * mp
      Case zxy
         v( no ) = rotz * rotx * roty * translate * mp
      Case zyx
         v( no ) = rotz * roty * rotx * translate * mp
      Case Else
   End Select
   number = no
End Sub
bluatigro
Posts: 651
Joined: Apr 25, 2012 10:35
Location: netherlands

Re: matrix 3d problem

Postby bluatigro » May 07, 2012 11:42

update :
-replaced the link sub
-corrected the feet of the man
-added some coments

wil put somting like it in my opengl projects
this wil be build into my raytracer to

it works as expected now

Code: Select all

''create matrix type to hold position & orentation
type matrix
  dim as single m( 3 , 3 )
end type
''create multyplycation operator for matrix
operator * ( a as matrix , b as matrix ) as matrix
  dim as integer i , j , k
  dim uit as matrix
  for i = 0 to 3
    for j = 0 to 3
''      uit.m( i , j ) = 0
      for k = 0 to 3
''        uit.m( i , j ) += a.m( i , k ) * b.m( k , j )
        uit.m( j , k ) += a.m( j , i ) * b.m( i , k )
      next k
    next j
  next i
  return uit
end operator
''create array of matrix's
dim shared as matrix v( 20 )
''create unity matrix
v( 0 ).m( 0 , 0 ) = 1
v( 0 ).m( 1 , 1 ) = 1
v( 0 ).m( 2 , 2 ) = 1
v( 0 ).m( 3 , 3 ) = 1
''create array to hold skeletal angles
dim shared as single sk( 64 , 2 )
''create some stuf for 3D engine
declare sub link( no as integer , x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , ax as integer , p as integer )
declare sub child( no as integer , x as single , y as single , z as single _
, lim as integer , ax as integer , p as integer )
declare sub spot( byref x as single , byref y as single , byref z as single )
declare sub rotate( byref k as single , byref l as single , deg as single )
declare function rad( x as single ) as single
dim shared as integer number
const as single pi = atn( 1 ) * 4
dim shared as single cam( 6 )
declare sub camara( x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , zoom as single )
declare function pend( f as single , a as single ) as single
declare sub skelet( no as integer , x as single , y as single , z as single )

const as integer xyz = 0
const as integer xzy = 1
const as integer yxz = 2
const as integer yzx = 3
const as integer zxy = 4
const as integer zyx = 5


''  graphics

''primary colors
const as integer black   = &h000000
const as integer red     = &hff0000
const as integer green   = &h00ff00
const as integer yellow  = &hffff00
const as integer blue    = &h0000ff
const as integer magenta = &hff00ff
const as integer cyan    = &h00ffff
const as integer white   = &hffffff
''mix colors
const as integer orange  = &hff7f00
const as integer gray    = &h7f7f7f
const as integer pink    = &hff7f7f
const as integer purple  = &h7f007f

''  lijn world

declare sub lijn( x1 as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
declare sub cube( x1 as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
declare sub dodeca( x as single , y as single , z as single _
, d as single , dik as integer )
declare sub lijnman( kl as integer )
''create lim numbers for 4 legged skelet
const as integer arm = 0
const as integer elbow = 1
const as integer wrist = 2
const as integer leg = 3
const as integer knee = 4
const as integer enkle = 5
const as integer neck = 6
const as integer head = 7
const as integer eye = 8
const as integer lr = 10

screen 20 , 32 , 2
dim frame as single
do
  cls
 
  ''walking man skeletal animation
  skelet leg , pend( frame * 5 , 30 ) , 0 , 0
  skelet knee , pend( frame * 5 - 90 , 30 ) + 30  , 0 , 0
  skelet leg + lr , pend( frame * 5 + 180 , 30 ) , 0 , 0
  skelet knee + lr , pend( frame * 5 + 90 , 30 ) + 30 , 0 , 0
  skelet arm , pend( frame * 5 + 180 , 30 ) , 0 , 0
  skelet elbow , -30 , 0 , 0
  skelet arm + lr , pend( frame * 5 , 30 ) , 0 , 0
  skelet elbow + lr , -30 , 0 , 0
 
  link 1 , -250,0,0 , frame,frame,0 , 0 , 0
    dodeca 0,0,0 , 100 , cyan
   
  link 1 , 0,0,0 , frame,0,0 , 0 , 0
    lijnman yellow
   
  link 1 , 250,0,0 , -frame,0,0 , 0 , 0
    lijnman magenta

  frame = frame + 1
  sleep 40
  flip
loop while inkey = ""
end

''                                    lijn world

sub lijnman( kl as integer )
''draws a man made op of lines
''uses seletal animation
''example of a to animate avatar
    lijn 30,0,0 ,-30,0,0 , kl
    lijn 0,0,0 , 0,120,0 , kl
    lijn 50,100,0 , -50,100,0 , kl
    cube 0,140,0 , 15,15,15 , kl
    child 2 , 30,0,0 , leg , yzx , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , knee , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
        lijn 0,-70,0 , 0,-70,-20 , kl
    child 2 , -30,0,0 , leg + lr , yzx , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , knee + lr , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
        lijn 0,-70,0 , 0,-70,-20 , kl
    child 2 , 50,100,0 , arm , xzy , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , elbow , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
    child 2 , -50,100,0 , arm + lr , xzy ,  1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , elbow + lr , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
end sub
sub dodeca( x as single , y as single , z as single , d as single , dik as integer )
''draw a dodecaherdron
dim f as single
  f = ( sqr( 5 ) - 1 ) / 2
  ''(±1, ±1, ±1)
  ''(0, ±1/f, ±f)
  ''(±1/f, ±f, 0)
  ''(±f, 0, ±1/f)
  lijn x + d , y + d , z + d , x , y + 1/f*d , z + f*d ,dik
  lijn x + d , y + d , z + d , x + 1/f*d , y + f*d , z ,dik
  lijn x + d , y + d , z + d , x + f*d , y , z + 1/f*d ,dik
  lijn x - d , y - d , z - d , x , y - 1/f*d , z - f*d ,dik
  lijn x - d , y - d , z - d , x - 1/f*d , y - f*d , z ,dik
  lijn x - d , y - d , z - d , x - f*d , y , z - 1/f*d ,dik
  lijn x+1/f*d,y+f*d,z,x+1/f*d,y-f*d,z,dik
  lijn x-1/f*d,y-f*d,z,x-1/f*d,y+f*d,z,dik
  lijn x,y+1/f*d,z+f*d,x,y+1/f*d,z-f*d,dik
  lijn x,y-1/f*d,z-f*d,x,y-1/f*d,z+f*d,dik
  lijn x-f*d,y,z-1/f*d,x+f*d,y,z-1/f*d,dik
  lijn x+f*d,y,z+1/f*d,x-f*d,y,z+1/f*d,dik
  lijn x+1/f*d,y+f*d,z,x+d,y+d,z-d,dik
  lijn x-1/f*d,y-f*d,z,x-d,y-d,z+d,dik
  lijn x+f*d,y,z+1/f*d,x-f*d,y,z+1/f*d,dik
  lijn x-f*d,y,z-1/f*d,x+f*d,y,z-1/f*d,dik
  lijn x-f*d,y,z+1/f*d,x-d,y+d,z+d,dik
  lijn x+f*d,y,z-1/f*d,x+d,y-d,z-d,dik
  lijn x+f*d,y,z-1/f*d,x+d,y+d,z-d,dik
  lijn x-f*d,y,z+1/f*d,x-d,y-d,z+d,dik
  lijn x-d,y+d,z+d,x,y+1/f*d,z+f*d,dik
  lijn x+d,y-d,z-d,x,y-1/f*d,z-f*d,dik
  lijn x-d,y+d,z+d,x-1/f*d,y+f*d,z,dik
  lijn x+d,y-d,z-d,x+1/f*d,y-f*d,z,dik
  lijn x+f*d,y,z+1/f*d,x+d,y-d,z+d,dik
  lijn x-f*d,y,z-1/f*d,x-d,y+d,z-d,dik
  lijn x+d,y-d,z+d,x,y-1/f*d,z+f*d,dik
  lijn x-d,y+d,z-d,x,y+1/f*d,z-f*d,dik
  lijn x+d,y+d,z-d,x,y+1/f*d,z-f*d,dik
  lijn x-d,y-d,z+d,x,y-1/f*d,z+f*d,dik
  lijn x+d,y-d,z+d,x+1/f*d,y-f*d,z,dik
  lijn x-d,y+d,z-d,x-1/f*d,y+f*d,z,dik
end sub
sub cube( x as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
''draw a cube
  lijn x + x2 , y + y2 , z + z2 , x - x2 , y + y2 , z + z2 , kl
  lijn x + x2 , y + y2 , z - z2 , x - x2 , y + y2 , z - z2 , kl
  lijn x + x2 , y - y2 , z + z2 , x - x2 , y - y2 , z + z2 , kl
  lijn x + x2 , y - y2 , z - z2 , x - x2 , y - y2 , z - z2 , kl
 
  lijn x + x2 , y + y2 , z + z2 , x + x2 , y - y2 , z + z2 , kl
  lijn x + x2 , y + y2 , z - z2 , x + x2 , y - y2 , z - z2 , kl
  lijn x - x2 , y + y2 , z + z2 , x - x2 , y - y2 , z + z2 , kl
  lijn x - x2 , y + y2 , z - z2 , x - x2 , y - y2 , z - z2 , kl
 
  lijn x + x2 , y + y2 , z + z2 , x + x2 , y + y2 , z - z2 , kl
  lijn x + x2 , y - y2 , z + z2 , x + x2 , y - y2 , z - z2 , kl
  lijn x - x2 , y + y2 , z + z2 , x - x2 , y + y2 , z - z2 , kl
  lijn x - x2 , y - y2 , z + z2 , x - x2 , y - y2 , z - z2 , kl
end sub
sub lijn( x1 as single , y1 as single , z1 as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
''draw a line using the curent matrix
  spot x1 , y1 , z1
  spot x2 , y2 , z2
  dim as single a1 , b1 , a2 , b2
  a1 = 1024 / 2 + x1 / ( z1 + 1000 ) * 1000
  b1 = 768 / 2 - y1 / ( z1 + 1000 ) * 1000
  a2 = 1024 / 2 + x2 / ( z2 + 1000 ) * 1000
  b2 = 768 / 2 - y2 / ( z2 + 1000 ) * 1000
  line ( a1 , b1 ) - ( a2 , b2 ) , kl
end sub

''                                    3d engine

function pend( f as single , a as single ) as single
''pendular motion for animation
''looks verry natural
  return sin( rad( f ) ) * a
end function
sub skelet( lim as integer , x as single , y as single , z as single )
''set angles of skeletal lim
''for animated avatars
  if lim < 0 or lim > 64 then exit sub
  sk( lim , 0 ) = x
  sk( lim , 1 ) = y
  sk( lim , 2 ) = z
end sub
sub camara( x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , zoom as single )
''set look from point & look angles
  cam( 0 ) = x
  cam( 1 ) = y
  cam( 2 ) = z
  cam( 3 ) = pan
  cam( 4 ) = tilt
  cam( 5 ) = rol
  cam( 6 ) = zoom
end sub
Sub link( no As Integer, x As Single, y As Single, z As Single, pan As Single, tilt As Single, rol As Single, ax As Integer, p As Integer )
''set curent matrix wil afect folowing drawing comands
   If no < 1 Or no > 20 Then Exit Sub
   If p < 0 Or p > 20 Then Exit Sub
   If p = no Then Exit Sub
   ''create some lokal matrix's and fill them
   Dim As matrix mp, rotx, roty, rotz, translate
   mp = v( p )
   rotx = v( 0 )
   roty = v( 0 )
   rotz = v( 0 )
   translate = v( 0 )
   rotz.m( 0, 0 ) = Cos( rad( rol ))
   rotz.m( 0, 1 ) = -Sin( rad( rol ))
   rotz.m( 1, 0 ) = Sin( rad( rol ))
   rotz.m( 1, 1 ) = Cos( rad( rol ))
   roty.m( 0, 0 ) = Cos( rad( pan ))
   roty.m( 0, 2 ) = Sin( rad( pan ))
   roty.m( 2, 0 ) = -Sin( rad( pan ))
   roty.m( 2, 2 ) = Cos( rad( pan ))
   rotx.m( 1, 1 ) = Cos( rad( tilt ))
   rotx.m( 1, 2 ) = -Sin( rad( tilt ))
   rotx.m( 2, 1 ) = Sin( rad( tilt ))
   rotx.m( 2, 2 ) = Cos( rad( tilt ))
   translate.m( 3, 0 ) = x
   translate.m( 3, 1 ) = y
   translate.m( 3, 2 ) = z
   ''angles can permutate 6 ways
   Select Case ax
      Case xyz
         v( no ) = rotx * roty * rotz * translate * mp
      Case xzy
         v( no ) = rotx * rotz * roty * translate * mp
      Case yxz
         v( no ) = roty * rotx * rotz * translate * mp
      Case yzx
         v( no ) = roty * rotz * rotx * translate * mp
      Case zxy
         v( no ) = rotz * rotx * roty * translate * mp
      Case zyx
         v( no ) = rotz * roty * rotx * translate * mp
      Case Else
   End Select
   number = no
End Sub
sub child( no as integer , x as single , y as single , z as single _
, lim as integer , ax as integer , p as integer )
''set curent matrix for lim of animated avatar
''wil efect folowing drawings
  if lim < 0 or lim > 64 then exit sub
  link no , x , y , z , sk( lim , 1 ) , sk( lim , 0 ) , sk( lim , 2 ), ax , p
end sub
sub spot( byref x as single , byref y as single , byref z as single )
''calulate world coordinates from lokal coordinates
''using curent matrix
  dim as single hx , hy , hz
  dim as integer i
  ''use curent matrix
  i = number
  hx = x * v( i ).m( 0 , 0 ) + y * v( i ).m( 1 , 0 ) _
  + z * v( i ).m( 2 , 0 ) + v( i ).m( 3 , 0 )
  hy = x * v( i ).m( 0 , 1 ) + y * v( i ).m( 1 , 1 ) _
  + z * v( i ).m( 2 , 1 ) + v( i ).m( 3 , 1 )
  hz = x * v( i ).m( 0 , 2 ) + y * v( i ).m( 1 , 2 ) _
  + z * v( i ).m( 2 , 2 ) + v( i ).m( 3 , 2 )
  x = hx
  y = hy
  z = hz
  ''use camara matrix
  x += - cam( 0 )
  y += - cam( 1 )
  z += - cam( 2 )
  rotate x , z , -cam( 3 )
  rotate y , z , -cam( 4 )
  rotate x , y , -cam( 5 )
end sub
sub rotate( byref k as single , byref l as single , deg as single )
''help sub for rotating coordinates
 dim as single hk , hl , s , c
  s = sin( rad( deg ) )
  c = cos( rad( deg ) )
  hk = k * c - l * s
  hl = k * s + l * c
  k = hk
  l = hl
end sub
function rad( x as single ) as single
''help function degrees to radians
  return x * pi / 180
end function

bluatigro
Posts: 651
Joined: Apr 25, 2012 10:35
Location: netherlands

Re: matrix 3d problem

Postby bluatigro » May 10, 2012 11:43

now i can do things like this :

Code: Select all

''create matrix type to hold position & orentation
type matrix
  dim as single m( 3 , 3 )
end type
''create multyplycation operator for matrix
operator * ( a as matrix , b as matrix ) as matrix
  dim as integer i , j , k
  dim uit as matrix
  for i = 0 to 3
    for j = 0 to 3
''      uit.m( i , j ) = 0
      for k = 0 to 3
''        uit.m( i , j ) += a.m( i , k ) * b.m( k , j )
        uit.m( j , k ) += a.m( j , i ) * b.m( i , k )
      next k
    next j
  next i
  return uit
end operator
''create array of matrix's
dim shared as matrix v( 20 )
''create unity matrix
v( 0 ).m( 0 , 0 ) = 1
v( 0 ).m( 1 , 1 ) = 1
v( 0 ).m( 2 , 2 ) = 1
v( 0 ).m( 3 , 3 ) = 1
''create array to hold skeletal angles
dim shared as single sk( 64 , 2 )
''create some stuf for 3D engine
declare sub link( no as integer , x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , ax as integer , p as integer )
declare sub child( no as integer , x as single , y as single , z as single _
, lim as integer , ax as integer , p as integer )
declare sub spot( byref x as single , byref y as single , byref z as single )
declare sub rotate( byref k as single , byref l as single , deg as single )
declare function rad( x as single ) as single
dim shared as integer number
const as single pi = atn( 1 ) * 4
dim shared as single cam( 6 )
declare sub camara( x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , zoom as single )
declare function pend( f as single , a as single ) as single
declare sub skelet( no as integer , x as single , y as single , z as single )

const as integer xyz = 0
const as integer xzy = 1
const as integer yxz = 2
const as integer yzx = 3
const as integer zxy = 4
const as integer zyx = 5


''  graphics

''primary colors
const as integer black   = &h000000
const as integer red     = &hff0000
const as integer green   = &h00ff00
const as integer yellow  = &hffff00
const as integer blue    = &h0000ff
const as integer magenta = &hff00ff
const as integer cyan    = &h00ffff
const as integer white   = &hffffff
''mix colors
const as integer orange  = &hff7f00
const as integer gray    = &h7f7f7f
const as integer pink    = &hff7f7f
const as integer purple  = &h7f007f

''  lijn world

declare sub lijn( x1 as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
declare sub cube( x1 as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
declare sub dodeca( x as single , y as single , z as single _
, d as single , dik as integer )
declare sub lijnman( kl as integer )
declare sub tree( no as integer , l as single , kl as integer )

''  sphere world

dim shared as single height
declare sub sphere( x as single , y as single , z as single , d as single , kl as single )
declare function mix( kla as integer , f as single , klb as single ) as integer
declare sub egg( x1 as single , y1 as single , z1 as single , d1 as single _
, x2 as single , y2 as single , z2 as single , d2 as single _
, dm as single , kl as integer , no as integer )

''create lim numbers for 4 legged skelet
const as integer arm = 0
const as integer elbow = 1
const as integer wrist = 2
const as integer leg = 3
const as integer knee = 4
const as integer enkle = 5
const as integer neck = 6
const as integer head = 7
const as integer eye = 8
const as integer lr = 10

screen 20 , 32 , 2
dim frame as single

  cls
 
  ''walking man skeletal animation
  skelet leg , pend( frame * 5 , 30 ) , 0 , 0
  skelet knee , pend( frame * 5 - 90 , 30 ) + 30  , 0 , 0
  skelet leg + lr , pend( frame * 5 + 180 , 30 ) , 0 , 0
  skelet knee + lr , pend( frame * 5 + 90 , 30 ) + 30 , 0 , 0
  skelet arm , pend( frame * 5 + 180 , 30 ) , 0 , 0
  skelet elbow , -30 , 0 , 0
  skelet arm + lr , pend( frame * 5 , 30 ) , 0 , 0
  skelet elbow + lr , -30 , 0 , 0
 
''  link 1 , -250,0,0 , frame,frame,0 , 0 , 0
''    dodeca 0,0,0 , 100 , cyan
  for height = -400 to 400
  link 1 , 0,-400,0 , 30,0,0 , 0 , 0
    tree 2 , 200 , yellow
  next height
   
''  link 1 , 250,0,0 , -frame,0,0 , 0 , 0
''    lijnman magenta

  frame = frame + 1
  sleep 40
  flip
do
loop while inkey = ""
end

''                                    lijn world
sub tree( no as integer , l as single , kl as integer )
  link no , 0,l*1.414,0 , 90,60,0 , xyz , no-1
    egg 0,0,0 , l*.1 , 0,l,0 , l*.0707 , l*.08585 , kl , 0
    if l > 30 then tree no + 1 , l * 0.707 , kl
  link no , 0,l*1.414,0 , -90,60,0 , xyz , no-1
    egg 0,0,0 , l*.1 , 0,l,0 , l*.0707 , l*.08585 , kl , 0
    if l > 30 then tree no + 1 , l * 0.707 , kl
end sub

sub sphere( x as single , y as single , z as single , d as single , kl as single )
  spot x , y , z
  dim dd as single , kl1 as integer
  if abs( height - y ) < d then
    dd = sqr( d ^ 2 - ( height - y ) ^ 2 + .001 )
    kl1 = mix( kl , .5 - ( height - y ) / d / 2 , black )
    circle ( 1024 / 2 + x , 768 / 2 - height - z / 4 ) , dd , kl1 , , , 1/4 , f
  end if
end sub
sub egg( x1 as single , y1 as single , z1 as single , d1 as single _
, x2 as single , y2 as single , z2 as single , d2 as single _
, dm as single , kl as integer , no as integer )
  dim as single af , dx , dy , dz , dd , dh
  dim i as integer
  af = sqr( ( x1 - x2 ) ^ 2 _
  + ( y1 - y2 ) ^ 2 + ( z1 - z2 ) ^ 2 + 1 )
  dx = ( x2 - x1 ) / af
  dy = ( y2 - y1 ) / af
  dz = ( z2 - z1 ) / af
  dd = ( d2 - d1 ) / af
  dh = ( d1 + d2 ) / 2
  if no < 2 then no = af
  if no > af then no = af
  for i = 0 to af step af / no
    sphere x1 + dx * i _
    , y1 + dy * i , z1 + dz * i _
    , d1 + dd * i + sin( i * pi / af ) _
    * ( dm - dh ) , kl
  next i
end sub
function mix( kla as integer , f as single , klb as single ) as integer
  dim as integer ra , ga , ba , rb , gb , bb , r , g , b
  ra = ( kla shr 16 ) and 255
  ga = ( kla shr 8 ) and 255
  ba = kla and 255
  rb = ( klb shr 16 ) and 255
  gb = ( klb shr 8 ) and 255
  bb = klb and 255
  r = ra + ( rb - ra ) * f
  g = ga + ( gb - ga ) * f
  b = ba + ( bb - ba ) * f
  return rgb( r , g , b )
end function

''  lijn world

sub lijnman( kl as integer )
''draws a man made op of lines
''uses seletal animation
''example of a to animate avatar
    lijn 30,0,0 ,-30,0,0 , kl
    lijn 0,0,0 , 0,120,0 , kl
    lijn 50,100,0 , -50,100,0 , kl
    cube 0,140,0 , 15,15,15 , kl
    child 2 , 30,0,0 , leg , yzx , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , knee , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
        lijn 0,-70,0 , 0,-70,-20 , kl
    child 2 , -30,0,0 , leg + lr , yzx , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , knee + lr , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
        lijn 0,-70,0 , 0,-70,-20 , kl
    child 2 , 50,100,0 , arm , xzy , 1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , elbow , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
    child 2 , -50,100,0 , arm + lr , xzy ,  1
      lijn 0,0,0 , 0,-70,0 , kl
      child 3 , 0,-70,0 , elbow + lr , 0 , 2
        lijn 0,0,0 , 0,-70,0 , kl
end sub
sub dodeca( x as single , y as single , z as single , d as single , dik as integer )
''draw a dodecaherdron
dim f as single
  f = ( sqr( 5 ) - 1 ) / 2
  ''(±1, ±1, ±1)
  ''(0, ±1/f, ±f)
  ''(±1/f, ±f, 0)
  ''(±f, 0, ±1/f)
  lijn x + d , y + d , z + d , x , y + 1/f*d , z + f*d ,dik
  lijn x + d , y + d , z + d , x + 1/f*d , y + f*d , z ,dik
  lijn x + d , y + d , z + d , x + f*d , y , z + 1/f*d ,dik
  lijn x - d , y - d , z - d , x , y - 1/f*d , z - f*d ,dik
  lijn x - d , y - d , z - d , x - 1/f*d , y - f*d , z ,dik
  lijn x - d , y - d , z - d , x - f*d , y , z - 1/f*d ,dik
  lijn x+1/f*d,y+f*d,z,x+1/f*d,y-f*d,z,dik
  lijn x-1/f*d,y-f*d,z,x-1/f*d,y+f*d,z,dik
  lijn x,y+1/f*d,z+f*d,x,y+1/f*d,z-f*d,dik
  lijn x,y-1/f*d,z-f*d,x,y-1/f*d,z+f*d,dik
  lijn x-f*d,y,z-1/f*d,x+f*d,y,z-1/f*d,dik
  lijn x+f*d,y,z+1/f*d,x-f*d,y,z+1/f*d,dik
  lijn x+1/f*d,y+f*d,z,x+d,y+d,z-d,dik
  lijn x-1/f*d,y-f*d,z,x-d,y-d,z+d,dik
  lijn x+f*d,y,z+1/f*d,x-f*d,y,z+1/f*d,dik
  lijn x-f*d,y,z-1/f*d,x+f*d,y,z-1/f*d,dik
  lijn x-f*d,y,z+1/f*d,x-d,y+d,z+d,dik
  lijn x+f*d,y,z-1/f*d,x+d,y-d,z-d,dik
  lijn x+f*d,y,z-1/f*d,x+d,y+d,z-d,dik
  lijn x-f*d,y,z+1/f*d,x-d,y-d,z+d,dik
  lijn x-d,y+d,z+d,x,y+1/f*d,z+f*d,dik
  lijn x+d,y-d,z-d,x,y-1/f*d,z-f*d,dik
  lijn x-d,y+d,z+d,x-1/f*d,y+f*d,z,dik
  lijn x+d,y-d,z-d,x+1/f*d,y-f*d,z,dik
  lijn x+f*d,y,z+1/f*d,x+d,y-d,z+d,dik
  lijn x-f*d,y,z-1/f*d,x-d,y+d,z-d,dik
  lijn x+d,y-d,z+d,x,y-1/f*d,z+f*d,dik
  lijn x-d,y+d,z-d,x,y+1/f*d,z-f*d,dik
  lijn x+d,y+d,z-d,x,y+1/f*d,z-f*d,dik
  lijn x-d,y-d,z+d,x,y-1/f*d,z+f*d,dik
  lijn x+d,y-d,z+d,x+1/f*d,y-f*d,z,dik
  lijn x-d,y+d,z-d,x-1/f*d,y+f*d,z,dik
end sub
sub cube( x as single , y as single , z as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
''draw a cube
  lijn x + x2 , y + y2 , z + z2 , x - x2 , y + y2 , z + z2 , kl
  lijn x + x2 , y + y2 , z - z2 , x - x2 , y + y2 , z - z2 , kl
  lijn x + x2 , y - y2 , z + z2 , x - x2 , y - y2 , z + z2 , kl
  lijn x + x2 , y - y2 , z - z2 , x - x2 , y - y2 , z - z2 , kl
 
  lijn x + x2 , y + y2 , z + z2 , x + x2 , y - y2 , z + z2 , kl
  lijn x + x2 , y + y2 , z - z2 , x + x2 , y - y2 , z - z2 , kl
  lijn x - x2 , y + y2 , z + z2 , x - x2 , y - y2 , z + z2 , kl
  lijn x - x2 , y + y2 , z - z2 , x - x2 , y - y2 , z - z2 , kl
 
  lijn x + x2 , y + y2 , z + z2 , x + x2 , y + y2 , z - z2 , kl
  lijn x + x2 , y - y2 , z + z2 , x + x2 , y - y2 , z - z2 , kl
  lijn x - x2 , y + y2 , z + z2 , x - x2 , y + y2 , z - z2 , kl
  lijn x - x2 , y - y2 , z + z2 , x - x2 , y - y2 , z - z2 , kl
end sub
sub lijn( x1 as single , y1 as single , z1 as single _
, x2 as single , y2 as single , z2 as single , kl as integer )
''draw a line using the curent matrix
  spot x1 , y1 , z1
  spot x2 , y2 , z2
  dim as single a1 , b1 , a2 , b2
  a1 = 1024 / 2 + x1 / ( z1 + 1000 ) * 1000
  b1 = 768 / 2 - y1 / ( z1 + 1000 ) * 1000
  a2 = 1024 / 2 + x2 / ( z2 + 1000 ) * 1000
  b2 = 768 / 2 - y2 / ( z2 + 1000 ) * 1000
  line ( a1 , b1 ) - ( a2 , b2 ) , kl
end sub

''                                    3d engine

function pend( f as single , a as single ) as single
''pendular motion for animation
''looks verry natural
  return sin( rad( f ) ) * a
end function
sub skelet( lim as integer , x as single , y as single , z as single )
''set angles of skeletal lim
''for animated avatars
  if lim < 0 or lim > 64 then exit sub
  sk( lim , 0 ) = x
  sk( lim , 1 ) = y
  sk( lim , 2 ) = z
end sub
sub camara( x as single , y as single , z as single _
, pan as single , tilt as single , rol as single , zoom as single )
''set look from point & look angles
  cam( 0 ) = x
  cam( 1 ) = y
  cam( 2 ) = z
  cam( 3 ) = pan
  cam( 4 ) = tilt
  cam( 5 ) = rol
  cam( 6 ) = zoom
end sub
Sub link( no As Integer, x As Single, y As Single, z As Single, pan As Single, tilt As Single, rol As Single, ax As Integer, p As Integer )
''set curent matrix wil afect folowing drawing comands
   If no < 1 Or no > 20 Then Exit Sub
   If p < 0 Or p > 20 Then Exit Sub
   If p = no Then Exit Sub
   ''create some lokal matrix's and fill them
   Dim As matrix mp, rotx, roty, rotz, translate
   mp = v( p )
   rotx = v( 0 )
   roty = v( 0 )
   rotz = v( 0 )
   translate = v( 0 )
   rotz.m( 0, 0 ) = Cos( rad( rol ))
   rotz.m( 0, 1 ) = -Sin( rad( rol ))
   rotz.m( 1, 0 ) = Sin( rad( rol ))
   rotz.m( 1, 1 ) = Cos( rad( rol ))
   roty.m( 0, 0 ) = Cos( rad( pan ))
   roty.m( 0, 2 ) = Sin( rad( pan ))
   roty.m( 2, 0 ) = -Sin( rad( pan ))
   roty.m( 2, 2 ) = Cos( rad( pan ))
   rotx.m( 1, 1 ) = Cos( rad( tilt ))
   rotx.m( 1, 2 ) = -Sin( rad( tilt ))
   rotx.m( 2, 1 ) = Sin( rad( tilt ))
   rotx.m( 2, 2 ) = Cos( rad( tilt ))
   translate.m( 3, 0 ) = x
   translate.m( 3, 1 ) = y
   translate.m( 3, 2 ) = z
   ''angles can permutate 6 ways
   Select Case ax
      Case xyz
         v( no ) = rotx * roty * rotz * translate * mp
      Case xzy
         v( no ) = rotx * rotz * roty * translate * mp
      Case yxz
         v( no ) = roty * rotx * rotz * translate * mp
      Case yzx
         v( no ) = roty * rotz * rotx * translate * mp
      Case zxy
         v( no ) = rotz * rotx * roty * translate * mp
      Case zyx
         v( no ) = rotz * roty * rotx * translate * mp
      Case Else
   End Select
   number = no
End Sub
sub child( no as integer , x as single , y as single , z as single _
, lim as integer , ax as integer , p as integer )
''set curent matrix for lim of animated avatar
''wil efect folowing drawings
  if lim < 0 or lim > 64 then exit sub
  link no , x , y , z , sk( lim , 1 ) , sk( lim , 0 ) , sk( lim , 2 ), ax , p
end sub
sub spot( byref x as single , byref y as single , byref z as single )
''calulate world coordinates from lokal coordinates
''using curent matrix
  dim as single hx , hy , hz
  dim as integer i
  ''use curent matrix
  i = number
  hx = x * v( i ).m( 0 , 0 ) + y * v( i ).m( 1 , 0 ) _
  + z * v( i ).m( 2 , 0 ) + v( i ).m( 3 , 0 )
  hy = x * v( i ).m( 0 , 1 ) + y * v( i ).m( 1 , 1 ) _
  + z * v( i ).m( 2 , 1 ) + v( i ).m( 3 , 1 )
  hz = x * v( i ).m( 0 , 2 ) + y * v( i ).m( 1 , 2 ) _
  + z * v( i ).m( 2 , 2 ) + v( i ).m( 3 , 2 )
  x = hx
  y = hy
  z = hz
  ''use camara matrix
  x += - cam( 0 )
  y += - cam( 1 )
  z += - cam( 2 )
  rotate x , z , -cam( 3 )
  rotate y , z , -cam( 4 )
  rotate x , y , -cam( 5 )
end sub
sub rotate( byref k as single , byref l as single , deg as single )
''help sub for rotating coordinates
 dim as single hk , hl , s , c
  s = sin( rad( deg ) )
  c = cos( rad( deg ) )
  hk = k * c - l * s
  hl = k * s + l * c
  k = hk
  l = hl
end sub
function rad( x as single ) as single
''help function degrees to radians
  return x * pi / 180
end function

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