$�>>> Ship constituted of springs
9�    Alain BROBECKER (baah/Arm's Tech) on ??-???-1997
�9:�
(�n       :�nb of brows
2�o       :�nb of edges
</�x(n),y(n),vx(n),vy(n),ax(n),ay(n) :�coords
F'�c=1�n:�x,y:x(c)=x+160:y(c)=y+128:�
Pvx()=0:vy()=0
Z/�s%(o),e%(o),l(o) :�edges lookup and length
d�c=1�o:�s%(c),e%(c):�
n@�c=1�o:l(c)=�((x(s%(c))-x(e%(c)))^2+(y(s%(c))-y(e%(c)))^2):�
x$k=0.25      :�springs' stiffness
�a=.96       :�absorption
�g=.1        :�gravity
�
�b%=1        :�screenbank
��
�$ �calculate isobarycenter coords
�1 x=0:y=0:�c=1�n:x+=x(c):y+=y(c):�:x=x/n:y=y/n
�@ �when player accelerate, we put this acceleration along the
�" �isobarycenter/1st brow axis.
�
 �(�57)�
�  dx=x(1)-x:dy=y(1)-y
�  d=�(dx^2+dy^2)
�  �d<>0�nx=dx/d:ny=dy/d

&  �c=1�n:ax(c)=nx/4:ay(c)=g+ny/4:�

 �

  ax()=0:ay()=g

" �

,L �when player rotates, we add to each brow an acceleration perpendicular

6% �to the isobarycenter/brow axis.

@
 �(�25)�

J  �c=1�n

T   dx=x(c)-x:dy=y(c)-y

^%   d=�(dx^2+dy^2):nx=dx/d:ny=dy/d

h   ax(c)+=ny/8:ay(c)-=nx/8

r  �

| �

� �(�121)�

�  �c=1�n

�   dx=x(c)-x:dy=y(c)-y

�%   d=�(dx^2+dy^2):nx=dx/d:ny=dy/d

�   ax(c)-=ny/8:ay(c)+=nx/8

�  �

� �

�7 Ȗ:ș"OS_Byte",&71,b%:b%=b%�3:ș"OS_Byte",&70,b%:�

�$ �Compute force for each spring 

� �c=1�o

�  dx=x(s%(c))-x(e%(c))

�  dy=y(s%(c))-y(e%(c))

�  l=�(dx^2+dy^2)
  ax=(l(c)-l)*k*dx/l
  ay=(l(c)-l)*k*dy/l
!  ax(s%(c))+=ax:ax(e%(c))-=ax
&!  ay(s%(c))+=ay:ay(e%(c))-=ay
0 �
:& �compute movements for each point
D �c=1�n
N  vx(c)=vx(c)*a+ax(c)
X  vy(c)=vy(c)*a+ay(c)
b  x(c)+=vx(c)
l  y(c)+=vy(c)
v!  �x(c)<0�x(c)=0:vx(c)=-vx(c)
�!  �y(c)<0�y(c)=0:vy(c)=-vy(c)
�%  �x(c)>319�x(c)=319:vx(c)=-vx(c)
�%  �y(c)>255�y(c)=255:vy(c)=-vy(c)
� �
�F �c=1�o:�x(s%(c))<<2,255-y(s%(c))<<2,x(e%(c))<<2,255-y(e%(c))<<2:�
���
��
�
��nb_coords & nb_edges
��3,3
��coords
�� 0,30, -15,-15, 15,-15
�
�edges
� 1,2, 1,3, 2,3
�

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00000010  6e 73 74 69 74 75 74 65  64 20 6f 66 20 73 70 72  |nstituted of spr|
00000020  69 6e 67 73 0d 00 14 39  f4 20 20 20 20 41 6c 61  |ings...9.    Ala|
00000030  69 6e 20 42 52 4f 42 45  43 4b 45 52 20 28 62 61  |in BROBECKER (ba|
00000040  61 68 2f 41 72 6d 27 73  20 54 65 63 68 29 20 6f  |ah/Arm's Tech) o|
00000050  6e 20 3f 3f 2d 3f 3f 3f  2d 31 39 39 37 0d 00 1e  |n ??-???-1997...|
00000060  08 eb 39 3a 87 0d 00 28  1a f3 6e 20 20 20 20 20  |..9:...(..n     |
00000070  20 20 3a f4 6e 62 20 6f  66 20 62 72 6f 77 73 0d  |  :.nb of brows.|
00000080  00 32 1a f3 6f 20 20 20  20 20 20 20 3a f4 6e 62  |.2..o       :.nb|
00000090  20 6f 66 20 65 64 67 65  73 0d 00 3c 2f de 78 28  | of edges..</.x(|
000000a0  6e 29 2c 79 28 6e 29 2c  76 78 28 6e 29 2c 76 79  |n),y(n),vx(n),vy|
000000b0  28 6e 29 2c 61 78 28 6e  29 2c 61 79 28 6e 29 20  |(n),ax(n),ay(n) |
000000c0  3a f4 63 6f 6f 72 64 73  0d 00 46 27 e3 63 3d 31  |:.coords..F'.c=1|
000000d0  b8 6e 3a f3 78 2c 79 3a  78 28 63 29 3d 78 2b 31  |.n:.x,y:x(c)=x+1|
000000e0  36 30 3a 79 28 63 29 3d  79 2b 31 32 38 3a ed 0d  |60:y(c)=y+128:..|
000000f0  00 50 11 76 78 28 29 3d  30 3a 76 79 28 29 3d 30  |.P.vx()=0:vy()=0|
00000100  0d 00 5a 2f de 73 25 28  6f 29 2c 65 25 28 6f 29  |..Z/.s%(o),e%(o)|
00000110  2c 6c 28 6f 29 20 3a f4  65 64 67 65 73 20 6c 6f  |,l(o) :.edges lo|
00000120  6f 6b 75 70 20 61 6e 64  20 6c 65 6e 67 74 68 0d  |okup and length.|
00000130  00 64 19 e3 63 3d 31 b8  6f 3a f3 73 25 28 63 29  |.d..c=1.o:.s%(c)|
00000140  2c 65 25 28 63 29 3a ed  0d 00 6e 40 e3 63 3d 31  |,e%(c):...n@.c=1|
00000150  b8 6f 3a 6c 28 63 29 3d  b6 28 28 78 28 73 25 28  |.o:l(c)=.((x(s%(|
00000160  63 29 29 2d 78 28 65 25  28 63 29 29 29 5e 32 2b  |c))-x(e%(c)))^2+|
00000170  28 79 28 73 25 28 63 29  29 2d 79 28 65 25 28 63  |(y(s%(c))-y(e%(c|
00000180  29 29 29 5e 32 29 3a ed  0d 00 78 24 6b 3d 30 2e  |)))^2):...x$k=0.|
00000190  32 35 20 20 20 20 20 20  3a f4 73 70 72 69 6e 67  |25      :.spring|
000001a0  73 27 20 73 74 69 66 66  6e 65 73 73 0d 00 82 1c  |s' stiffness....|
000001b0  61 3d 2e 39 36 20 20 20  20 20 20 20 3a f4 61 62  |a=.96       :.ab|
000001c0  73 6f 72 70 74 69 6f 6e  0d 00 8c 19 67 3d 2e 31  |sorption....g=.1|
000001d0  20 20 20 20 20 20 20 20  3a f4 67 72 61 76 69 74  |        :.gravit|
000001e0  79 0d 00 96 04 0d 00 a0  1c 62 25 3d 31 20 20 20  |y........b%=1   |
000001f0  20 20 20 20 20 3a f4 73  63 72 65 65 6e 62 61 6e  |     :.screenban|
00000200  6b 0d 00 aa 05 f5 0d 00  b4 24 20 f4 63 61 6c 63  |k........$ .calc|
00000210  75 6c 61 74 65 20 69 73  6f 62 61 72 79 63 65 6e  |ulate isobarycen|
00000220  74 65 72 20 63 6f 6f 72  64 73 0d 00 be 31 20 78  |ter coords...1 x|
00000230  3d 30 3a 79 3d 30 3a e3  63 3d 31 b8 6e 3a 78 2b  |=0:y=0:.c=1.n:x+|
00000240  3d 78 28 63 29 3a 79 2b  3d 79 28 63 29 3a ed 3a  |=x(c):y+=y(c):.:|
00000250  78 3d 78 2f 6e 3a 79 3d  79 2f 6e 0d 00 c8 40 20  |x=x/n:y=y/n...@ |
00000260  f4 77 68 65 6e 20 70 6c  61 79 65 72 20 61 63 63  |.when player acc|
00000270  65 6c 65 72 61 74 65 2c  20 77 65 20 70 75 74 20  |elerate, we put |
00000280  74 68 69 73 20 61 63 63  65 6c 65 72 61 74 69 6f  |this acceleratio|
00000290  6e 20 61 6c 6f 6e 67 20  74 68 65 0d 00 d2 22 20  |n along the..." |
000002a0  f4 69 73 6f 62 61 72 79  63 65 6e 74 65 72 2f 31  |.isobarycenter/1|
000002b0  73 74 20 62 72 6f 77 20  61 78 69 73 2e 0d 00 dc  |st brow axis....|
000002c0  0d 20 e7 a6 28 ac 35 37  29 8c 0d 00 e6 19 20 20  |. ..(.57).....  |
000002d0  64 78 3d 78 28 31 29 2d  78 3a 64 79 3d 79 28 31  |dx=x(1)-x:dy=y(1|
000002e0  29 2d 79 0d 00 f0 14 20  20 64 3d b6 28 64 78 5e  |)-y....  d=.(dx^|
000002f0  32 2b 64 79 5e 32 29 0d  00 fa 1b 20 20 e7 64 3c  |2+dy^2)....  .d<|
00000300  3e 30 8c 6e 78 3d 64 78  2f 64 3a 6e 79 3d 64 79  |>0.nx=dx/d:ny=dy|
00000310  2f 64 0d 01 04 26 20 20  e3 63 3d 31 b8 6e 3a 61  |/d...&  .c=1.n:a|
00000320  78 28 63 29 3d 6e 78 2f  34 3a 61 79 28 63 29 3d  |x(c)=nx/4:ay(c)=|
00000330  67 2b 6e 79 2f 34 3a ed  0d 01 0e 06 20 cc 0d 01  |g+ny/4:..... ...|
00000340  18 13 20 20 61 78 28 29  3d 30 3a 61 79 28 29 3d  |..  ax()=0:ay()=|
00000350  67 0d 01 22 06 20 cd 0d  01 2c 4c 20 f4 77 68 65  |g..". ...,L .whe|
00000360  6e 20 70 6c 61 79 65 72  20 72 6f 74 61 74 65 73  |n player rotates|
00000370  2c 20 77 65 20 61 64 64  20 74 6f 20 65 61 63 68  |, we add to each|
00000380  20 62 72 6f 77 20 61 6e  20 61 63 63 65 6c 65 72  | brow an acceler|
00000390  61 74 69 6f 6e 20 70 65  72 70 65 6e 64 69 63 75  |ation perpendicu|
000003a0  6c 61 72 0d 01 36 25 20  f4 74 6f 20 74 68 65 20  |lar..6% .to the |
000003b0  69 73 6f 62 61 72 79 63  65 6e 74 65 72 2f 62 72  |isobarycenter/br|
000003c0  6f 77 20 61 78 69 73 2e  0d 01 40 0d 20 e7 a6 28  |ow axis...@. ..(|
000003d0  ac 32 35 29 8c 0d 01 4a  0c 20 20 e3 63 3d 31 b8  |.25)...J.  .c=1.|
000003e0  6e 0d 01 54 1a 20 20 20  64 78 3d 78 28 63 29 2d  |n..T.   dx=x(c)-|
000003f0  78 3a 64 79 3d 79 28 63  29 2d 79 0d 01 5e 25 20  |x:dy=y(c)-y..^% |
00000400  20 20 64 3d b6 28 64 78  5e 32 2b 64 79 5e 32 29  |  d=.(dx^2+dy^2)|
00000410  3a 6e 78 3d 64 78 2f 64  3a 6e 79 3d 64 79 2f 64  |:nx=dx/d:ny=dy/d|
00000420  0d 01 68 1e 20 20 20 61  78 28 63 29 2b 3d 6e 79  |..h.   ax(c)+=ny|
00000430  2f 38 3a 61 79 28 63 29  2d 3d 6e 78 2f 38 0d 01  |/8:ay(c)-=nx/8..|
00000440  72 07 20 20 ed 0d 01 7c  06 20 cd 0d 01 86 0e 20  |r.  ...|. ..... |
00000450  e7 a6 28 ac 31 32 31 29  8c 0d 01 90 0c 20 20 e3  |..(.121).....  .|
00000460  63 3d 31 b8 6e 0d 01 9a  1a 20 20 20 64 78 3d 78  |c=1.n....   dx=x|
00000470  28 63 29 2d 78 3a 64 79  3d 79 28 63 29 2d 79 0d  |(c)-x:dy=y(c)-y.|
00000480  01 a4 25 20 20 20 64 3d  b6 28 64 78 5e 32 2b 64  |..%   d=.(dx^2+d|
00000490  79 5e 32 29 3a 6e 78 3d  64 78 2f 64 3a 6e 79 3d  |y^2):nx=dx/d:ny=|
000004a0  64 79 2f 64 0d 01 ae 1e  20 20 20 61 78 28 63 29  |dy/d....   ax(c)|
000004b0  2d 3d 6e 79 2f 38 3a 61  79 28 63 29 2b 3d 6e 78  |-=ny/8:ay(c)+=nx|
000004c0  2f 38 0d 01 b8 07 20 20  ed 0d 01 c2 06 20 cd 0d  |/8....  ..... ..|
000004d0  01 cc 37 20 c8 96 3a c8  99 22 4f 53 5f 42 79 74  |..7 ..:.."OS_Byt|
000004e0  65 22 2c 26 37 31 2c 62  25 3a 62 25 3d 62 25 82  |e",&71,b%:b%=b%.|
000004f0  33 3a c8 99 22 4f 53 5f  42 79 74 65 22 2c 26 37  |3:.."OS_Byte",&7|
00000500  30 2c 62 25 3a db 0d 01  d6 24 20 f4 43 6f 6d 70  |0,b%:....$ .Comp|
00000510  75 74 65 20 66 6f 72 63  65 20 66 6f 72 20 65 61  |ute force for ea|
00000520  63 68 20 73 70 72 69 6e  67 20 0d 01 e0 0b 20 e3  |ch spring .... .|
00000530  63 3d 31 b8 6f 0d 01 ea  1a 20 20 64 78 3d 78 28  |c=1.o....  dx=x(|
00000540  73 25 28 63 29 29 2d 78  28 65 25 28 63 29 29 0d  |s%(c))-x(e%(c)).|
00000550  01 f4 1a 20 20 64 79 3d  79 28 73 25 28 63 29 29  |...  dy=y(s%(c))|
00000560  2d 79 28 65 25 28 63 29  29 0d 01 fe 14 20 20 6c  |-y(e%(c))....  l|
00000570  3d b6 28 64 78 5e 32 2b  64 79 5e 32 29 0d 02 08  |=.(dx^2+dy^2)...|
00000580  18 20 20 61 78 3d 28 6c  28 63 29 2d 6c 29 2a 6b  |.  ax=(l(c)-l)*k|
00000590  2a 64 78 2f 6c 0d 02 12  18 20 20 61 79 3d 28 6c  |*dx/l....  ay=(l|
000005a0  28 63 29 2d 6c 29 2a 6b  2a 64 79 2f 6c 0d 02 1c  |(c)-l)*k*dy/l...|
000005b0  21 20 20 61 78 28 73 25  28 63 29 29 2b 3d 61 78  |!  ax(s%(c))+=ax|
000005c0  3a 61 78 28 65 25 28 63  29 29 2d 3d 61 78 0d 02  |:ax(e%(c))-=ax..|
000005d0  26 21 20 20 61 79 28 73  25 28 63 29 29 2b 3d 61  |&!  ay(s%(c))+=a|
000005e0  79 3a 61 79 28 65 25 28  63 29 29 2d 3d 61 79 0d  |y:ay(e%(c))-=ay.|
000005f0  02 30 06 20 ed 0d 02 3a  26 20 f4 63 6f 6d 70 75  |.0. ...:& .compu|
00000600  74 65 20 6d 6f 76 65 6d  65 6e 74 73 20 66 6f 72  |te movements for|
00000610  20 65 61 63 68 20 70 6f  69 6e 74 0d 02 44 0b 20  | each point..D. |
00000620  e3 63 3d 31 b8 6e 0d 02  4e 19 20 20 76 78 28 63  |.c=1.n..N.  vx(c|
00000630  29 3d 76 78 28 63 29 2a  61 2b 61 78 28 63 29 0d  |)=vx(c)*a+ax(c).|
00000640  02 58 19 20 20 76 79 28  63 29 3d 76 79 28 63 29  |.X.  vy(c)=vy(c)|
00000650  2a 61 2b 61 79 28 63 29  0d 02 62 11 20 20 78 28  |*a+ay(c)..b.  x(|
00000660  63 29 2b 3d 76 78 28 63  29 0d 02 6c 11 20 20 79  |c)+=vx(c)..l.  y|
00000670  28 63 29 2b 3d 76 79 28  63 29 0d 02 76 21 20 20  |(c)+=vy(c)..v!  |
00000680  e7 78 28 63 29 3c 30 8c  78 28 63 29 3d 30 3a 76  |.x(c)<0.x(c)=0:v|
00000690  78 28 63 29 3d 2d 76 78  28 63 29 0d 02 80 21 20  |x(c)=-vx(c)...! |
000006a0  20 e7 79 28 63 29 3c 30  8c 79 28 63 29 3d 30 3a  | .y(c)<0.y(c)=0:|
000006b0  76 79 28 63 29 3d 2d 76  79 28 63 29 0d 02 8a 25  |vy(c)=-vy(c)...%|
000006c0  20 20 e7 78 28 63 29 3e  33 31 39 8c 78 28 63 29  |  .x(c)>319.x(c)|
000006d0  3d 33 31 39 3a 76 78 28  63 29 3d 2d 76 78 28 63  |=319:vx(c)=-vx(c|
000006e0  29 0d 02 94 25 20 20 e7  79 28 63 29 3e 32 35 35  |)...%  .y(c)>255|
000006f0  8c 79 28 63 29 3d 32 35  35 3a 76 79 28 63 29 3d  |.y(c)=255:vy(c)=|
00000700  2d 76 79 28 63 29 0d 02  9e 06 20 ed 0d 02 a8 46  |-vy(c).... ....F|
00000710  20 e3 63 3d 31 b8 6f 3a  86 78 28 73 25 28 63 29  | .c=1.o:.x(s%(c)|
00000720  29 3c 3c 32 2c 32 35 35  2d 79 28 73 25 28 63 29  |)<<2,255-y(s%(c)|
00000730  29 3c 3c 32 2c 78 28 65  25 28 63 29 29 3c 3c 32  |)<<2,x(e%(c))<<2|
00000740  2c 32 35 35 2d 79 28 65  25 28 63 29 29 3c 3c 32  |,255-y(e%(c))<<2|
00000750  3a ed 0d 02 b2 06 fd a3  0d 02 bc 05 e0 0d 02 c6  |:...............|
00000760  04 0d 02 d0 19 f4 6e 62  5f 63 6f 6f 72 64 73 20  |......nb_coords |
00000770  26 20 6e 62 5f 65 64 67  65 73 0d 02 da 08 dc 33  |& nb_edges.....3|
00000780  2c 33 0d 02 e4 0b f4 63  6f 6f 72 64 73 0d 02 ee  |,3.....coords...|
00000790  1b dc 20 30 2c 33 30 2c  20 2d 31 35 2c 2d 31 35  |.. 0,30, -15,-15|
000007a0  2c 20 31 35 2c 2d 31 35  0d 02 f8 0a f4 65 64 67  |, 15,-15.....edg|
000007b0  65 73 0d 03 02 13 dc 20  31 2c 32 2c 20 31 2c 33  |es..... 1,2, 1,3|
000007c0  2c 20 32 2c 33 0d ff                              |, 2,3..|
000007c7