Growth algorithm making more possible

Prenote: how can i answer to a existing topic without creating a new one?
(remember I also asked that in the past ^^)

Well lets begin with the main course the theoretics behind my algorithm ide=
a(if your not in the mood just jump to the Practical part):
Ok, imagine making a mental snapshot/copy of a Fluidon creature which alrea=
dy has a stable form, now adjust the lengthes to the current state
(so that tension and pressure disappear) and increase the rigidty to maximu=
m. =

>From this nice, colorless and rigid structure you choose one intervall,
now imagine you cut this intervall in half and knot the ends together,
basically you replace
endpoint - line - endpoint
with
endpoint - line - midpoint - line- endpoint
Now what exactly has happened/changed with your structure?
Lets first look at the worst case of two possible:

The two endpoints can change their distance, they have gained an additional
degree of freedom, to move away or towards each other(on a bent line,or in =
the right coordinate system in a straight line).
The midpoint has two degrees of freedom:
First it can rotate around the connection axis of the two endpoins, this de=
gree of freedom is independant,its not related to the two endpoints.
Second it can change the radius it rotates around the axis, this degree
of freedom is dependant and directly related to the movement of the two end=
points.(In the right coordinate system:the midpoint moves on a circular sur=
face orthogonal to the connection line of the endpoints)

So what can we do to take away the degree of freedoms ,and define a stable
structure?
There are two choices:

Choice one: First we elimate the degree of freedom of the endpoints, for th=
is we must know, which points have stable distances relative to endpoint A =
and which have stable distances to endpoint B if we move the two endpoints =
away and towards each other.
Once we know this(by doing a test run) we connect a point stable to A with =
a point stable to B, trough this we also eliminated one degree of freedom o=
f the midpoint,the one related the endpoint.
The midpoint now rotates in a circle with a constant radius, note
that the freedom of a loose intervall(only connected) to one point is repre=
sented as spherical surface and this surface now has to cut the circle, the=
y cutpoints are the stable formations that are created when we merge the mi=
dpoint with the loose intervalls endpoint.

Choice two: We use two loose end intervalls (two spheres)originating from p=
oints stable to each other(so either both are Stable to A or both to B) to =
cut the circle surface created by the midpoint.
The first sphere creates a cutline on which the mid point can move if midpo=
int merges with loose intervall endpoit, the second creates two or one cutp=
oint which are stable formations, as the degree of freedom of the endpoints=
 was directly related to the degree of freedom of the midpoint. (note only =
at certain lengthes there is one instead of two two stable points, its when=
 the two stable  points merge with each other)
So why you might ask had the originating points of the loose intervalls be
stable to each other? Well cause otherwise if the endpoints tried to move
the orignating points could try to move with them(changing sphere position =
results in-->change of cut points) leading to a complicates movement patter=
n(although in some cases special conditions might prevent this, generally t=
here should result a certain freedom of movement)

The better case:
In the better case the endpoints can not move cause of other connections, i=
n this case, the midpoint has only one degree of freedom, and we only need =
one additional conection from the mid point to another point to stabilize t=
he system.


Practical:
Lets go back to our snapshooted rigid, tension- and pressureless structure,
(Created by copying a stable fluidom structure and adjusting all original l=
engthes to the current ones) =

after we have choosen one connection we expand and shrink just this one
and test if extensive stress is created(remember all is very rigid), if yes=
 the better case has appeared if no the worst case appeared.
Additional we test, which points did not change distance in relation to ,wh=
ich endpoint of the intervall, while we executed the expanding and shrinkin=
g.
(the following is done to the building plan of the new child) =

Now replace the line with two lines to each other, basically a long line wi=
th a midpoint [endpoint-line-midpoint-line-endpoint].
In the worst case connect the midpoint with one other point(originating poi=
nt),then choose either to connect the midpoint with another point stable to=
 the originating point of the first connection, or connect a point stable t=
o one endpoint with a point stable to the other endpoint.
In the better case connect the midpoint with an additional point.


Thats the whole method ,although you might still need some conditions where
to place the midpoint, when you only want to choose certain stable point, o=
r you might not want to much connections to far away points of your body,
but this relies totally on your taste.
-- =

"Ein Herz f=FCr Kinder" - Ihre Spende hilft! Aktion: www.deutschlandsegelt.=
de
Unser Dankesch=F6n: Ihr Name auf dem Segel der 1. deutschen America's Cup-Y=
acht!

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