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~ ~ In order to further constrain the design task, and to map to the flow
of a design from abstract to concrete, a set of abstract towers were
defined. Three abstract towers are allowed, each of which has a distinctive
shape. The design of a tower is guided by the abstract tower chosen to be the
model. The user then chooses components to build a tower as close to the
abstract ``ideal'' as possible. The abstract supports are replaced by actual
supports placed on top of each other, with angles between the joints determined
automatically according to the connectors at the joints.
There are three types of abstract towers supported by SNEAKERS. They
are the I-type, the A-type, and the X-type. Each is discussed below and in
Table 
.
An I-type abstract tower is the easiest tower to visualize. It is composed
of a single support. Its base and platform sizes are relatively meaningless,
since the support is placed in their center (see Figure ).
The supports which replace this support can, therefore, usually be snap-fitted
together and the tower can be designed to use a few longer supports and few
connectors to make up the height of the tower.
There is no bracing to support this tower, and therefore, the tower is also
the least stable. It is also the cheapest and quickest to build, because of
the small number of pieces required to build it. It is a good choice
for a tower that is not required to support a great deal of weight, or that
is not expected to encounter any great wind forces.
An A-type abstract tower has a wide base and a narrower platform level.
It has three supports placed at the corners of the base of the tower
(see Figure ).
The base and platform are isosceles triangles.
The longest side of each triangle is twice as long as the shorter sides.
This is done to simplify the math needed to place components.
Because arbitrary angles are not
available to the connectors, an A-tower design may significantly deviate from
the original abstract tower, when the abstract support guides are replaced by actual supports
and connectors. The resulting tower may look quite different, depending on the
angles required to achieve the chosen height, base, and platform measurements.
Any angle can be simulated using the proper arrangement of support lengths and
angles. However, some angles will require a larger number of pieces to model,
increasing the cost and construction time. It is very sturdy, but it also
requires a large building site. It will not topple, and is not likely to
buckle.
An X-type abstract tower is generally the most stable. It is composed of
crossing supports, connected by bracing at the center. The supports attach
to the corners of the base and platform (see Figure ).
The abstract support guides are replaced by supports and connectors in the same way
that the A-tower's support guides are replaced, bringing out similar concerns
about number of pieces, and following the model. A further concern is the
need to make the supports
cross at a point where two supports end, so that they can be connected by
a single connector. Failing this, they have to be placed one inside the other,
seriously decreasing the stability of the tower. It is a greater effort to
design and build one of these towers. But it is even sturdier than the A-tower
and the crossed supports allow extra support against buckling. It, too,
is not prone to toppling.
