A Woodworker’s Easy Fix
By Marc Alexa
hence the mixed discrete-continuous
Nonetheless, the authors of the following paper have found a way to provide the user with instant feedback on
how to fix unstable or toppling wooden
panel constructions. They formulate
the desired goal as finding small design
changes, that is, the length of the vector
of design parameter changes is minimal.
The solution to this problem requires
several key ingredients: First, it is easier
to check for validity in the space of joint
forces. So, for the current design, they
linearize the connection between the
design space and the ‘force space’ (and
make some additional simplifying assumptions). This allows them to quickly
check if a small change in the design
space leads to a feasible construction.
Still, the dimension of the design space is
too large to find short vectors that make
the construction feasible. The second
main idea is to limit the change to only
a few independent parameters, while
the rest stay fixed. This limitation drastically reduces the dimension of the search
space, not only making it feasible to compute solutions (for all possible combinations of changeable parameters), but also
easier to understand the suggested modification for the human user in the loop.
Lastly, discrete changes are restricted to
adding a panel, and the location of the
panel is based on established rules.
Together with some additional features in the user interface, the resulting
system really solves the problem of developing, rather than just checking, wood
panel constructions. As a woodworker, I
cannot wait to get my hands on this system. As a computer scientist, I am more
interested in the general solution for the
interactive search of feasible solutions in
a high-dimensional design space—this
solution will serve as a blueprint for a
variety of related design problems.
Marc Alexa is a professor in the Department of Computer
Science at Technische Universität Berlin, Germany.
Copyright held by author.
I LIKE WOODWORKING. I have built quite a
number of pieces of furniture, like cabinets, shelves, beds, and tables, as well as
a ladder, a shack, and other things. Not
being professionally trained, I restrict
myself to simple construction projects,
for which I trust my intuition on stability.
For more complex constructions I stick
to the standards I find in books. This obviously limits my freedom.
As a computer scientist, I know it
would be possible to check the validity of
a construction using physical simulation.
If the panels chosen are the right type
(thickness or kind of wood), the main
structural problems are where the pieces come together—in the joints. Each
joint bears linear and rotational forces;
the result of the weight of the wood itself and the stuff being put onto or into
the object (for example, the person on a
ladder). There are natural limits to these
forces in the joints, which I could find in
the literature. Given all this information
(combinatorial structure of the panels,
dimensions, loads, limits on joint forces)
checking validity is a straightforward
project in scientific computing.
Now, what would I have gained from
this programming project? If the computer tells me my construction is stable
I can go ahead and build it. But what if it
does not confirm? I would change my design and try again. This is obviously a tedious exercise. Nonetheless, this “
workflow” is the current design standard.
Wouldn’t it be much better if the
computer told me how to fix my construction? Or, even better, offered several ways to fix it, so that I could just chose
one? Certainly yes, but this is a difficult
problem. Just as in NP problems: deciding if a given answer is correct is easy, but
finding one is hard. Here, the technical
difficulty is the large dimension and the
mixed discrete-continuous nature of the
design space: each panel has two dimensions, each joint has numerous parameters, and some constructions can only
be fixed by changing the combinatorial structure (typically adding a panel),
To view the accompanying paper,
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