autoAssembler allows users to import 2D cutting plans into a
3D editor, here kyub. AutoAssembler accomplishes the
2D to 3D conversion by searching the exponential space of
possibilities in search of the most plausible configuration.
The benefit of converting to 3D is that it makes it easy to
apply parametric changes, such as the adjustment of the focal
range on this VR headset. The main contribution of
autoAssembler is that it performs this conversion in an
automatic fashion. AutoAssembler uses a beam search algorithm to
search the space of ways to combine the plates in a model.
It starts out with a plate that has the most joints.
AutoAssembler then generates new versions by adding matching
plates. AutoAssembler now estimates how likely their
respective model is still correct. Testing showed that a
beam width of four was sufficient to reach a high
success rate. This means that it takes the four best scoring
candidates and generates new children from these.
AutoAssembler recursively performs this procedure until
all plates are assembled. The key to the success of this
algorithm is the heuristic function, that calculates the
scores based on the weighed sum of six heuristics and two
procedural steps to narrow down the search space at each stage.
1) AutoAssembler prefers candidates with small bounding
boxes. Here for example, adding the red plate increases the size
of the bounding box. AutoAssembler thus prefers to
add in this green plate. Because typical laser-cut models are
constructed in a compact way. 2) Inserting the bearing for the
wheels of this train wagon causes the plates to intersect.
AutoAssembler avoids intersecting plates, even at the
expense of producing a model with larger bounding box. 3)
There is a large number of ways to insert this plate into the
model. The real problem is the plate autoAssembler inserted
before this plate, which had four different matching joints
in 16 orientations. AutoAssembler prevents this from
happening by preferring this candidate, which has only one
other joint in two orientations. Assembling that plate first,
poses constraints to later on minimize plausible orientations
of the joints on other plates. 4) This red plate adds multiple
unmatched joints to the candidate. This heavily
increases the number of candidates to consider on the
next stage. AutoAssembler therefore prefers this
candidate, as it only adds one new unmatched joint.
5) This red plate can be inserted in at least four ways.
The green plate in contrast is constrained by all other plates.
AutoAssembler thus prefers to insert this plate first, the
plate introduces additional constraints into the model
disambiguating the subsequent placement of the red plate. 6)
On this stage autoAssembler picks these four candidates
which all assemble different plates and joints. Even though
the first four candidates received the highest score, only
one of those is correct. So every single one of them has a
reduced probability. Sampling broader increases the chance to
pursue a good assembly here. 7) The red plate in this candidate
does not adhere to the symmetry axis of the bottom plate, it is
flipped the wrong way around. AutoAssembler thus prefers to
assemble the plate as shown here in green.
8) This plate is symmetric, the top half is the same as the
bottom half. AutoAssembler recognizes this and thus only
tries to assemble this plate in one orientation. The same goes
for this plate with a vertical symmetry axis. AutoAssembler
reduces the search space further by deduplicating plates that are
the same. This barrel model, consisting of 12 plates with 58
joints is reduced to three types of plates with 19 joints.
In our technical evaluation with 66 models, autoAssembler
achieved a 79% success rate in a median runtime of 0.3 seconds.
AutoAssembler completed an additional 18% of models by
letting users manually disambiguate the results. For
this purpose, we added two tools to the menu. Fixing a model
required on average 2.7 clicks. In conclusion, autoAssembler
allows users to automatically convert 2D cutting plans to 3D
models for laser cutting. This grants users access to laser cut
models found online, almost as if these have been shared in 3D
in the first place