The experiments presented in the previous section show that the incremental representation of constraints and parameter optimization search does produce shape fitting that satisfies the constraints with low error. The experiments also show that the least-square error grows as the constraints are applied; however, what is important is reconstructing shapes that satisfy the given constraints, while also binding the remaining unconstrainted shape parameters using the range information. The magnitude of the actual least-square error, even relative to the least-square error of the unconstrained fit, is unimportant relative to the constraint satisfaction. The amount of change in position of the constrained surfaces relative to the original position is similarly very irrelevant.
The option of adding the constraints incrementally has also been
investigated. We have chosen to start from the previous optimal position
when a new constraint is added and to keep the weight of the previous
constraints at the fixed maximum value of
. The experiments confirmed that a previous constraint is almost not
affected when a new constraint is added.
The optimization procedure used here produces solutions in a few minutes or less, which is suitable for CAD work.
The work here assumed that the range measurements were already segmented into groups associated with features. This is a reasonable assumption, but how to achieve this in difficult cases is an open problem.
Finally, real parts usually have more than just the constrained developable surfaces. The optimization procedure discussed above manipulates the constrained surface positions and shapes, but not the other surfaces. Consequently, a complete system would need to consider how to move and transform the other connected surfaces as the constrained features move.
Naoufel Werghi