How to Sample and Reconstruct Curves With Unusual Features
Tobias Lenz · 2006
This work generalizes the ideas in the Nearest-Neighbor-Crust algorithm by Dey and Kumar. It allows to reconstruct smooth closed curves from ε-samples with ε ≤ 0.48 which is a big improvement compared to the original bound. Further generaliza-tion leads to a new algorithm which reconstructs arbi-trary curves (open, closed, smooth, with corners, with intersections) in any dimension. The algorithm works well in practice but lacks a nice sampling condition comparable to the well-known ε-sampling condition. This shortcoming is posed as an open problem. 1