Journal
COMPUTER GRAPHICS FORUM
Volume 41, Issue 5, Pages 161-173Publisher
WILEY
DOI: 10.1111/cgf.14611
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Funding
- NSF [DBI-1759836, EF-1921728, AF-1907612, AF-2106672]
- Washington University in St. Louis
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This study presents a method for removing unwanted topological features from a sequence of nested shapes, and demonstrates its effectiveness and superiority through empirical evaluation.
We present a method for removing unwanted topological features (e.g., islands, handles, cavities) from a sequence of shapes where each shape is nested in the next. Such sequences can be found in nature, such as a multi-layered material or a growing plant root. Existing topology simplification methods are designed for single shapes, and applying them independently to shapes in a sequence may lose the nesting property. We formulate the nesting-constrained simplification task as an optimal labelling problem on a set of candidate shape deletions (cuts) and additions (fills). We explored several optimization strategies, including a greedy heuristic that sequentially propagates labels, a state-space search algorithm that is provably optimal, and a beam-search variant with controllable complexity. Evaluation on synthetic and real-world data shows that our method is as effective as single-shape simplification methods in reducing topological complexity and minimizing geometric changes, and it additionally ensures nesting. Also, the beam-search strategy is found to strike the best balance between optimality and efficiency.
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