# Geometric Path Generation on Klein bottle Canonical words L=10

Source: [Geometric Path Generation on Klein bottle Canonical words L=10](<https://www.sota2.com/research/sota/geometric-path-generation-on-klein-bottle-canonical-words-l-10>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-18T08:11:47.393Z

Evaluation of geometric path generation performance on the Klein bottle Canonical words dataset (L=10), measured using per-segment Chamfer distance.

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

| Scope | Recorded value |
| --- | --- |
| Task | Geometric path generation |
| Dataset (including any stated split) | Klein bottle Canonical words L=10 |
| Metric | Per-segment Chamfer Distance |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 4 of 4 |
| Coverage | All results currently returned for this benchmark |

Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol.

## Metrics

- [Per-segment Chamfer Distance](<https://www.sota2.com/research/sota/geometric-path-generation-on-klein-bottle-canonical-words-l-10.md?metric=Per-segment%20Chamfer%20Distance>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Per-segment Chamfer Distance | Result date | Report paper |
| --- | --- | --- | --- |
| Homotopy | 0.82 | Not recorded | 69ba31ab0636e5bf4afc09ba |
| Transport | 0.84 | Not recorded | 69ba31ab0636e5bf4afc09ba |
| Cover | 1.57 | Not recorded | 69ba31ab0636e5bf4afc09ba |
| Transf. (WC) | 2.28 | Not recorded | 69ba31ab0636e5bf4afc09ba |

### Homotopy

Per-segment Chamfer Distance: 0.82. Result ID: 69ba5e1f47f34ce924a41c9f.

[Reporting paper](<https://www.sota2.com/research/paper/69ba31ab0636e5bf4afc09ba.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69ba31ab0636e5bf4afc09ba.md>)

Recorded evaluation configuration: {"Type":"B"}. This record does not assert independent reproduction.

### Transport

Per-segment Chamfer Distance: 0.84. Result ID: 69ba5e1f47f34ce924a41c9e.

[Reporting paper](<https://www.sota2.com/research/paper/69ba31ab0636e5bf4afc09ba.md>)

[Method origin paper](<https://www.sota2.com/research/paper/69ba31ab0636e5bf4afc09ba.md>)

Recorded evaluation configuration: {"Type":"B"}. This record does not assert independent reproduction.

### Cover

Per-segment Chamfer Distance: 1.57. Result ID: 69ba5e1f47f34ce924a41c9c.

[Reporting paper](<https://www.sota2.com/research/paper/69ba31ab0636e5bf4afc09ba.md>)

Recorded evaluation configuration: {"Type":"A"}. This record does not assert independent reproduction.

### Transf. (WC)

Per-segment Chamfer Distance: 2.28. Result ID: 69ba5e1f47f34ce924a41c9d.

[Reporting paper](<https://www.sota2.com/research/paper/69ba31ab0636e5bf4afc09ba.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa703d1e209131cea49db1.md>)

[Implementation](<https://github.com/tensorflow/tensor2tensor>)

Recorded evaluation configuration: {"Type":"A"}. This record does not assert independent reproduction.

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