# An Adaptive Hybrid Sampling Method for Free-Form Surfaces Based on Geodesic Distance

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Free-Form Surface Modeling

## 3. Geodesic Distance

## 4. Sampling Strategy

#### 4.1. Determine the Sampling Quantity

#### 4.2. Determine the Sampling Position

- (a)
- Isoparametric distribution

- (b)
- Poisson distribution

- (c)
- Hammersley distribution

- (d)
- NRook distribution

#### 4.3. Error Comparison Method between the Reconstructed Surface and Original Surface

## 5. Experiment and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Sampling distribution (

**a**) Isoparametric distribution; (

**b**) Poisson distribution; (

**c**) Hammersley distribution; (

**d**) NRook distribution.

**Figure 9.**Sampling point distribution of the free-form surface and surface reconstruction: (

**a**) Isoparametric; (

**b**) Poisson; (

**c**) Hammersley; (

**d**) NRook; (

**e**) Adaptive hybrid Poisson; (

**f**) Adaptive hybrid Hammersley; (

**g**) Adaptive hybrid NRook.

**Figure 10.**Reconstructed surface ME distribution map: (

**a**) Isoparametric; (

**b**) Poissson; (

**c**) Hammersley; (

**d**) NRook; (

**e**) Adaptive hybrid Poisson; (

**f**) Adaptive hybrid Hammersley; (

**g**) Adaptive hybrid NRook.

Segment | Distance/mm |
---|---|

1 | 7750 |

2 | 7816 |

3 | 7578 |

4 | 7171 |

Segment | Distance/mm |
---|---|

11 | 4207 |

12 | 4305 |

13 | 3983 |

14 | 3714 |

21 | 4174 |

22 | 4186 |

23 | 3824 |

24 | 3728 |

31 | 3546 |

32 | 3442 |

33 | 4059 |

34 | 4004 |

41 | 3366 |

42 | 3427 |

43 | 4069 |

44 | 4163 |

Segment | Sample Size |
---|---|

11 | 131 |

12 | 144 |

13 | 119 |

14 | 106 |

21 | 181 |

22 | 194 |

23 | 169 |

24 | 156 |

31 | 69 |

32 | 56 |

33 | 94 |

34 | 81 |

41 | 6 |

42 | 19 |

43 | 31 |

44 | 44 |

Sampling Method | ME/mm | RMSE/mm |
---|---|---|

Isoparametric | 0.1855 | 0.0266 |

Poisson | 0.2613 | 0.0467 |

Adaptive hybrid Poisson | 0.0981 | 0.0202 |

Hammersley | 0.2864 | 0.0708 |

Adaptive hybrid Hammersley | 0.1084 | 0.0189 |

NRook | 0.3123 | 0.1226 |

Adaptive hybrid NRook | 0.1480 | 0.0213 |

Adaptive sampling method [24] | 0.3252 | 0.0486 |

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**MDPI and ACS Style**

Chen, C.; Jia, H.; Lu, Y.; Zhang, X.; Chen, H.; Yu, L.
An Adaptive Hybrid Sampling Method for Free-Form Surfaces Based on Geodesic Distance. *Sensors* **2023**, *23*, 3224.
https://doi.org/10.3390/s23063224

**AMA Style**

Chen C, Jia H, Lu Y, Zhang X, Chen H, Yu L.
An Adaptive Hybrid Sampling Method for Free-Form Surfaces Based on Geodesic Distance. *Sensors*. 2023; 23(6):3224.
https://doi.org/10.3390/s23063224

**Chicago/Turabian Style**

Chen, Chen, Huakun Jia, Yang Lu, Xiaodong Zhang, Haohan Chen, and Liandong Yu.
2023. "An Adaptive Hybrid Sampling Method for Free-Form Surfaces Based on Geodesic Distance" *Sensors* 23, no. 6: 3224.
https://doi.org/10.3390/s23063224