# Free-Form Surface Partitioning and Simulation Verification Based on Surface Curvature

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Free-Form Surface Representation Geometry

#### 3.1. Free-Form Surface Representation

#### 3.2. Surface GEOMETRY

## 4. Division of Free-Form Surfaces

#### 4.1. Surface Rough Division

#### 4.2. Free-Form Surface Subdivision

#### 4.3. Surface Boundary Definition

## 5. Program Flow

## 6. Simulation Experiment

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison of FCM and K−means clustering effects under the same number of clusters: (

**a**). K−means Algorithm, the circles represent the clustering centers of K−means; (

**b**). FCM Algorithm, the stars represent the clustering centers of FCM.

**Figure 4.**(

**a**) Empty characteristic, (

**b**) Minimum angle maximization characteristic. A, B, C, D are any four points in space.

**Figure 7.**Preliminary division of the surface based on curvature, □ stands for convex area, ▽ stands for saddle area, ◇ stands for concave area.

**Figure 12.**Sample 2 sub-domain machining process: (

**a**) rough machining process; (

**b**) convex area machining process; (

**c**) saddle area machining process; (

**d**) concave area machining process.

Gaussian Curvature (K) | Mean Curvature (H) | Point Feature | Local Surface Shape |
---|---|---|---|

K > 0 K > 0 K < 0 K = 0 K = 0 K = 0 | H > 0 H < 0 H > 0 or H < 0 H = 0 H > 0 H < 0 | Oval Oval Hyperbola Parabola Parabola Parabola | Concave area Convex area Saddle area Flat area Concave area Convex area |

Simulation Results | Toolpath Length/(mm) | Processing Time/(s) | |
---|---|---|---|

Processing Method | |||

Traditional method | 45,280 | 2717 | |

Proposed method | 29,110 | 1747 |

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**MDPI and ACS Style**

Liu, H.; Zhang, E.; Sun, R.; Gao, W.; Fu, Z.
Free-Form Surface Partitioning and Simulation Verification Based on Surface Curvature. *Micromachines* **2022**, *13*, 2163.
https://doi.org/10.3390/mi13122163

**AMA Style**

Liu H, Zhang E, Sun R, Gao W, Fu Z.
Free-Form Surface Partitioning and Simulation Verification Based on Surface Curvature. *Micromachines*. 2022; 13(12):2163.
https://doi.org/10.3390/mi13122163

**Chicago/Turabian Style**

Liu, Hongwei, Enzhong Zhang, Ruiyang Sun, Wenhui Gao, and Zheng Fu.
2022. "Free-Form Surface Partitioning and Simulation Verification Based on Surface Curvature" *Micromachines* 13, no. 12: 2163.
https://doi.org/10.3390/mi13122163