# Constructing Coupling Model of Generalized B-Spline Curve and Crown (CMGBCC) to Explore the 3D Modeling of Chinese Fir Polymorphism

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Constructing CMGBCC

_{k}(t) of the k-th interpolation only related to the base point t and was expressed as:

_{i+1}and t

_{i}which are two adjacent points and φ(t) is the cubic b-spline system, the for which expression was:

_{i}(t), g′

_{i}(t), and g″

_{i}(t) at each base point in Equation (1), the following conclusions could be drawn:

_{0}, a

_{1}, and a

_{2}presented the three points on the left curve that approached the vertex. Additionally, a

_{n}, a

_{n+1}, and a

_{n+2}were three points on the right curve that approached the vertex.

_{i,3}(t) was calculated and the value at each point was:

#### 2.3. Constructing Coupling Model of 3D Chinese Fir Trunk, Branches Model and Withered State

#### 2.4. Simulations of Three Types of the Tree Polymorphism

## 3. Results

#### 3.1. 3D Models of Chinese Fir Trunk and Branch

#### 3.1.1. 3D Models of Chinese Fir Trunk

#### 3.1.2. 3D Models of Chinese Fir Branch

#### 3.2. The Result of CMGBCC

#### 3.3. 3D Modeling and Verification of Chinese Fir Polymorphism

## 4. Discussion

## 5. Conclusions

- Constructing CMGBCC improved the fitting function for the crown curve.
- We considered the influence of different withered state branches on the whole shape in 3D tree modeling.
- We simulated three types of polymorphisms, including natural pruning, crown displacement, and crown shape difference.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 14.**Comparison of real photos and simulation results of observation point 1 in sample plot 1.

**Figure 15.**Comparison of real photos and simulation results of observation point 2 in sample plot 1.

**Figure 16.**Comparison of real photos and simulation results of observation point 3 in sample plot 1.

Type | Height/m | DBH/cm | UBH/m | HMCW/m | Crown Width/m | Age/a |
---|---|---|---|---|---|---|

Max | 30.4 | 36.5 | 14.6 | 18.1 | 4.0 | 30 |

Min | 8.8 | 8.3 | 4.5 | 7.2 | 0.4 | 12 |

Average | 17.8 | 23.6 | 8.0 | 13.9 | 1.7 | 24 |

The Level of Branch | Index | Description |
---|---|---|

first-level branch | withered state | amount of needle cover on branches |

first-level branch | elevation angle | the angle between the branch and the vertical direction of the trunk |

first-level branch | branch length | length of branch |

first-level branch | base diameter | branch base diameter |

second-level branch | elevation angle | the angle between the branch and the vertical direction of the primary branch |

second-level branch | azimuth | the angle between the branches in the horizontal direction of the primary branch |

second-level branch | undershoot | length between the branch point and base |

Tree Height Range | Model Height/m | DBH/cm |
---|---|---|

8.0~9.0 | 8.8 | 13.5 |

14.0~15.0 | 14.5 | 20 |

20.0~21.0 | 20.5 | 27.3 |

26.0~27.0 | 26.4 | 29.7 |

30.0~31.0 | 30.4 | 31.2 |

Index | b-Spline Interpolation | CMGBCC |
---|---|---|

Derivative value at the top point | Add manually and uncontrollable factors of the model | It does not need to manually input the derivative value at the top point, simplifying the model construction process and reducing the error caused by humans |

Collection rules of type value points | Equal distance acquisition | It can be collected according to the crown shape change rules |

Collection interval of type value points | Equal distance acquisition | Acquisition at any distance |

Model complexity | The model form is relatively simple | The model form is relatively complex |

Type | Height/m | DBH/cm | UBH/m | HMCW/m | Crown Width/m |
---|---|---|---|---|---|

Max | 28.3 | 34.2 | 14.2 | 17.0 | 3.8 |

Min | 9.6 | 9.3 | 4.9 | 8.6 | 0.4 |

Average | 17.0 | 20.4 | 8.3 | 13.1 | 1.9 |

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## Share and Cite

**MDPI and ACS Style**

Cui, Z.; Zhang, H.; Liu, Y.; Zhang, J.; Yang, T.; Zuo, Y.; Lei, K.
Constructing Coupling Model of Generalized B-Spline Curve and Crown (CMGBCC) to Explore the 3D Modeling of Chinese Fir Polymorphism. *Forests* **2023**, *14*, 1267.
https://doi.org/10.3390/f14061267

**AMA Style**

Cui Z, Zhang H, Liu Y, Zhang J, Yang T, Zuo Y, Lei K.
Constructing Coupling Model of Generalized B-Spline Curve and Crown (CMGBCC) to Explore the 3D Modeling of Chinese Fir Polymorphism. *Forests*. 2023; 14(6):1267.
https://doi.org/10.3390/f14061267

**Chicago/Turabian Style**

Cui, Zeyu, Huaiqing Zhang, Yang Liu, Jing Zhang, Tingdong Yang, Yuanqing Zuo, and Kexin Lei.
2023. "Constructing Coupling Model of Generalized B-Spline Curve and Crown (CMGBCC) to Explore the 3D Modeling of Chinese Fir Polymorphism" *Forests* 14, no. 6: 1267.
https://doi.org/10.3390/f14061267