# 3D Cadastral Data Model Based on Conformal Geometry Algebra

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## Abstract

**:**

## 1. Introduction

## 2. Basic Idea

## 3. Methods

#### 3.1. Geometrically and Topologically Unified Representation in CGA

#### 3.2. 3D Cadastral Object Data Model Based on CGA

#### 3.2.1. Initial Conditions

#### 3.2.2. 3D Cadastral Object Reconstruction in CGA

#### 3.3. 3D Cadastral Data Organization Based on CGA in A Database

## 4. Case Studies

## 5. Discussion

## 6. Conclusion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Processing flow of the CGA (conformal geometric algebra) -based 3D (three-dimensional) cadastral data model.

**Figure 6.**Process of integrating the representation of the geometry and topology of a 3D cadastral spatial unit in CGA.

**Figure 9.**Multidimensional unified expression for a cadastral object within the multivector structure.

Object | Drawing | Outer Production | Grade |
---|---|---|---|

Point | Null | 1 | |

Point pair | $PP={P}_{1}^{P}_{2}$ | 2 | |

Line | $L={P}_{1}^{P}_{2}^{e}_{\infty}$ | 3 | |

Circle | $C={P}_{1}^{P}_{2}^{P}_{3}$ | 3 | |

Plane | $P={P}_{1}^{P}_{2}^{P}_{3}^{e}_{\infty}$ | 4 | |

Sphere | $S={P}_{1}^{P}_{2}^{P}_{3}^{P}_{4}$ | 4 |

CGA-Based Model | OO3D Model | SSS Model | |
---|---|---|---|

time(sec) | 3.76 | 3.71 | 4.19 |

memory(kb) | 905 | 968 | 1491 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.-y.; Yin, P.-c.; Li, G.; Gu, H.-h.; Zhao, H.; Fu, J.-c.
3D Cadastral Data Model Based on Conformal Geometry Algebra. *ISPRS Int. J. Geo-Inf.* **2016**, *5*, 20.
https://doi.org/10.3390/ijgi5020020

**AMA Style**

Zhang J-y, Yin P-c, Li G, Gu H-h, Zhao H, Fu J-c.
3D Cadastral Data Model Based on Conformal Geometry Algebra. *ISPRS International Journal of Geo-Information*. 2016; 5(2):20.
https://doi.org/10.3390/ijgi5020020

**Chicago/Turabian Style**

Zhang, Ji-yi, Peng-cheng Yin, Gang Li, He-he Gu, Hua Zhao, and Jian-chun Fu.
2016. "3D Cadastral Data Model Based on Conformal Geometry Algebra" *ISPRS International Journal of Geo-Information* 5, no. 2: 20.
https://doi.org/10.3390/ijgi5020020