<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>The primary data model of the current point cloud is still the organization of discrete points. Point clouds and patterns are independent of each other. Firstly, this paper establishes the data structure of multi-layer integrated ancient buildings based on the point cloud model. The purpose is to adapt to ancient buildings’ laser point cloud processing technology. Then this paper uses Lagrangian mathematics to model the point cloud pattern. Finally, the paper verifies that the cartographic model of ancient buildings established by the Lagrangian formula is smooth and accurate. The model can express detailed information about ancient buildings. </p>
</abstract>

The primary data model of the current point cloud is still the organization of discrete points. Point clouds and patterns are independent of each other. Firstly, this paper establishes the data structure of multi-layer integrated ancient buildings based on the point cloud model. The purpose is to adapt to ancient buildings’ laser point cloud processing technology. Then this paper uses Lagrangian mathematics to model the point cloud pattern. Finally, the paper verifies that the cartographic model of ancient buildings established by the Lagrangian formula is smooth and accurate. The model can express detailed information about ancient buildings.

Ancient Building Surveying and Mapping Modeling Protection System Based on Lagrangian Mathematical Equation 

Applied Mathematics and Nonlinear Sciences

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