## 2 Innovative Methodology
### Data Redundancy Identification
\begin{array}{l}0,if:d_{y}\frac{z_{j}-z_{j-1}}{x_{ j}-x_{j-1}}<0\\ 3\frac{z_{j}-z_{j-1}}{x_{j}-x_{j-1}}if:|e_{z}|>3\left|\frac{z_{j}-z_{j-1}}{x_{j}-x _{j-1}}\right|\delta\frac{(z_{j}-z_{j-1})(z_{j-1}-z_{j-2})}{(x_{j}-y_{j-1})(x_ {j-1}-x_{j-2})}<0\end{array} \right.^{\prime}, \tag{9}\]  
in which  
\[\left\{ \begin{array}{l}e_{y}=\frac{(2x_{j}-x_{j-1}-x_{j-2})(y_{j}-y_{j-1})} {(x_{j}-x_{j-1})(x_{j}-x_{j-2})}-\frac{(x_{j}-x_{j-1})(y_{j-1}-y_{j-2})}{(x_{ j}-x_{j-2})(x_{j}-x_{j-2})}\\ e_{z}=\frac{(2x_{j}-x_{j-1}-x_{j-2})(z_{j}-z_{j-1})}{(x_{j}-x_{j-1})(x_{j}-x_{ j-2})}-\frac{(x_{j}-x_{j-1})(z_{j}-z_{j-2})}{(x_{j}-x_{j-1})(x_{j}-x_{j-2})} \end{array} \right.. \tag{10}\]  
Herein, based on the compressed point cloud data flow from Step 2, the shape-preserving piecewise bicubic Hermite polynomials can be created according to the above algorithm. Then, Hermite extrapolation is performed to create a predicted curve, which is marked in blue as shown in Figure 4, and its analytical formula can be described as follows:  
\[\left\{ \begin{array}{l}H_{y}(x)=y_{j-1}\alpha_{j-1}(x)+y_{j}\alpha_{j}(x)+ y^{\prime}_{j-1}\beta_{j-1}(x)+y^{\prime}_{j}\beta_{j}(x)\\ H_{z}(x)=z_{j-1}\alpha_{j-1}(x)+z_{j}\alpha_{j}(x)+z^{\prime}_{j-1}\beta_{j-1}( x)+z^{\prime}_{j}\beta_{j}(x)\end{array} \right.. \tag{11}\]  
After that, an estimated point \(P_{est}\) is created to move along the predicted curve with a stepping distance of \(\lambda\). \(P_{t,j}\) is the starting point of \(P_{est}\). Meanwhile, a bounding sphere is built with point \(P_{est}\) as the center. The radius of the sphere is  
\[R_{sph}=\kappa h_{ls}, \tag{12}\]  
in which \(\kappa\in[1,2]\) is the radius adjustment coefficient, and \(h_{ls}\) is the distance between two parallel scannning layers. As shown in Figure 4, the predicted curve with estimated point \(P_{est}\) are used to search for the neighbor point \(P_{nb}\) from the previous scanning line \(i\)\(-\)1. The necessary and sufficient conditions for point \(P_{nb}\) as the neighbor point of \(P_{est}\) are \(\left|\overline{P_{est}P_{nb}}\right|\leq R_{sph}\), which means that \(P_{nb}\) is inside the bounding sphere with point \(P_{est}\) as its center. At the very beginning, \(P_{est}\) coincides with \(P_{t,j}\). At this point, there are two possibilities: (i) \(P_{i-1,u}\) is inside the bounding sphere (i.e., \(\left|\overline{P_{i-1,u}P_{i,j}}\right|\leq R_{sph}\)), or (ii) \(P_{i-1,u}\) is outside the bounding sphere. In case (i), \(P_{i-1,u}\) is the first found neighbor point. As \(P_{est}\) moves along the scanning direction with a stepping distance of \(\lambda\), if \(\left|\overline{P_{est}P_{i-1,u}}\right|<\left|\overline{P_{i,p}P_{i-1,u}}\right|\), then \(P_{i-1,u}\) is the neighbor point of \(P_{est}\); otherwise, discard point \(P_{i-1,u}\), as it is not the neighbor point of \(P_{est}\) but of \(P_{t,j}\). In case (ii), there is no operation because no neighbor point has been found. After case (i) or case (ii) is completed, point \(P_{est}\) continues to move forward along the scanning direction until the neighbor point \(P_{nb}\) of \(P_{est}\) is found; if the neighbor point cannot be found, the search is stopped. If the neighbor point \(P_{nb}\) is found in line \(i-1\) (e.g., \(P_{i-1,u+1}\) in Figure 4), then a new bounding sphere is built with \(P_{i-1,u+1}\) as the center and the radius is \(R_{sph}\). After that, we use this new bounding sphere to search for the neighbor point of \(P_{i-1,u+1}\) in line \(i-2\); and if the neighbor point cannot be found, we stop searching. Next, we take the new neighbor point in line \(i-2\) (e.g., \(P_{i-2,p+1}\)) as a new center to build a bounding sphere and repeat the above process until we find three neighbor points in different scanning lines (e.g., \(P_{i-1,u+1}\), \(P_{i-2,p+1}\), \(P_{i-3,p+1}\) in Figure 4). Based on the neighbor point set \(\{P_{i-1,u+1},P_{i-2,v+1},P_{i-3,w+1}\}\), the coordinates of estimated point \(P_{est}\) can be fixed uniquely. As shown in Figure 4, a bi-cubic Hermite curve is built, and it can be expressed as  
\[\left\{