# A Point Cloud Registration Algorithm Based on Weighting Strategy for 3D Indoor Spaces
## 5 Discussion  
We decompose a complete rigid-body transformation into a superposition of many tiny rigid-body transformations. For instance, a 120-degree rigid-body transformation is essentially a combination of numerous short-time, small-angle rigid-body transformations. By breaking down complex transformations into smaller, simpler components, we can better understand and analyze the overall motion of the rigid body. This decomposition method allows us to study the effects of each individual transformation and how they contribute to the overall movement of the object. By studying these small-angle transformations, we can gain insights into the mechanics and dynamics of rigid-body motion. Within each of these tiny rigid-body transformations, the angle is extremely small, enabling the application of approximation theory. This decomposition allows us to break down complex transformations into simpler, more manageable steps that can be analyzed and understood more easily. By applying approximation theory to each small angle transformation, we can accurately model and predict the behavior of the overall rigid-body transformation. This approach is particularly useful in robotics, computer graphics, and other fields where precise control and understanding of rigid-body movements are crucial. This small angle allows the algorithm to quickly iterate to the optimal solution. During the subsequent experimental validation phase, we discover that the algorithm's running time increases with the size of the transformation angle, as it superimposes more tiny, rigid-body transformations. However, this decomposition fully utilizes the benefits of the new method for solving the iterative problem suggested in Section 3. Each small transformation exhibits high accuracy, which enhances the accuracy of the final superimposed changes. The original paper provides a theoretical derivation, and we set the amount of angular change in the rotation axis to \(1^{\circ}\) for each iteration of the algorithm in the subsequent experiments. This incremental approach allows us to achieve precise results with each iteration, ultimately leading to a highly accurate final transformation. By setting the rotation axis change to \(1^{\circ}\) for each iteration, we are able to control the granularity of the transformations and ensure \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Indicators** & & **ICP** & **NDT** & **PointNetLK** & **Weighted PP-ICP** \\ \hline \multirow{8}{*}{Time (s)} & \(15^{\circ}\) & 94.561 & 92.656 & 77.072 & 50.233 \\  & \(30^{\circ}\) & 157.958 & 192.108 & 141.939 & 108.381 \\  & \(45^{\circ}\) & 254.401 & 283.051 & 214.551 & 154.845 \\  & \(60^{\circ}\) & 322.314 & 374.898 & 289.913 & 201.934 \\  & \(75^{\circ}\) & 383.113 & 459.502 & 353.857 & 247.719 \\  & \(90^{\circ}\) & 445.865 & 541.271 & 427.142 & 311.205 \\  & \(105^{\circ}\) & 543.583 & 623.247 & 497.156 & 356.182 \\  & \(120^{\circ}\) & 608.738 & 717.924 & 563.291 & 407.393 \\ \hline \multirow{8}{*}{CPU Usage (\%)} & \(15^{\circ}\) & 76.979 & 9.433 & 69.557 & 64.061 \\  & \(30^{\circ}\) & 79.595 & 12.166 & 67.123 & 65.274 \\  & \(45^{\circ}\) & 82.988 & 16.437 & 70.858 & 67.763 \\  & \(60^{\circ}\) & 79.431 & 21.714 & 79.166 & 67.589 \\  & \(75^{\circ}\) & 90.211 & 26.924 & 81.871 & 71.298 \\  & \(90^{\circ}\) & 94.439 & 25.022 & 72.539 & 79.271 \\  & \(105^{\circ}\) & 87.991 & 34.421 & 83.143 & 82.918 \\  & \(120^{\circ}\) & 99.996 & 31.688 & 85.503 & 81.985 \\ \hline \multirow{8}{*}{Memory Usage (\%)} & \(15^{\circ}\) & 13.616 & 0.357 & 12.051 & 7.574 \\  & \(30^{\circ}\) & 17.889 & 6.623 & 15.977 & 9.417 \\ \cline{1-1}  & \(45^{\circ}\) & 22.252 & 5.628 & 19.077 & 11.785 \\ \cline{1-1}  & \(60^{\circ}\) & 27.025 & 12.498 & 17.448 & 13.237 \\ \cline{1-1}  & \(75^{\circ}\) & 33.719 & 10.491 & 20.011 & 17.593 \\ \cline{1-1}  & \(90^{\circ}\) & 37.199 & 15.371 & 13.174 & 19.088 \\ \cline{1-1}  & \(105^{\circ}\) & 44.998 & 19.999 & 21.456 & 21.618 \\ \cline{1-1}  & \(120^{\circ}\) & 49.523 & 20.215 & 26.034 & 19.893 \\ \hline \hline \end{tabular}
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