Point cloud completion recovers the complete point clouds from partial ones, providing numerous point cloud information for downstream tasks such as 3-D reconstruction and target detection. However, previous methods usually suffer from unstructured prediction of points in local regions and the discrete nature of the point cloud. To resolve these problems, we propose a point cloud completion network called TPDC. Representing the point cloud as a set of unordered features of points with local geometric information, we devise a Triangular Pyramid Extractor (TPE), using the simplest 3-D structure-a triangular pyramid-to convert the point cloud to a sequence of local geometric information. Our insight of revealing local geometric information in a complex environment is to design a Divide-and-Conquer Splitting Module in a Divide-and-Conquer Splitting Decoder (DCSD) to learn point-splitting patterns that can fit local regions the best. This module employs the Divide-and-Conquer approach to parallelly handle tasks related to fitting ground-truth values to base points and predicting the displacement of split points. This approach aims to make the base points align more closely with the ground-truth values while also forecasting the displacement of split points relative to the base points. Furthermore, we propose a more realistic and challenging benchmark, ShapeNetMask, with more random point cloud input, more complex random item occlusion, and more realistic random environmental perturbations. The results show that our method outperforms both widely used benchmarks as well as the new benchmark.