Recently, three-dimensional (3D) point-cloud analysis has been extensively utilized in the domain of machine vision, encompassing tasks include shape classification and segmentation. However the inherent disorder in point clouds poses a challenge in capturing relationships among points, particularly when dealing with mutilated and occluded data. To this end, We propose the Point Geometry Transformation (PointGT) method for 3D point-cloud classification and part segmentation, by exploring the underlying geometric structure in the local and global of points. Specifically, the efficacy of PointGT arises from the integration of a local abstraction (LA) module and an optimization strategy. The LA module is tailored to address the localized features inherent to point clouds. This module encapsulates the multidimensional attributes of local edge and inside points. The bi-directional cross-attention mechanism amalgamates these two constituents into the native channel with the primary objective of optimizing the exploitation of edge and inside delineations, thereby judiciously mitigating noise artifacts. Ultimately, the channel residual connections disseminate the postdownsampling point attributes, thereby inheriting the edge and inside delineations gleaned via post bi-directional attention. The effectiveness of the proposed method was verified through the validation of point-cloud classification and segmentation datasets. The empirical findings confirmed the efficacy of PointGT; accuracies of 93.2% and 87.8% were achieved for the ModelNet40 and ScanObjectNN datasets, respectively.