As a core data carrier for 3D visual applications, point clouds demand efficient compression owing to their massive scale and nonuniformity, which are critical for practical deployment. Traditional Point Cloud Compression (PCC) standards from MPEG rely on handcrafted rules, causing severe distortion at high compression ratios. Deep learning-based explicit methods require the direct modeling of discrete point cloud coordinates and attributes; however, their discrete representations struggle to capture continuous geometric topologies, making them prone to reconstruction artifacts in complex structural regions. The emerging Implicit Neural Representation (INR), which characterizes point cloud geometry via continuous function mapping, presents a novel direction for PCC. Nevertheless, it remains constrained by insufficient sampling of critical geometric regions and poor adaptability of fixed-frequency encoding, hindering further improvements in reconstruction quality and generalization performance. To address these bottlenecks, this study proposes a method termed Implicit Neural Representation with Structured Sampling and Hybrid Position Encoding for Point Cloud Compression (INR-SHPCC), to ensure sufficient coverage of both information-rich regions, such as edges and thin structures, and low-density areas, such as spatial gaps. A Structured Sampling Module (SSM) is designed, which optimizes the sampling distribution by incorporating geometric priors, including local curvature and density. We further propose a Hybrid Position Encoding Module (HPEM) that adaptively models the nonlinear mapping from spatial coordinates to occupancy values by integrating a fixed-frequency encoding branch with a learnable feature embedding branch. This hybrid design significantly enhances the expressiveness of the encoded features. Experimental results demonstrate that the proposed point cloud compression scheme achieved superior reconstruction performance on the public 8iVFB dataset.