This study combines geometric features based on Point Pair Features (PPFs) and spatial features under polar coordinates to innovatively design a series of new local feature descriptors. Through an exhaustive examination and comparison across four benchmark datasets (B3R, U3OR, U3M, and QuLD) in relation to these descriptors, along with the assessment against three contemporary descriptors (SHOT, LFSH, and SDASS), the superior efficacy of the novel descriptors becomes evident. Experimental findings showcase that, in terms of overall efficacy, f r (α 1 α 2 α 3 ) stands out as the most remarkable performer, showcasing exceptional compactness and efficiency. Upon rectifying LRF/A errors, descriptors founded on 'rea' exhibit optimal performance, underscoring their exceptional discriminative prowess. In contrast to established descriptors like SHOT, LFSH, and SDASS, the recently introduced descriptors, such as f r (α 1 α 2 α 3 ), f re (α 1 α 3 ), and f r (α 1 α 3 ), manifest significant advancements in terms of compactness and efficiency. The significance of this research lies in furnishing a set of local feature descriptors that excel in three-dimensional computer vision, and it elucidates their potential applications in 3D pairwise registration through empirical studies.