<p>Discontinuities in rock masses significantly influence their mechanical properties and are critical for engineering applications, making it essential to thoroughly understand their geometric parameters. 3D point clouds serve as fundamental data for efficiently and accurately analyzing discontinuity orientations. In this context, a novel semi-automated method that employs a Nutcracker Optimization Algorithm-improved Probabilistic Neural Network (NOA-PNN) is proposed. The NOA enables the PNN to quickly identify the optimal smoothing factor, balancing both accuracy and efficiency. This method utilizes not only normal vectors, but also point coordinates, curvature, and density, incorporating a broader set of features to accurately identify points on discontinuities. The NOA-PNN model, trained on manually selected samples, swiftly identifies discontinuity sets while efficiently filtering out noise. Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is then used to extract single discontinuities within each set. Each discontinuity is fitted to a plane using a Principal Component Analysis (PCA)-based least squares method, facilitating the measurement of their spatial geometric parameters. Validation through two cases demonstrated that the proposed method achieved an average deviation of less than 5° in both dip direction and dip angle, exhibiting potential advantages in terms of accuracy and efficiency when compared to other important studies or software. This method significantly improves computational efficiency and achieves satisfactory results with only a small number of randomly selected samples. Its low requirements for sample quality and operator expertise make it highly operable and easily adaptable for practical engineering applications.</p>