A Novel Explainable AI–Driven Framework for Parametric Knot Vector Estimation in NURBS Surfaces

Non-uniform rational B-spline (NURBS) surfaces are effective for accurately modeling curved geometries, and research in this area has recently increased. In this study, point cloud data obtained from two challenging test environments (a convex wooden object and the widely used Stanford Bunny dataset from the literature) were used to predict the u and v parameter values corresponding to positions in the knot vectors, to determine the knot points of NURBS surfaces. The u and v parameters were predicted with accuracies of 92.60% and 93.20% for the wooden object, and 85.50% and 84.40% for the Stanford Bunny. The models’ decision-making processes were analyzed using explainable artificial intelligence (XAI) methods, including SHapley Additive exPlanations (SHAP) and Local Interpretable Model-Agnostic Explanations (LIME). Predicted knot points were compared with the calculated knot points, which are considered as actual, yielding root mean square errors (RMSE) of 0.09 mm for the wooden object and 0.02 mm for the Stanford Bunny. This study fills a gap in the literature by predicting knot points and providing XAI-based analyses, demonstrating that the approach effectively preserves the characteristic features of NURBS surfaces across different geometries.