Language-Augmented Semantic Priors for B-Spline Surface Fitting

The use of B-splines and Non-Uniform Rational B-Splines surfaces constitutes the mathematical foundation of contemporary computer-aided design (CAD) systems. Despite long-term progress, geometric kernels in traditional CAD still rely heavily on predetermined heuristic initialization for surface fitting and parameterization. Meanwhile, the procedural semantics and design intent encoded in modeling histories are largely ignored during geometry generation. This disconnect creates a gap between high-level design intent and solver-executable geometric configuration, often leading to suboptimal and semantically inconsistent fitting results. To bridge this gap, we introduce LASP, a Language-Augmented Semantic Priors framework that leverages large language models (LLMs) to infer structured, solver-usable B-spline priors from procedural modeling histories. Rather than modifying the geometric kernel itself, LASP operates as a semantic reasoning layer above existing solvers. It first translates modeling histories into rich textual descriptions that capture design intent, geometric context, and functional relationships, and then uses a fine-tuned LLM to predict structured B-spline prior parameters. LASP is trained through a two-stage scheme that combines local geometric regularities with long-range contextual dependencies, producing priors that are both interpretable and semantically coherent. This approach furnishes inductive signals that direct the conventional B-spline fitting process toward solutions that more accurately encapsulate the intended design objectives and demonstrate heightened semantic coherence. Compared to traditional machine learning schemes, the experiments demonstrate that language-driven reasoning can serve as a powerful inductive bias for geometric solving, establishing a new paradigm of language-guided geometric optimization in modern CAD systems.