PaperlayerView exact revision on arXiv

Source-linked AI summary

Language-Augmented Semantic Priors for B-Spline Surface Fitting

Yunzhong Lou, Yusheng Luo, Jiahao Li, Yu Song, Xiangdong Zhou

arXiv:2609.11708v1cs.CVcs.AI

TL;DR

Traditional CAD fitting relies on heuristic initialization while largely ignoring procedural design intent, leaving a gap between symbolic histories and solver configurations. LASP adds a language-based semantic layer that converts histories into rich descriptions and structured B-spline priors for existing solvers. It reports stronger parameter prediction and fitting performance, while its theoretical semantic objective remains conceptual rather than directly optimized in the geometric kernel.

  • Problem

    Traditional CAD solvers use predetermined heuristic initialization and largely ignore procedural semantics, limiting access to design intent during B-spline fitting.

  • Method

    LASP uses rich-text semantic reasoning and a fine-tuned LLM to predict structured B-spline priors that configure existing geometric solvers, trained in two stages.

  • Results

    LASP outperforms baselines in parameter prediction and improves engine-level RMS, Hausdorff, and median fitting errors.

  • Takeaways & Limitations

    Language-derived semantic priors can provide transferable inductive biases that guide conventional geometric solving toward more semantically coherent surface reconstruction.

  • Takeaways & Limitations

    The semantic energy expression is conceptual, and the current framework does not explicitly optimize that semantic term inside the geometric kernel.

Abstract

from arXiv · show

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.

1. Introduction

LASP addresses the disconnect between procedural design intent and heuristic B-spline solver initialization by using language-derived semantic priors above existing geometric kernels. Its two-stage training captures both local geometric regularities and long-range dependencies, while experiments show improved prediction and fitting outcomes.

  • 1. Introduction: Traditional CAD solvers rely on fixed degrees, knot vectors, and control-point layouts, limiting adaptation to procedural design intent.These heuristics constrain the feasible parameter space before deterministic fitting begins.
  • 1. Introduction: LASP bridges symbolic modeling histories and continuous geometric solvers by providing semantic initialization that biases fitting toward valid, coherent configurations.This preserves the existing solver while adding design-context information to its initialization.
  • 1. Introduction: LASP translates modeling histories into rich semantic descriptions and predicts structured B-spline priors covering geometry, topology, continuity, and surface roles.The priors configure existing solvers rather than replacing their numerical optimization procedures.
  • 1. Introduction: Its two-stage scheme first learns operation-specific local geometry and then models long-range dependencies across full modeling histories.The second stage captures continuity propagation, curvature transitions, and semantic role consistency.
  • 1. Introduction: LASP improves parameter prediction and engine-level fitting, outperforming baselines while reducing RMS, Hausdorff, and median fitting errors.The framework achieves these gains without modifying the geometric kernel, using semantic priors to configure downstream fitting.

2. Related Work

Related work spans symbolic reasoning with language models, semantic CAD representations, learned CAD generation, and B-spline solving. LASP differs by producing interpretable semantic priors that directly configure downstream geometric solvers while preserving kernel internals.

  • 2.1. LLMs for Structured and Symbolic Reasoning: LLMs can process structured symbolic sequences, motivating the treatment of procedural modeling histories as inputs for geometric-intent inference.Contextual descriptions expose operation intent and semantics that conventional numerical solvers cannot access directly.
  • 2. Related Work: Classical CAD representations encode geometry and topology but generally lack scalable, high-level semantic interpretability.Manual and rule-based semantic enrichment has limited scalability.
  • 2. Related Work: Existing CAD-generation methods primarily produce programs or modeling sequences, whereas LASP infers interpretable priors for downstream geometric solvers.This distinction places LASP between symbolic procedural representations and numerical surface fitting.
  • 2. Related Work: Conventional B-spline kernels use fixed initialization and deterministic optimization independently of procedural or functional context.Uniform knots and predefined degrees support geometric validity but do not incorporate design intent.
  • 2. Related Work: Prior B-spline improvements remain heuristic and local, while LASP injects LLM-inferred semantic priors without modifying kernel internals.The framework uses language to provide global intent and the kernel to enforce local geometric validity.

3. Method

LASP adds a language-based semantic reasoning layer between procedural modeling histories and conventional B-spline solvers. It predicts structured surface priors through a two-stage process that combines local geometric regularities with long-range contextual dependencies.

  • Semantic Prior Prediction: LASP maps symbolic modeling histories and rich-text semantic descriptions to structured B-spline priors using a fine-tuned instruction-tuned LLM.The mapping outputs operation-level prior sequences in a text-to-structured-text format.
  • Solver Integration: LASP leaves kernel internals unchanged and uses inferred priors as semantic biases for solver-accessible surface-fitting configurations.These priors regularize fitting through choices such as polynomial degrees, control-point grids, rational flags, trimming, and continuity.
  • Symbolic and Linguistic Representations: Procedural histories are represented as ordered parametric operations, while rich-text descriptions add design context, intent, geometry, and function.The rich-text representation serves as the linguistic complement to the symbolic history.
  • Semantic Prior Prediction: Each operation prior encodes geometric parameters and semantic attributes, including degrees, control-point counts, rationality, trimming, continuity, curvature, and surface role.The complete prior sequence represents geometric regularities and semantic relations across the modeling process.
  • Two-Stage Training: Stage I learns operation-level geometric regularities, and Stage II extends them across full histories to model continuity propagation, curvature transitions, and semantic role coherence.Stage I supervises numerical attributes with controlled perturbations, while Stage II captures dependencies created by shared topology and design intent.

4. Experiments

LASP is evaluated for parameter prediction, solver-level fitting, and component contributions using procedural histories and B-spline reconstruction metrics. Across these evaluations, semantic priors improve parameter quality and fitting accuracy without modifying geometric solver internals.

  • 4. Experiments: The evaluation uses ABC procedural histories paired with BRep geometries and focuses mainly on Fillet, Chamfer, and Shell operations.Both training stages use Qwen3-14B fine-tuning and OpenCascade for reconstruction and quantitative evaluation.
  • 4.2. Parameter-Level Evaluation: LASP achieves F1=0.95 for B-spline detection and mean degree accuracy of 0.85, while surpassing GPT-5 and DeepSeek-v3.2 on ContinuityClass and SurfaceRole.The reported higher-level semantic scores are ContinuityClass F1=0.698 and SurfaceRole F1=0.979.
  • 4.2. Parameter-Level Evaluation: With fixed ground-truth control points, LASP predicts parameters yielding the highest geometric fidelity and preserving fine curvature transitions and local continuity.This isolates predicted-prior quality from downstream solver effects.
  • 4.3. Engine-Level Evaluation via Solver Configuration Instantiation.: RMS deviation falls by 71.2% and Hausdorff distance by 85.6% (p<0.001) with semantically guided solver configurations.Table 2 evaluates solver-accessible parameterization settings using RMS, Hausdorff, and median fitting errors.
  • 4.3. Engine-Level Evaluation via Solver Configuration Instantiation.: LASP-derived priors produce smoother, more coherent fitted surfaces than default configurations across extrusion, revolution, and blending examples.Figure 4 compares ground truth, default fitting, and semantic-prior-guided fitting, with color indicating z-axis height.
  • 4.4. Ablation Study: Ablations show that rich-text semantics most affect high-level reasoning, Stage I pretraining primarily improves numerical precision, and augmentation supports robust generalization.Removing rich-text semantics changes SurfaceRole F1 from 0.98 to 0.91 and ContinuityClass F1 from 0.70 to 0.62; removing Stage I changes Pole-MAE from 0.56 to 0.66.

5. Conclusion

LASP introduces contextual semantic reasoning into B-spline construction through an external layer that guides conventional fitting. Its language-driven inductive bias connects symbolic design intent with numerical optimization.

  • LASP uses contextual semantic reasoning as an inductive bias for geometric solving, connecting symbolic intent with numerical optimization.
Loading 2609.11708v1…