语言增强的语义先验用于B样条曲面拟合

中文摘要 AI 辅助

B样条和非均匀有理B样条（NURBS）曲面的使用构成了当代计算机辅助设计（CAD）系统的数学基础。尽管长期取得了进展，传统CAD中的几何内核在曲面拟合和参数化方面仍严重依赖预定的启发式初始化。与此同时，建模历史中编码的程序性语义和设计意图在几何生成过程中在很大程度上被忽略。这种脱节在高层次设计意图与求解器可执行的几何配置之间造成了鸿沟，常常导致次优且语义不一致的拟合结果。为弥合这一鸿沟，我们引入了LASP，一个语言增强的语义先验框架，利用大语言模型（LLMs）从程序性建模历史中推断出结构化、求解器可用的B样条先验。LASP并非修改几何内核本身，而是作为现有求解器之上的语义推理层运行。它首先将建模历史转化为丰富的文本描述，以捕捉设计意图、几何上下文和功能关系，然后使用微调后的LLM预测结构化的B样条先验参数。LASP通过两阶段方案进行训练，该方案将局部几何规律与长距离上下文依赖相结合，产生既可解释又语义连贯的先验。这种方法提供了归纳信号，引导传统B样条拟合过程朝着更准确体现预期设计目标并展现更高语义连贯性的解决方案发展。与传统机器学习方案相比，实验表明语言驱动的推理可以作为几何求解的强大归纳偏置，在现代CAD系统中建立了语言引导的几何优化的新范式。

英文摘要

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.

发表机构

• College of Computer Science and Artificial Intelligence, Fudan University（复旦大学计算机科学与人工智能学院）

机构由 AI 辅助整理，请以论文原文为准。