LASP：利用大语言模型语义先验辅助 CAD 样条曲面拟合

My Thoughts on LASP and Language-Guided Geometric Optimization

So, here's the deal: B-splines and NURBS are the bedrock of modern CAD systems. We've come a long way, sure, but the geometric kernels in traditional CAD still lean way too heavily on pre-determined, heuristic initializations for surface fitting and parameterization. It's like, the process semantics and the design intent encoded in the modeling histories get completely lost in the geometry generation phase. That disconnect? It creates this massive gap between what the designer wants and what the solver can actually do, leading to fitting results that are, frankly, suboptimal and don't make sense semantically. To fix this, I'm introducing LASP, a Language-Augmented Semantic Priors framework. It leverages large language models to infer these structured, solver-usable B-spline priors directly from the procedural modeling histories. It doesn't mess with the geometric kernel itself; instead, LASP works as a semantic reasoning layer sitting on top of the existing solvers. First, LASP translates those modeling histories into rich textual descriptions that capture the design intent, the geometric context, and all the functional relationships. Then, it uses a fine-tuned LLM to predict structured B-spline prior parameters. This framework is trained using a two-stage scheme that combines local geometric regularities with long-range contextual dependencies, generating priors that are both interpretable and make sense semantically. This approach furnishes inductive signals to the conventional B-spline fitting process, guiding it towards solutions that more accurately encapsulate the intended design objectives and demonstrate increased semantic coherence. Compared to standard machine learning schemes, the experiments demonstrate that language-driven reasoning can act as a powerful inductive bias for geometric solving, establishing a new paradigm of language-guided geometric optimization in modern CAD systems.

B样条和非均匀有理B样条（NURBS）曲面的应用构成了现代计算机辅助设计（CAD）系统的数学基础。尽管历经长足发展，传统CAD中的几何内核在曲面拟合与参数化方面仍严重依赖预设的启发式初始化。与此同时，建模历史中所蕴含的过程语义与设计意图在几何生成过程中在很大程度上被忽略。这种脱节在高层设计意图与求解器可执行的几何配置之间造成了鸿沟，往往导致次优且语义不一致的拟合结果。为弥合这一鸿沟，我们提出了LASP——一种语言增强语义先验（Language-Augmented Semantic Priors）框架，该框架利用大语言模型（LLM）从过程化建模历史中推断出结构化且求解器可用的B样条先验。LASP并未直接修改几何内核本身，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捕获了设计意图、几何上下文和功能关系的丰富文本描述，然后使用微调的大语言模型预测结构化的B样条先验参数。LASP通过结合局部几何规律与长程上下文依赖的两阶段方案进行训练，从而生成兼具可解释性与语义连贯性的先验。该方法提供了归纳信号，引导传统的B样条拟合过程寻得能够更精确涵盖预期设计目标且展现出更高语义连贯性的解。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系统中确立了语言引导几何优化的新范式。