LLM-based Visual Code Completion for Aerospace Geometric Design

Large Language Models (LLMs) can generate Computer-Aided Design (CAD), yet lack physical comprehension required for reliable engineering design. Instead of attempting to implicitly learn physical laws from data, we propose a Hybrid Agentic-Physical Architecture that embeds validated knowledge-based engineering tools directly into the decision making loop of autonomous AI agents. In this framework, engineering design is formulated as a closed-loop, sequential decision making process guided by explicit physical verification. Based on a load case, dedicated agents iteratively plan, generate, evaluate, and revise engineering designs using knowledge-based tools as a feedback signal. We introduce a benchmark dataset and metrics for assessing functional validity in generative CAD. Our system generates more complex and physically verified designs, with a 4.2 increase in structural complexity and improving compile rate by 3.5% compared to similar agentic methods. The codebase, prompts and dataset will be made publicly available to support reproducibility and future research.

Recent advances in Large Language Models (LLMs) and Vision-Language Models (VLMs) enable the automatic generation of parametric 3D designs from natural-language specifications. This chapter presents an empirical study of foundation models for automatic Computer-Aided Design (CAD) generation of mechanical parts, using a unified evaluation pipeline and a curated benchmark of 97 engineering design problems. We introduce LLMForge, a multi-model text-to-CAD framework integrating JSON-schema validation, analytic feature scoring, mesh synthesis, and multi-round iterative refinement, studied under two critique regimes. IterTracer uses a Phong-shaded ray-trace renderer with analytic visual metrics (silhouette IoU, hole visibility, edge clearance, aspect-ratio conformance) for lightweight geometry-aware feedback across rounds. IterVision replaces the analytic scorer with a VLM semantic critic (Qwen2.5-VL-72B) that evaluates rendered views via chain-of-thought visual reasoning, assessing spatial coherence and design intent. On a benchmark spanning four canonical geometry families (plates with holes and bolt circles, multi-feature boxes, flanged cylinders, and L-brackets), we evaluate seven foundation models: DeepSeek-V3.2, Qwen3-235B-A22B, Llama-3.3-70B, Gemma-3-27B, GLM-4.5, MiniMax-M2.1, and INTELLECT. Under IterTracer, the four highest-ranked models form a tight cluster (overall mean in [0.885, 0.890]) with 98.97% mesh success, showing that compact instruction-tuned models can match substantially larger systems. VLM-based critique in IterVision yields 100% watertight mesh generation on the leading model while surfacing systematic difficulty on rotationally symmetric geometries such as cylinders, where visual and semantic scoring diverge most. We discuss benchmark design, failure modes, CAD-oriented prompting, and implications for industrial workflows and scalable automated mechanical design.

Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive process when developing related code. Currently, some existing GA software packages rely on manually written scripts for code generation and visualization, but their high learning curve hinders widespread adoption. Meanwhile, methods based on Large Language Models (LLMs) often produce logical errors when generating specific GA scripts, such as GAALOPScript, resulting in generally low accuracy. To address these issues, this study proposes GA-VisAgent -- a multi-agent interactive learning application for GA code generation and visualization -- building upon a Geometric algebra large language model (GAGPT). Integrating task planning mechanisms with ReAct reasoning strategies, GA-VisAgent can decompose complex operations into five standardized subtasks, including core operations like geometric products, rotations, and reflections. It supports natural language and mathematical formulas as input to automatically generate executable code, accompanied by interactive visualizations to aid user comprehension. Experimental results show that GA-VisAgent achieved a 90% code generation success rate across 40 typical Conformal GA tasks, representing a 70% improvement over GPT-4o. This application introduces an extensible new paradigm for teaching GA and developing visualization tools for related mathematical concepts. The online service for this project will be available at http://gagis.cn/gacrac.