用逻辑约束生成可构建迷宫的路径，支持平面与立体结构。
From Patterns to Maze Structures: SMT-Based Path Synthesis and 2D/3D Construction
- 将迷宫路径生成建模为SMT约束问题，确保连通性与无交叉
- 单次调用即可求解固定范围内的路径，支持自避或分层穿插
- 适用于艺术设计、教育演示中的2D/3D迷宫构造
我们提出一种从文本或图形等输入模式生成迷宫结构的流程。核心路径合成问题通过满足模理论（SMT）编码为邻接性、连通性及模式约束覆盖的全局约束，使每个有界实例可在一次调用中求解。生成的路径为平面自避路线或具有指定上下穿插的分层遍历，作为平面迷宫和编织式三维迷宫的骨架。本报告在已发表的Bridges 2026论文基础上，增加了更具代表性的SMT-LIB示例，并更完整地说明了合成路径如何转化为二维与三维实际构造。
原文摘要 · Abstract (English)
We present a pipeline for constructing maze structures from input patterns such as text or shapes. The central path-synthesis problem is encoded in Satisfiability Modulo Theories as global constraints on adjacency, continuity, and pattern-constrained coverage, allowing each fixed-bound instance to be solved in one call. The resulting path is either a planar, self-avoiding route or a layered traversal with prescribed over--under crossings, and it serves as a scaffold for constructing planar mazes and three-dimensional realizations of woven mazes. This report extends the published Bridges 2026 conference paper with more representative SMT-LIB examples and a fuller account of how synthesized paths become concrete maze constructions in planar and three-dimensional form.
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