Structural Tree Extraction from 3D Surfaces

Abstract: This paper introduces a method to extract a hierarchical tree representation from 3D unorganized polygonal data. The proposed approach first extracts a graph representation of the surface, which serves as the foundation for structural analysis. A Steiner tree is then generated to establish an optimized connection between key terminal points, defined according to application-specific criteria. The structure can be further refined by leveraging line-of-sight constraints, reducing redundancy while preserving essential connectivity. Unlike traditional skeletonization techniques, which often assume volumetric interpretations, this method operates directly on the surface, ensuring that the resulting representation remains relevant for navigation-aware geometric analysis. The method is validated through two use cases: extracting structural representations from tile-based elements for procedural content generation, and identifying key points and structural metrics for automated level analysis. Results demonstrate its ability to produce simplified, coherent representations, supporting applications in procedural generation, spatial reasoning, and map analysis.