We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around compactness and reconstruction accuracy in existing skeletal representations. Our approach augments the continuous elements in the medial axis representation to effectively shift the complexity away from discrete elements. To that end, we introduce generalized enveloping primitives, an enhancement of the standard primitives in medial axis, which ensures efficient coverage of intricate local features of the input shape and substantially reduces the number of discrete elements required. Moreover, we present a computational framework that constructs a medial skeletal diagram from an arbitrary closed manifold mesh. Our optimization pipeline ensures that the resulting medial skeletal diagram comprehensively covers the input shape with the fewest primitives. Additionally, each optimized primitive undergoes a post-refinement process to guarantee an accurate match with the source mesh in both geometry and tessellation. We validate our approach on a comprehensive benchmark of 100 shapes, demonstrating its compactness of the discrete elements and superior reconstruction accuracy across a variety of cases. Furthermore, we exemplify the versatility of our representation in downstream applications such as shape optimization, shape generation, mesh decomposition, mesh alignment, mesh compression, and user-interactive design.

翻译：我们提出中轴骨架图，一种新型骨架表示方法，旨在解决现有骨架表示中紧凑性与重建准确性的核心问题。该方法通过增强中轴表示中的连续元素，有效将复杂度从离散元素中转移。为此，我们引入广义包络基元——对标准中轴基元的增强改进，确保高效覆盖输入形状的复杂局部特征，并大幅减少所需离散元素的数量。此外，我们提出一个从任意封闭流形网格构建中轴骨架图的计算框架。优化管线确保生成的中轴骨架图以最少基元全面覆盖输入形状，且每个优化后的基元均经过后精修处理，确保在几何形状与细分网格层面均与原始网格精确匹配。我们在包含100个形状的综合基准上验证了该方法，证明了其在多种场景下离散元素的紧凑性与优越的重建准确性。最后，我们通过形状优化、形状生成、网格分解、网格对齐、网格压缩及用户交互设计等下游应用，展示了该表示方法的通用性。