We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around skeleton sparsity 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 the discrete elements. To that end, we introduce generalized enveloping primitives, an enhancement over the standard primitives in the medial axis, which ensure efficient coverage of intricate local features of the input shape and substantially reduce the number of discrete elements required. Moreover, we present a computational framework for constructing 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 the sparsity of the discrete elements and superior reconstruction accuracy across a variety of cases. Finally, we exemplify the versatility of our representation in downstream applications such as shape generation, mesh decomposition, shape optimization, mesh alignment, mesh compression, and user-interactive design.

翻译：我们提出了一种新颖的骨架表示方法——中轴骨架图，旨在解决现有骨架表示中普遍存在的骨架稀疏性和重建精度问题。该方法通过增强中轴表示中的连续元素，有效将复杂性从离散元素中转移出来。为此，我们引入了广义包络基元，这是对中轴中标准基元的增强，能够高效覆盖输入形状的复杂局部特征，并显著减少所需离散元素的数量。此外，我们提出了一个计算框架，用于从任意封闭流形网格构建中轴骨架图。我们的优化流程确保生成的中轴骨架图能够以最少的基元全面覆盖输入形状。同时，每个优化后的基元都会经过后处理细化，以保证在几何和网格划分上与源网格精确匹配。我们在包含100个形状的综合基准测试上验证了我们的方法，证明了该方法在不同案例中离散元素的稀疏性和卓越的重建精度。最后，我们展示了该表示在下游应用中的多功能性，例如形状生成、网格分解、形状优化、网格对齐、网格压缩和用户交互式设计。