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.

中文翻译：

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内侧骨骼图：用于紧凑 3D 形状表示的广义内侧轴方法


我们提出了内侧骨骼图，这是一种新颖的骨骼表示，它解决了现有骨骼表示中围绕骨骼稀疏性和重建准确性的普遍问题。我们的方法增强了内侧轴表示中的连续元素，以有效地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，这是对内侧轴上标准基元的增强，可确保有效覆盖输入形状的复杂局部特征，并大大减少所需的离散元件数量。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内侧骨骼图。我们的优化管道可确保生成的内侧骨骼图以最少的基元全面覆盖输入形状。此外，每个优化的基本体都经过后细化过程，以保证在几何体和曲面细分中与源网格精确匹配。我们在 100 种形状的综合基准上验证了我们的方法，证明了离散元件的稀疏性和在各种情况下的卓越重建精度。最后，我们举例说明了我们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设计。