Motivated by the fact that the medial axis transform is able to encode the shape completely, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select new medial balls, in a top-down style, to enlarge the region spanned by the existing medial balls. The key spirit of the selection strategy is to encourage large medial balls while imposing given geometric constraints. We further propose a speedup technique based on a provable observation that the intersection of medial balls implies the adjacency of power cells (in the sense of the power crust).

We further elaborate the selection rules in combination with two closely related applications. One application is to develop an easy-to-use ball-stick modeling system that helps non-professional users to quickly build a shape with only balls and wires, but any penetration between two medial balls must be suppressed. The other application is to generate porous structures with convex, compact (with a high isoperimetric quotient) and shape-aware pores where two adjacent spherical pores may have penetration as long as the mechanical rigidity can be well preserved.

中文翻译：

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基于贪心极点选择的自顶向下形状抽象

由于中轴变换能够完全编码形状这一事实，我们建议使用尽可能少的中间球来近似边界表面的原始封闭体积。我们以自上而下的方式逐步选择新的内侧球，以扩大现有内侧球所跨越的区域。选择策略的主要精神是在施加给定的几何约束的同时鼓励大的内侧球。我们进一步提出了一种基于可证明观察的加速技术，即内侧球的交叉意味着动力电池的邻接（在动力外壳的意义上）。

我们结合两个密切相关的应用程序进一步阐述了选择规则。一个应用是开发一个易于使用的球棒建模系统，帮助非专业用户快速构建一个只有球和线的形状，但必须抑制两个中间球之间的任何穿透。另一个应用是生成具有凸面、致密（具有高等周商数）和形状感知孔的多孔结构，其中两个相邻的球形孔可能具有渗透性，只要能很好地保持机械刚度。