A large number of geometric representations have been proposed to address the needs of specific engineering applications. This, in turn, exacerbates the inherent challenges associated with system interoperability for downstream engineering applications.

In this paper, we define the Maximal Disjoint Ball Decomposition (MDBD) as the location of the largest d-dimensional closed balls recursively placed in the interior of a d-dimensional domain and show that the proposed decomposition can be used to provide an underlying common analysis framework for geometric models using different representation schemes. Importantly, our decomposition only relies on the ability of an existing geometric representation to compute distances, which must be supported by any valid geometric representation scheme, and does not require an explicit representation conversion. Moreover, MDBD is unique for a given domain up to rigid body transformation, reflection, as well as uniform scaling, and its formulation suggests appealing stability and robustness properties against small boundary modifications.

Furthermore, we show that MDBD can be used as a universal shape descriptor to perform shape similarity of models coming from various geometric representation schemes. A salient attribute of this decomposition is that it provides adequate support for key downstream applications for models coming from disparate geometric representations. For example, MDBD can be naturally used to carry out meshless solutions to boundary value problems; efficient collision detection; and 3D mesh generation of models that use any valid geometric representation scheme. Finally, our hierarchical formulation of the proposed Maximal Disjoint Ball Decomposition allows for a choice of model complexity at run-time to match the available computational resources.

已经提出了许多几何表示来解决特定工程应用的需求。反过来，这加剧了与下游工程应用程序的系统互操作性相关的固有挑战。

在本文中，我们将最大不相交球分解（MDBD）定义为最大d维封闭球的递归放置在d维域内部的位置，并表明所提出的分解可用于提供潜在的共同点使用不同表示方案的几何模型的分析框架。重要的是，我们的分解仅依赖于现有的几何表示来计算距离的能力，这必须由任何有效的几何表示方案来支持，并且不需要显式的表示转换。此外，MDBD对于给定的范围（直到刚体变形，反射以及均匀缩放）都是唯一的，其表示形式对较小的边界修改具有吸引人的稳定性和鲁棒性。

此外，我们表明MDBD可用作通用形状描述符，以执行来自各种几何表示方案的模型的形状相似性。这种分解的一个显着属性是，它为来自不同几何表示的模型的关键下游应用程序提供了足够的支持。例如，MDBD可以自然地用于执行无网格解决方案来解决边值问题。高效的碰撞检测；和使用任何有效几何表示方案的3D网格模型生成。最后，我们提出的最大不相交球分解的层次结构表示法允许在运行时选择模型复杂度以匹配可用的计算资源。