Surface representations play a major role in a variety of applications throughout a diverse collection of fields, such as biology, chemistry, physics, or architecture. From a simulation point of view, it is important to simulate the surface as good as possible, including the usage of a wide range of different approximating elements. However, when it comes to manufacturing, it is desirable to have as few different building blocks as possible, as these can then be produced cost-efficiently.

Our paper adds a procedure to be used in the simulation of natural phenomena as well as within the designers' creative toolbox. It represents a surface via a collection of equally sized spheres. In the first part of the paper, we give a mathematically precise definition of the underlying problem: How to cover as much as possible of a surface by single-sized spheres. This leads to questions regarding the extremal intersection area of spheres with reasonably well-behaved surfaces, for which we present upper and lower bounds. From these, we deduce how many spheres of a certain, fixed radius can be used at least and at most when interpolating a surface.

Following these theoretical results, we compare a depth-first, a breadth-first, and a heuristic algorithm for the generation of surface coverings by single-sized spheres. As opposed to the mathematical description, we show that our algorithms also work for surfaces with boundary elements or sharp features such as edges or corners. We prove the applicability of our algorithm by a multitude of experiments and compare our procedure to ellipsoidal and multi-sized sphere methods.

在各种领域（例如生物学，化学，物理学或建筑学）中，表面表示在各种应用程序中都起着重要作用。从模拟的角度来看，尽可能地好模拟表面非常重要，包括使用各种不同的近似元素。但是，当涉及制造时，希望具有尽可能少的不同构件，因为这样可以成本有效地生产这些构件。

我们的论文增加了一个程序，可用于模拟自然现象以及设计师的创意工具箱。它通过大小相等的球体集合表示一个表面。在本文的第一部分中，我们对潜在问题进行了数学上的精确定义：如何用单个大小的球体尽可能覆盖一个表面。这就引起了关于具有合理行为良好的表面的球体的极交相交区域的问题，为此我们给出了上下边界。从这些推论中，我们推断出在插入表面时至少可以使用多少个固定半径的球。

根据这些理论结果，我们比较了深度优先，宽度优先和启发式算法生成单个尺寸球体的表面覆盖的情况。与数学描述相反，我们证明了我们的算法也适用于具有边界元素或尖锐特征（如边缘或拐角）的表面。我们通过大量实验证明了该算法的适用性，并将我们的程序与椭圆形和多尺寸球面方法进行了比较。