We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting segment between the two surface points serves as the guidance for the sliding direction, and the distance between them decreases gradually. The minimum distance is established when the connecting segment becomes perpendicular to the ellipsoid surfaces, at which point the net effect of the segment tension disappears and the surface points no longer move. Demonstration examples are carefully designed, and excellent numerical performance is observed, including accuracy, consistency, stability, and robustness. Furthermore, compared to other existing techniques, this surface-sliding approach has several attractive features, such as clear geometric representation, concise formulation, a simple algorithm, and the potential to be extended straightforwardly to other situations. This method is expected to be useful for future studies in computer graphics, engineering design, material modeling, and scientific simulations.

翻译：我们提出了一种新颖的迭代过程来建立两个椭球体之间的最小间隔。该方法在每个表面上保持一个点，并在θ-φ参数空间中更新它们的位置。两个表面点之间连接段上的张应力作为滑动方向的引导，它们之间的距离逐渐减小。当连接段与椭球表面垂直时，达到最小距离，此时段张力的净效应消失，表面点不再移动。精心设计了演示示例，并观察到了优异的数值性能，包括准确性、一致性、稳定性和鲁棒性。此外，与现有的其他技术相比，这种表面滑动方法具有几个吸引人的特点，例如清晰的几何表示、简洁的公式、简单的算法，以及能够直接扩展到其他场景的潜力。预期该方法将对计算机图形学、工程设计、材料建模和科学模拟等领域的未来研究有所裨益。