The distribution of the solutions to the Perspective 3-Point Problem (P3P) has been studied for a few decades, and some understanding of this issue has emerged. However, the present article is the first to comprehensively describe, for a given location p in space, the number of other points that solve the same P3P setup that p solves, and where to find these related points. A dynamic approach is employed to solve this problem. The related points are restricted to certain regions in space, defined by certain “basic” toroids and by a surface called the “companion surface to the danger cylinder.” The nature of this surface is explored in detail, along with its intersections with the basic toroids, and the pairwise intersection of these toroids.

透视 3 点问题 (P3P) 的解的分布已经研究了几十年，并且已经出现了对这个问题的一些理解。然而，本文首次全面描述了对于空间中的给定位置p，解决与p解决的相同 P3P 设置的其他点的数量，以及在哪里可以找到这些相关点。使用动态方法来解决这个问题。相关点仅限于空间中的某些区域，由某些“基本”环面和称为“危险圆柱体的伴随表面”的表面定义。详细探讨了这个表面的性质，以及它与基本环面的交点，以及这些环面的成对交点。