A new, geometric and easy to understand approach to finite population sampling is presented. In this approach, first-order inclusion probabilities (FIPs) are represented by bars in a two-dimensional coordinate system, and their different arrangements lead to different designs. Only based on the geometric approach, designs can be fully implemented, without the need for mathematical algorithms. An special arrangement of the bars, is equivalent to Madow 1949 systematic method, which easily, with rearranging the bars, while keeping the FIPs unchanged, results in different second-order inclusion probabilities (SIPs) equivalent to other famous finite population sampling designs, such as Poisson sampling, maximum entropy sampling, etc. Geometric visualization of sampling designs leads to increased creativity of researchers to provide new efficient designs. This approach opens a new gate to finite population sampling that can deal with problems such as optimal designs, implementation of maximum entropy sampling, etc.

翻译：本文提出了一种新颖且易于理解的几何方法，用于有限总体抽样。在该方法中，一阶包含概率被表示为二维坐标系中的条形，其不同排列方式对应不同的抽样设计。仅基于几何方法即可完全实现这些设计，无需依赖数学算法。条形的特殊排列等价于Madow 1949年的系统抽样方法，通过重新排列条形（同时保持FIP不变），可轻松获得与泊松抽样、最大熵抽样等著名有限总体抽样设计等价的不同二阶包含概率。抽样设计的几何可视化能提升研究者设计新型高效抽样的创造力。该方法为有限总体抽样开辟了新途径，可处理最优设计、最大熵抽样实现等问题。