Circle packing is widely used in visualization due to its aesthetic appeal and simplicity, particularly in tasks where the spatial arrangement and relationships between data are of interest, such as understanding proximity relationships (e.g., images with categories) or analyzing quantitative data (e.g., housing prices). Many applications require preserving neighborhood relationships while encoding a quantitative attribute using radii for data analysis. To meet these two requirements simultaneously, we present a neighborhood-preserving non-uniform circle packing method, NCP. This method preserves neighborhood relationships between the data represented by non-uniform circles to comprehensively analyze similar data and an attribute of interest. We formulate neighborhood-preserving non-uniform circle packing as a planar graph embedding problem based on the circle packing theorem. This formulation leads to a non-convex optimization problem, which can be solved by the continuation method. We conduct a quantitative evaluation and present two use cases to demonstrate that our NCP method can effectively generate non-uniform circle packing results.

翻译：圆填充因其美学吸引力和简洁性在可视化中广泛应用，特别是在关注数据空间排列与关系的任务中，例如理解邻近关系（如带类别的图像）或分析定量数据（如房价）。许多应用需要在保持邻域关系的同时，通过半径编码定量属性以进行数据分析。为同时满足这两项要求，我们提出了一种邻域保持非均匀圆填充方法NCP。该方法通过非均匀圆表示的数据间保持邻域关系，以综合分析相似数据及关注属性。我们将邻域保持非均匀圆填充建模为基于圆填充定理的平面图嵌入问题。该建模导出了一个非凸优化问题，可通过延拓法求解。我们进行了定量评估并展示两个应用案例，证明我们的NCP方法能有效生成非均匀圆填充结果。