# CircleVis: A Visualization Tool for Circular Labeling Arrangements and Overlap Removal
## 1 Introduction  
In mathematics, geometric forms are created by connecting points to generate a desired pattern [1] such as circles, rectangles, etc. Several studies in cognitive psychology have shown that humans prefer curved items and tend to be more attracted by curvilinear forms, particularly circular ones [2]. Circles are extensively used to depict information in various domains ranging from statistics, data mining, machine learning, etc. Labeled circles are frequently used in information visualization (InfoVis) for visual encoding of datasets [3], as well as with a variety of techniques such as sunburst, pie, and chord, to name a few. Furthermore, they can be used on problem-driven approaches [4] to represent statistics, tree structure, and data levels, among others. Using labeled circles to design a visualization system that assists in problem-solving has become popular. This enables people to analyze, explore, compare, and summarize data when they do not know a priori what questions to ask. For this purpose, circles can be encoded using classical representation as weighted arcs with associated labels. Another encoding approach consists of deploying hierarchical levels with other circles from the middle to outside.  
In literature, labeling arrangement techniques [5, 6] are divided into two main classes: internal and external. For external labeling, labels are placed outside the circle because of the free space, allowing designers to display more data dimension. Internal labeling is often incorporated with zoom and fish-eye interactions to visualize more details. Users orresearchers may choose the desired technique to display labels depending on the required interpretation level and the available free space. This work is more concerned with the external labeling [7] of radial contouring [8] than with circle division by arcs or other forms of visual encoding. Furthermore, label arrangements can have an overlapping problem, especially for large amounts of data. Many approaches have been proposed to remove overlaps for 1D [9] and 2D [10; 11; 12]) graph layout between nodes or labels. However, no studies have focused on circular layout and how to relate labels to sub-divisions (sub-features) of circular layout.  
Hence, in this work we propose CircleVis, a visualization tool for encoding circles using various label arrangement techniques and label overlap removal. The following are the main contributions of this work. First, the state of the art of current labeled-circle studies on InfoVis is presented, with a focus on problem-driven approaches. Following that, a classification of the various approaches to label placement in circle layout is proposed. This study also introduces a new linear improved arrangement method for using circles with single/multiple levels while optimizing the available space. In addition, for each proposed arrangement to be implemented in the tool, a mathematical formulation is derived. A new method for detecting and removing possible label overlapping is proposed for 1D graph overlapped labels. Furthermore, CircleVis incorporates various interactions to reduce overlapping in 2D arrangement methods. Finally, a use case using COVID-19 datasets is analyzed to test, evaluate, and improve the proposed tool's functionalities.  
The rest of the paper is organized as follows. First, we present a state of the art of labeled-circle approaches and overlap removal (Section 2). A classification of the various methods for label arrangements in circular layouts is suggested in Section 3.1. In addition, methods to remove overlaps are proposed in Section 3.2). Our proposed approaches are implemented in CircleVis (Section 3.3), a new visualization tool to visualize a labeled circular layout. Finally, we assess our proposed approaches and tool in Section 4.