Drawing Trees: How Many Circles to Use? - Yuntao Jia; John C. Hart (University of Illinois, 2008)
In this paper, we proposed a new approach for drawing rooted trees on circles. Previous approaches either draw entire tree on a single circle or draw too many circles that every node and its children are on a new circle. As a result, they only work well on limited kinds of trees. In contrary, our approach adaptively choose how many circles to use based on a single user input and it can be generalized well to all kinds of trees. Our approach has three phases. First, we recursively divide the tree into a hierarchy of subtrees according to the user input. The subtrees are then processed from bottom to top of the hierarchy and each of them is drawn around a separated circle. Finally, layout of subtrees are assembled together to form the layout of the entire tree. Comparing to previous methods, our approach obtains both compact and pleasing tree drawings with less bends. Furthermore, our method naturally supports visualization interactions, such as locally zooming in/out, when user navigates the drawings. Several examples are provided to demonstrate the effectiveness of our approach.