Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree
where the weight of each node is the sum of the weights of its children. A treemap for
is a hierarchical partition of a rectangle into simply connected regions, usually rectangles. Each region represents a node of
and its area is proportional to the weight of the corresponding node. An important quality criterion for treemaps is the aspect ratio of its regions. One cannot bound the aspect ratio if the regions are restricted to be rectangles. In contrast,
, that use convex polygons, can have bounded aspect ratio. We are the first to obtain convex partitions with optimal aspect ratio
still depends on the input tree. Hence we introduce a new type of treemaps, namely
, where regions representing leaves are rectangles, L-, and S-shapes, and regions representing internal nodes are orthoconvex polygons. We prove that any input tree, irrespective of the weights of the nodes and the depth of the tree, admits an orthoconvex treemap of constant aspect ratio.