Optimized 2D ball trees for shape layout applications

Abstract

The interactive creation of 2D layouts involving irregular shapes such as text or images is typically carried out using a pointing device to select elements and drag them to new positions on a page. We propose augmenting layout interaction with two operations: overlap avoidance and grouping by distance. Since these are computationally expensive and may hinder the fluidity of the interaction, we examine several techniques that aim at implementing these features in an efficient manner. These techniques involve the approximation of 2D shapes by collections of balls (circles) which are then organized in ball trees, a bounding volume hierarchy. In particular, we discuss a new algorithm for approximating shapes with a reduced set of balls, as well as enhanced ball tree construction algorithms. These are used to implement algorithms to group shapes hierarchically by distance and to allow dragging with collision avoidance, in the context of a proof-of-concept web application for laying out shapes extracted from segmented images.