Mapping a node-link structure to a rendering space beginning from any node

Abstract

A node-link structure laid out in a space with negative curvature, such as the hyperbolic plane, is mapped to a rendering space, such as the unit disk, beginning from a starting element that has both a parent and a child. Data identifying the starting element are obtained, such as based on user signals. The starting element can be located at a starting position in the unit disk. Then a set of other elements can be mapped, each reachable from the starting element by a path that leads only through elements in the set. Each element's position in the negatively curved space relative to a preceding element on its path and the position of the preceding element in the rendering space can be used to obtain the element's position in the rendering space. The positions in the unit disk can then be used to present a representation of the node-link structure. The set of elements can include only a mapping root and descendants, where the mapping root is on an upward path from the starting element, but precedes the first element that maps to a position in the unit disk outside a precision horizon. A criterion can be applied to determine whether to map each element's descendants. If the rendering space has an active region within the precision horizon, it may not be necessary to map descendants if an element is outside the precision horizon or is outside the active region but has a parent inside the active region.