DC-Focus: A Hyperbolic Focus+Context Formalism for Scalable Feature-Model Visualization

Feature models in industrial-scale Software Product Lines (SPL) routinely exceed a thousand features, yet the dominant visual metaphor for exploring them remains the Euclidean tree, whose readability degrades sharply as the number of nodes grows. Existing hyperbolic tree browsers address the general rendering problem but do not natively capture feature-model semantics — typed nodes (root/branch/child), a dependency relation separate from the tree structure, and cross-tree constraints — which is the specific gap this paper addresses. This paper presents a formal focus+context visualization model that embeds a feature model as a labelled graph in the Poincare disk and defines a Mobius-transformation-based re-centring operator to bring any selected feature into visual focus while preserving the surrounding structural context. We define the model as a seven-tuple over feature nodes, directed relationships, a type function, a root, a dependency relation, visualization attributes, and cross-tree constraints, and we specify five supporting algorithms for node insertion, focus navigation, node update, node deletion, and ancestry tracing. We show that the focus transformation is an isometry of the disk and therefore preserves the topological structure of the underlying feature model under re-centring. The model underlies a working browser-based prototype; this paper's contribution is the formal model, the isometry proof, and the algorithmic specification, and we do not report quantitative scalability results here. A worked numerical example illustrates the transformation on a small feature tree, and we discuss the architectural realization of the model as a four-layer, browser-based system.