Recent hierarchical global illumination algorithms permit the generation of images with a high degree of realism. Nonetheless, appropriate refinement of light transfers, high quality meshing and accurate visibility calculation can be challenging tasks. This is particularly true for scenes containing multiple light sources and scenes lit mainly by indirect light. We present solutions to these problems by extending a global visibility data structure, the Visibility Skeleton. This extension allows us to calculate exact point-to-polygon form-factors at vertices created by subdivision. The structure also provides visibility information for all light interactions, allowing intelligent refinement strategies. High-quality meshing is effected based on a perceptually-based ranking strategy which results in appropriate insertions of discontinuity curves into the meshes representing illumination. We introduce a hierarchy of triangulations which allows the generation of a hierarchical radiosity solution using accurate visibility and meshing. Results of our implementation show that our new algorithm produces high quality view-independent lighting solutions for direct illumination, for scenes with multiple lights and also scenes lit mainly by indirect illumination.