Abstract: Interactively manipulating the geometry of complex, globally illuminated scenes has to date proven an elusive goal. Previous attempts have failed to provide interactive updates of global illumination and have not been able to offer well-adapted algorithms controlling the frame rate. The need for such interactive updates of global illumination is becoming increasingly important as the field of application of radiosity algorithms widens. To address this need, we present a novel algorithm which provides interactive update rates of global illumination for complex scenes with moving objects. In the context of clustering for hierarchical radiosity, we introduce the idea of an implicit line-space hierarchy. This hierarchy is realized by augmenting the links between hierarchical elements (clusters or surfaces) with shafts, representing the set of lines passing through the two linked elements. We show how line-space traversal allows rapid identification of modified links, and simultaneous cleanup of subdivision no longer required after a geometry move. The traversal of line-space also limits the amount of work required to update and solve the new hierarchical system after a move, by identifying the modified paths in the scene hierarchy. The implementation of our new algorithm allows interactive updates of illumination after object motion for scenes containing several thousand polygons, including global illumination effects. Finally, the line-space hierarchy traversal provides a natural control mechanism allowing the regulation of the tradeoff between image quality and frame rate.