We present an integrated global illumination algorithm including non-diffuse light transport which can handle complex scenes and enables rapid incremental updates. We build on a unified algorithm which uses hierarchical radiosity with clustering and particle tracing for diffuse and non-diffuse transport respectively. We present a new algorithm which chooses between reconstructing specular effects such as caustics on the diffuse radiosity mesh, or special purpose caustic textures, when high frequencies are present. Algorithms are presented to choose the resolution of these textures and to reconstruct the high-frequency non-diffuse lighting effects. We use a dynamic spatial data structure to restrict the number of particles re-emitted during the local modifications of the scene. By combining this incremental particle trace with a line-space hierarchy for incremental update of diffuse illumination, we can locally modify complex scenes rapidly. We also develop an algorithm which, by permitting slight quality degradation during motion, achieves quasi-interactive updates. We present an implementation of our new method and its application to indoors and outdoors scenes.