The increasing availability of streaming data is a consequence of the continuing advancement of data acquisition technology. Such data provides new challenges to the various data analysis communities. Clustering has long been a fundamental procedure for acquiring knowledge from data, and new tools are emerging that allow the clustering of data streams. However the dynamic, temporal components of streaming data provide extra challenges to the development of stream clustering and associated visualisation techniques. In this work we combine a streaming clustering framework with an extension of a static cluster visualisation method, in order to construct a surface that graphically represents the clustering structure of the data stream. The proposed method, OpticsStream, provides intuitive representations of the clustering structure as well as the manner in which this structure changes through time.