The goal of this paper is the proposal and evaluation of a ray-casting strategy that takes advantage of the spatial and temporal coherence in image-space as well as in object-space in order to speed up rendering. It is based on a double structure: in image-space, a temporal buffer that stores for each pixel the next instant of time in which the pixel must be recomputed, and in object-space a Temporal Run-Length Encoding of the voxel values through time. The algorithm skips empty and unchanged pixels through three different space-leaping strategies. It can compute the images sequentially in time or generate them simultaneously in batch. In addition, it can handle simultaneously several data modalities. Finally, an on-purpose out-of-core strategy is used to handle large datasets. The tests performed on two medical datasets and various phantom datasets show that the proposed strategy significantly speeds-up rendering.