Rendering deformable volume data currently needs separate processes for deformation and rendering, and is expensive in terms of both computational and memory costs. Recognizing the importance of unifying these processes, we present a new approach to the direct rendering of deformable volumes without explicitly constructing the intermediate deformed volumes. The volume deformation is done by a radial basis function that is piecewise linearly approximated by an adaptive subdivision of the octree encoded target volume. The octree blocks in the target volume are then projected, reverse morphed and texture mapped, using the SGI 3D texture mapping hardware, in a back-to-front order. A template based Z-plane/block intersection method is used to expedite the block projection computation.