Converting a tetrahedral volumetric data into regular volumetric data by an octree can improve the interactivity of the system effectively. When the depth of the octree is higher, the rendering results will be better. However, memory consumption and processing time will also increase. This paper proposes an adaptive regularization reformulation algorighm to construct the octree, improving the original single sampling strategy, combining with the depth information to transfer the sampling results into an octree texture which allows for random access in GPU. Then we use ray casting algorighm to render the regular volumetric data. Because of varying characteristics of the regional depth, the sampling algorithm responds with different step-size strategy. The experimental results show that this method reduces the memory consumption and processing time of the data, and at the same time improves the rendering quality as well as the rendering efficiency.