Visualization of volume data is difficult to realize and control because the most common output device is a two-dimensional (2D) display and the most common input device is a mouse, which only allows 2D operation. For example, volume rendering projects the data structure onto a 2D image plane, but this type of view-dependent method gives rise to occlusion. In addition, 2D mouse operation does not allow direct selection of three-dimensional (3D) regions or coordinates. In this article, we propose a method that expands the octree structure of volume data onto a 2D plane. The proposed method uses the self-similarity of the fractal diagram and achieves multi-scale visualization of volume data in two dimensions. With this method, we can browse the entire domain of volume data without occlusion. For greater effectiveness, we combined the proposed method and existing 3D-based methods. Since each cell has a one-to-one correspondence with squares in the Sierpinski carpet, we can assign arbitrary 3D regions or positions by selecting the corresponding squares. This provides direct access to 3D regions and coordinates by 2D mouse operation. We propose some functions for interactive visualization and discuss how to exploit the advantages and lessen the disadvantages of the proposed method.
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