Volume Characteristics

 Volumetric datasets are usually handled as an array of volume elements, called voxels, or as an array of cells. In the voxel method, the voxel surrounds the central gridpoint and the data value is constant in the voxel. There is no interpolation used and the image may appear chunky. In the cell method, the corners of each cell are the grid points and the values inside the cell are interpolated. Images using this method are smoother than with the voxel method. However, the interpolation of the data implicitly makes assumptions about the data that are not present in the voxel method. The splatting algorithm avoids this issue. When voxel or cell methods are interchangeable, we will use the term "element".

There are different types of possible grids and lattices, discussed below in order of increasing generality.

 For a Cartesian grid, all elements are identical cubes aligned with the principle axes. A regular grid has all elements identical and axis-aligned rectangular parallelepiped (not cubes). Elements of a rectilinear grid are all axis-aligned and hexahedral but are not necessarily identical. Elements in a structured grid are non-axis-aligned hexahedra. A block structured grid is a set of structured grids that are put together to fill a space. Examples of structured grids include spherical and curvilinear lattices. An unstructured volume contains polyhedra with no implicit connectivity, e.g. cells can be tetrahedra, hexahedra, pyramids, etc.

A hybrid volume is a combination of any of the above grids. The techniques discussed are restricted to Cartesian grids.

All images in this document are from T. Todd Elvins San Diego Supercomputer Center, Introduction to Volume Visualization: Imaging Multi-dimensional Scientific Data, SIGGRAPH 94 Course #10 Notes, 25 JULY 1994