In this section, we review the fundamental concepts of volume rendering. First, we discuss how we can represent a volume. In scientific visualization, as in many other fields of visualization, volumes are most often represented as a mesh (sometimes known also as a grid). A mesh is a collection of volumetric elements called cells. The cells themselves are defined over a set of points called vertices. Geometry and topology define a mesh. The geometry describes the layout of vertices in space. The topology (sometimes referred to also as the connectivity) connects vertices to form cells.
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| Uniform Mesh | Rectilinear Mesh |
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| Structured Mesh | Unstructured Mesh |
Figure 1.3 shows four different classifications of meshes. A uniform mesh has both the topology and geometry fixed such that the vertices are in an orthographic grid and the cells are the axes aligned boxes formed by the vertices. In three dimensions, these cells are voxels. A rectilinear mesh is the same as a uniform mesh except that geometry is relaxed such that the spacing of the vertices may change. A general structured mesh has the same topology of a regular grid, but the geometry is free to place the vertices anywhere in space so long as the topology remains consistent. An unstructured mesh is nonrestrictive. It is free to have any type of geometry or topology.
To synthesize an image of a volume, a rendering system first has to determine which cells in the volume contribute to which parts of the image. There are two general approaches. The first approach is ray casting, where the rendering system casts rays from the viewpoint through each pixel of the image into the volume. The second approach is cell projection, where the rendering system projects each cell onto the viewing plane.
Once it has determined the location of each part of the volume in the viewing plane, the rendering system must compute the intensity of light emitted by the volume. I discuss this computation in detail in Chapter 1.