Volumetric Radiosity

The ray tracing algorithm described in the previous section can be used to capture spectacular interactions between objects in a scene. In reality, most scenes are dominated by diffuse interactions, which are not accounted for in the standard ray tracing illumination model, but are accounted for by a radiosity algorithm for volumetric data [63]. In volumetric radiosity, the basic "patch" element of classical radiosity is replaced by a "voxel." As opposed to previous methods that use participating media to augment geometric scenes [24,57], this method moves the radiosity equations into volumetric space, and renders scenes consisting solely of volumetric data. Each voxel can emit, absorb, scatter, reflect, and transmit light. Both isotropic and diffuse emission of light are allowed, where "isotropic" implies directional independence, and "diffuse"

implies Lambertian reflection (i.e., dependent on normal or gradient). Light is scattered isotropically and is reflected diffusely by a voxel. Light entering a voxel that is not absorbed, scattered, or reflected by the voxel is transmitted unchanged.

In order to cope with the high number of voxel interactions required, a hierarchical technique similar to [18] can be used. The basic hierarchical concept is that the radiosity contribution from some voxel vi to another voxel v; is similar to the radiosity contribution from v{ to vk if the distance between v;- and vk is small, and the distance between v{ and v;- is large. For each volume, a hierarchical radiosity structure is built by combining each subvolume of eight voxels at one level to form one voxel at the next higher level. An iterative algorithm [9] is then used to shoot voxel radiosities, where several factors govern the highest level in the hierarchy at which two voxels can interact. These factors include the distance between the two voxels, the radiosity of the shooting voxel, and the reflectance and scattering coefficients of the voxel receiving the radiosity. This hierarchical technique can reduce the number of interactions required to converge on a solution by more than four orders of magnitude. After the view-independent radiosities have been calculated, a view-dependent image is generated using a ray casting technique, where the final pixel value is determined by compositing radiosity values along the ray.

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