A Survey of Volumetric Illumination Techniques for Interactive Volume Rendering <s> Basis Function Based Techniques ( ) <s> Pr e-computed radiance transfer (PRT) has been used to render volumetric data under distant low-frequency illumination at real-time rates, including natural illumination, soft shadows, attenuation from semi-transparent occluders and multiple scattering. PRT requires a lengthy pre-process, which is acceptable only for static volume data. However, in practical volume rendering, general transfer functions are used. Manipulating such a transfer function will result in a dynamic radiance transfer which has to be re-computed. This work proposes a fast way for this re-computation. While previous work has used CPU Monte Carlo ray-tracing for pre-computation and requires time in the order of many minutes, our GPU implementation uses a hierarchical visibility approximation implemented entirely on the GPU and requires only a few seconds for typical scenes. <s> BIB001 </s> A Survey of Volumetric Illumination Techniques for Interactive Volume Rendering <s> Basis Function Based Techniques ( ) <s> We present a new, real-time method for rendering diffuse and glossy objects in low-frequency lighting environments that captures soft shadows, interreflections, and caustics. As a preprocess, a novel global transport simulator creates functions over the object's surface representing transfer of arbitrary, low-frequency incident lighting into transferred radiance which includes global effects like shadows and interreflections from the object onto itself. At run-time, these transfer functions are applied to actual incident lighting. Dynamic, local lighting is handled by sampling it close to the object every frame; the object can also be rigidly rotated with respect to the lighting and vice versa. Lighting and transfer functions are represented using low-order spherical harmonics. This avoids aliasing and evaluates efficiently on graphics hardware by reducing the shading integral to a dot product of 9 to 25 element vectors for diffuse receivers. Glossy objects are handled using matrices rather than vectors. We further introduce functions for radiance transfer from a dynamic lighting environment through a preprocessed object to neighboring points in space. These allow soft shadows and caustics from rigidly moving objects to be cast onto arbitrary, dynamic receivers. We demonstrate real-time global lighting effects with this approach. <s> BIB002
The group of basis function based techniques covers those approaches where the light source radiance and transparency (visibility) T ( x i , x j ), from the position x i to the position x j (usually border of volume), is separated and represented using a basis function. Since radiance and visibility are computed independently, light sources may be dynamically changed without an expensive visibility update, which is the case for many other methods. Furthermore, the light source composition may be complex as they are projected to another basis that is independent of the number of light sources. To this end, the only basis function used in the area of volume rendering are spherical harmonics. However, to be able to incorporate future techniques into our classification, we have decided to keep this group more general. It is beyond the scope of this article to provide a detailed introduction to spherical harmonic based lighting, we focus on the volume rendering specific properties only, and refer to the work by Sloan et al. BIB002 for further details. This being said, we will mention two important properties. The first property is that efficient integral evaluation can be performed, which supports real-time computation of the incoming radiance over the sphere. The second property is that it can be rotated on the fly, and thus supports dynamic light sources. While spherical harmonics were first used in volume rendering by Beason et al. [BGB * 06] to enhance isosurface shading, in this section, we cover algorithms applying spherical harmonics in direct volume rendering. Spherical Harmonics was first applied to direct volume rendering by Ritschel BIB001 to simulate low-frequency shadowing effects. To enable interactive rendering, a GPU-based approach is exploited for the computation of the required spherical harmonic coefficients. Therefore, a multiresolution data structure similar to a volumetric mipmap is computed and stored on the GPU. Whenever the spherical harmonic coefficients need to be recomputed, this data structure is accessed and the ray traversal is performed with increasing step size. The increasing step size is realized by sampling the multiresolution data structure in different levels, whereby the level of detail decreases as the sampling proceeds further away from the voxel for which the coefficients need to be computed.