LÓGICA HORIZONTAL DE LA MATRIZ DE MARCO LÓGICO

In terms of soft shadows within ray tracing, variations of the distribution ray trac- ing approach [108] have become the most often used technique. An example is the work using distribution ray tracing for linear and area light sources [463] and curve light sources [33]. By distribution ray tracing, we mean shooting a number of rays towards the extended light to come up with an average for the shadow occlusion fraction or to estimate the radiance at each sample. This does not imply that it always requires stochastic sampling as implemented in the orig- inal work of Cook et al. [108]. Deterministic sampling approaches (e.g., adap- tive supersampling [629], stratified supersampling [340], Hammersley and Hal- ton point sequences [637], N-rooks with a static multijittered table [617], and blue-noise tiling patterns [442], etc.) for distribution ray tracing can work just as effectively.

An important aspect in favor of distribution ray tracing [108] is that noise is far more visually acceptable than banding, and when viewed over a sequence of frames, the noise is hardly noticeable. Thus, stochastically shooting shadow rays, hitting different points on the extended light over a sequence of frames, can achieve good results. Other variations of the distribution ray tracing techniques are listed below, mainly focusing on how to reduce the number of shadow rays while main- taining good quality results.

For the rest of this section, a set of disjoint papers are presented. They have little in common except that they discuss soft shadows computed by a distribution of rays.

Shirley et al. [527, 621, 528] compute good estimators of probabilistic locations on the extended light source for lighting and shadow computation used within a distribution ray tracing environment. Ideal probabilistic locations are discussed for various types of extended light sources. See a more detailed description of this work in Section 2.5.3.

Jensen and Christensen [269] apply a preprocessing step for computing a pho- ton map [273] by sending photons from the light source. For each photon inter- secting a surface, a shadow photon is continued along the same direction as if the original photon had not hit any surface. To compute the illumination at a particular point P, the nearest photons around P are gathered. If they are all shadow photons, then P is considered in complete shadow. If they are all regular photons, then P is fully lit. If they consist of both regular and shadow photons, then P is either on the boundary of the shadow or it is in the penumbra of an extended light. One can take the number of regular and shadow photons to determine the shadowing fraction, but the authors [273] indicate that the result is not very good unless a very large number of photons are generated from the light. Instead, shadow rays are shot to the light source to determine shadowing. In essence, the photon map is applied as a shadow “feeler.” Using this technique, the authors claim that as many as 90% of shadow rays do not need to be cast. However, the preprocessing cost may be

large for scenes only directly illuminated, and because the photons are shot based on probabilities, small objects can be missed.

Genetti et al. [189] use pyramidal tracing to quickly compute soft shadows from extended lights. A pyramid from the point to be shaded to the extended light is formed. If there are different objects in this pyramid, then the pyramid is subdi- vided into smaller pyramids as in typical adaptive supersampling approaches [629]. The subdivision criteria remain the same geometric identification the authors use in their earlier work [188], which means that the same limitations still hold, i.e., the criterion of the presence of different polygons is used to determine how complex that pyramid region might be and thus drives how many rays need to be shot. This may be ideal for higher-order surfaces, or large polygons, but not ideal for polyg- onal meshes, as they will always require many shadow rays to be shot based on the above criterion.

Hart et al. [225] precompute an occluder list per image pixel per light source by tracing a very small number of shadow rays. When an occluder is found, a check is done to determine if adjacent image pixels also “see” the same occluder so that the adjacent pixels can also register this occluder. During the shading of the pixel, the pixel’s occluders are projected and clipped against the extended light to analytically determine the visible portions of the light. This algorithm ensures consistency of occluders between adjacent pixels but can result in missed occluders (i.e., light-leaking problems), especially for small geometry occluders. The storage of occluders per pixel can also be large.

Distribution ray tracing has enjoyed much faster performance with SIMD in- structions, parallel systems on either the CPU or GPU, and ray packets for locality of reference [64, 45]. Another optimization exploiting locality of reference can be applied to the geometry itself, using hierarchical penumbra casting [325]. In this approach, all shadow rays are identified first, then a loop through each triangle occurs where the algorithm finds all shadow rays that intersect this triangle.

Additional reading on other distribution ray tracing optimizations includes ● Extensions of the hemicube data structure towards area sources [407]. ● Extensions of the mailbox/rayID optimization to reduce computation of the

non-first shadow ray [643].

● Approximate contour integration to compute illumination from diffuse area sources using distribution ray tracing only for the occluded or partially oc- cluded cases [603].

● Use of the Minkowski operators [178, 372] and frequency analysis [148] and gradients (normals) analysis [473] to focus the regions where shadow rays need to be shot to get the desired details. Additional advanced frequency analysis has been researched [154, 153].

● Prefiltering and storing local occlusion information. Shadow rays can ter- minate earlier based on ray differential and the local occlusion informa- tion [321].