Soft shadows play an important role in photo-realistic rendering. Although there are many efficient soft shadow algorithms, most of them focus on the one-side light source situation, where a planar light source is on the outside of the scene. In fact, in many situations, such as games, light sources are omnidirectional. They may be surrounded by a number of 3D objects. This paper proposes a soft shadow algorithm for the omnidirectional situation. We develop a concentric spherical representation to model the behaviour of omnidirectional light sources. To provide better rendering results, a novel summed area table based filtering scheme for spherical functions is proposed. In addition, we utilize unicube mapping, which samples the spherical space more uniformly, to further improve the filtering quality.
Dual paraboloid mapping is an approach for environment mapping. Its major advantage is its fast map generation speed. For graphics applications, when filtering is needed, the filtering tool would naturally be mipmapping. However, directly applying mipmapping to dual paraboloid mapping would give us three problems. They are the discontinuity across the dual paraboloid map boundary, the non‐uniform sampling problem and the depth testing issue. We propose three approaches to solve these problems. Our approaches are based on some closed form equations derived via theoretical analysis. Using these equations, we modify the coordinates involved during the rendering process. In other words, these problems are handled just by using dual paraboloid maps and mipmaps differently, instead of fundamentally altering their data structures. Consequently, we are fixing the problems without damaging the map generation speed advantage. Applying all three approaches, we improve the rendering quality of dual paraboloid map mipmaps to a level equivalent to that of cubemap mipmaps, while preserving its fast map generation speed advantage. This gives dual paraboloid map mipmaps the potential to be a better choice than cubemap mipmaps for the devices with less computational power. The effectiveness and the efficiency of the proposed approaches are demonstrated using a glossy reflection application and an omnidirectional soft shadow generation application.
Vectorized visibility is a powerful visibility representation for rendering direct illumination with all frequency quality. However, the existing rendering method requires the visibility functions to be synthesized three times, followed with three radiance evaluation, for each triangle of the 3D model. We propose an alternative method to enhance vectorized visibility, such that we can directly interpolate the vectorized visibility, and therefore, reduce the computation bottleneck, i.e. the radiance evaluation, to just once. To facilitate the interpolation, we need to generate the correspondence among the three sampled visibility functions for each triangular patch. This paper uses spherical Voronoi diagram as a tool to conduct a preliminary correspondence generation, instead of doing brute force search. Additional treatments are also implemented to ensure that the interpolated visibility functions have smooth transition across the 3D model. With our method, we have more flexibility to manipulate the visibility functions in the favour of rendering speed and render the all frequency direct illumination twice as fast as the previous method.
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