Light scattering in refractive media is an important optical phenomenon for computer graphics. While recent research has focused on multiple scattering, there has been less work on accurate solutions for single or low-order scattering. Refraction through a complex boundary allows a single external source to be visible in multiple directions internally with different strengths; these are hard to find with existing techniques. This paper presents techniques to quickly find paths that connect points inside and outside a medium while obeying the laws of refraction. We introduce: a half-vector based formulation to support the most common geometric representation, triangles with interpolated normals; hierarchical pruning to scale to triangular meshes; and, both a solver with strong accuracy guarantees, and a faster method that is empirically accurate. A GPU version achieves interactive frame rates in several examples.

Interactivity requires tradeoffs to achieve the right balance between rendering quality and speed. In practice, today’s applications restrict lighting to mainly direct illumination, sometimes augmented by precomputed transfer techniques for diffuse global effects. Dynamic high-frequency specular effects, such as caustics, are largely lacking due to the high costs for recomputation each frame. Recent work has introduced a variety of related caustics approximations that interactively render light-space photons into a photon buffer, gather them into a caustic map, and project this map onto the scene similar to shadow mapping. While the process is simple and straightforward, the discretization of light into a finite number of uniformly-distributed photons leads to undersampling and aliasing artifacts. This paper examines two techniques for reducing these artifacts using varying sized photon splats. Conceptually, these are similar to the variable-radius k-nearest neighbor search used in photon mapping, allowing noise reduction in areas of low photon density while maintaining crisp caustics at focal points. Our techniques improve image quality at a modest cost that is significantly cheaper than supersampling the photon buffer. 1

Caustics are important visual phenomena, as well as challenging global illumination effects in computer graphics. Physically caustics can be interpreted from one of two perspectives: in terms of photons gathered on scene geometry, or in terms of a pair of caustic surfaces. These caustic surfaces are swept by the foci of light rays. In this paper, we develop a novel algorithm to approximate caustic surfaces of sampled rays. Our approach locally parameterizes rays by their intersections with a pair of parallel planes. We show neighboring ray triplets are constrained to pass simultaneously through two slits, which rule the caustic surfaces. We derive a ray characteristic equation to compute the two slits, and hence, the caustic surfaces. Using the characteristic equation, we develop a GPU-based algorithm to render the caustics. Our approach produces sharp and clear caustics using much fewer ray samples than the photon mapping method and it also maintains high spatial and temporal coherency. Finally, we present a normal-ray surface representation that locally parameterizes the normals about a surface point as rays. Computing the normal ray caustic surfaces leads to a novel real-time discrete shape operator.

Abstract This paper proposes a robust algorithm to compute caustics caused by multiple reflections and refractions on the GPU. The proposed algorithm solves two problems of previous methods, caustic light leaks and caustic undersampling. In order to eliminate caustic light leaks, terminal photon hits are stored and caustic patterns are reconstructed on the faces of a layered distance map attached to the caustic generator. To avoid undersampling, we propose caustic triangles to be drawn instead of splatting photon hits. Unlike splatting, caustic triangles adapt to the local density of the uneven photon distribution, always form continuous patterns, do not cause excessive blurring, and do not require manual user intervention to set the size of these splats.

We present an optimization of the height-field water-column based approach for water simulation, providing three-dimensional animation of water flow on natural terrains. Our approach eliminates the storage and management of redundant virtual pipes between columns of water and also removes output dependency for parallel implementation, making it efficient for interactive computer graphics applications. We show a GPU implementation of the proposed method that runs at interactive frame rates with rich lighting effects on the water surface, including light wavelength dependent attenuation and light scattering.

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