If we store world-space Euclidean distance in texels, the cube map becomes similar to a sphere map (Patow 1995 and Szirmay-Kalos et al. To consider all directions, we should use a cube map instead of a single depth image. The oldest application of this idea is the depth map used by shadow algorithms (Williams 1978), which stores light-space z coordinates for the part of the geometry that is seen from the light position through a window. On the other hand, the scene geometry can also be stored in a sampled form. If the scene geometry is too complex, simple proxy geometries can be used that allow fast approximate intersections (Bjorke 2004 and Popescu et al. Scene objects can be encoded as the set of parameters of the surface equation, similar to classical ray tracing (Havran 2001, Purcell et al. Because fragment shaders may access global (that is, uniform) parameters and textures, this requirement can be met if the scene geometry is stored in uniform parameters or in textures. To trace these rays, the fragment shader should have access to the scene. This approach is ideal for primary rays, but not for the secondary rays needed for the specular reflection and refraction terms of the radiance, because these rays do not share the same origin. The photographic process involves rasterizing the scene geometry and exploiting the z-buffer to find the first hits of the rays passing through the pixels. GPUs trace rays of the same origin very efficiently, taking a "photo" from the shared ray origin and using the fragment shader unit to compute the radiance of the visible points. To obtain a complete path, we should continue ray tracing at the hit point to get a second point and further scattering points. The basic operation for solving the visibility problem of a point at a direction is to trace a ray. This condition means that the radiance computation of a point recursively generates new visibility and color computation tasks to determine the intensity of the indirect illumination. However, for ideal reflectors and refractors, the radiance of a point depends also on the illumination of other points thus, points cannot be shaded independently. This independent and parallel shading concept is heavily exploited in current GPUs, owing its appealing performance to the parallel architecture made possible by the local illumination model. Each point is shaded independently, which opens up a lot of possibilities for parallel computation. Local illumination models compute the radiance from local properties-such as the position, normal vector, and material data-in addition to global light source parameters. Image synthesis computes the radiance of points that are visible through the pixels of the virtual camera. The implementation of our proposed method requires dynamic branching support. The resulting algorithm is simple to implement, runs in real time, and is accurate enough to render self-reflections. The intensity of the reflected ray is calculated according to a simplified Fresnel formula that is also appropriate for metals. These higher-order rays are traced similar to how the first reflection ray was traced by the fragment shader. To compute multiple reflections and refractions, the normal vector stored at the distance maps is read and used to generate the reflected/refracted rays. The search process starts with ray marching, which makes sure that no ray surface intersection is missed, and continues with a secant search, which provides accuracy.Īfter we introduce the general machinery for tracing secondary rays, we present the applications, including single and multiple reflections and refractions on curved surfaces. The algorithm searches this representation to trace secondary rays. The texels of these cube maps contain not only color information, but also the distance from a reference point and the surface normal, so the texels can be interpreted as sampled representations of the scene. Each layer is stored as a cube map in the texture memory. To allow the fragment shader to access the geometric description of the whole scene when looking for the hit points of secondary rays, we first render the scene into a layered distance map. In this chapter, we present a robust algorithm to compute single and multiple reflections and refractions on the GPU. Robust Multiple Specular Reflections and Refractionsīudapest University of Technology and Economics You can also subscribe to our Developer News Feed to get notifications of new material on the site.Ĭhapter 17. The CD content, including demos and content, is available on the web and for download. GPU Gems 3 GPU Gems 3 is now available for free online!
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