We present a new Monte Carlo method for solving the light transport problem, inspired by the Metropolis sampling method in computational physics. To render an image, we generate a sequence of light transport paths by randomly mutating a single current path (e.g. adding a new vertex to the path). Each mutation is accepted or rejected with a carefully chosen probability, to ensure that paths are sampled according to the contribution they make to the ideal image. We then estimate this image by sampling many paths, and recording their locations on the image plane. Our algorithm is unbiased, handles general geometric and scattering models, uses little storage, and can be orders of magnitude more e#cient than previous unbiased approaches. It performs especially well on problems that are usually considered di#cult, e.g. those involving bright indirect light, small geometric holes, or glossy surfaces. Furthermore, it is competitive with previous unbiased algorithms even for relatively simple ...

Morse theory shows how the topology of an implicit surface is affected by its function's critical points, whereas catastrophe theory shows how these critical points behave as the function's parameters change. Interval analysis finds the critical points, and they can also be tracked efficiently during parameter changes. Changes in the function value at these critical points cause changes in the topology. Techniques for modifying the polygonization to accommodate such changes in topology are given. These techniques are robust enough to guarantee the topology of an implicit surface polygonization, and are efficient enough to maintain this guarantee during interactive modeling. The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.

Figure 1: Volume renderings of a 64 3 synthetic volume with four different curvature measures. Left to right: first principal curvature κ

We present an efficient and robust algorithm for finding points of collision between time-dependent parametric and implicit surfaces. The algorithm detects simultaneous collisions at multiple points of contact. When the regions of contact form curves or surfaces, it returns a finite set of points uniformly distributed over each contact region. Collisions can be computed for a very general class of surfaces: those for which inclusion functions can be constructed. Included in this set are the familiar kinds of surfaces and time behaviors encountered in computer graphics. We use a new interval approach for constrained minimization to detect collisions, and a tangency condition to reduce the dimensionality of the search space. These approaches make interval methods practical for multi-point collisions between complex surfaces. An interval Newton method based on the solution of the interval linear equation is used to speed convergence to the collision time and location. This method is mor...

Antialiasing of ray traced images is typically performed by supersampling the image plane. While this type of filtering works well for many algorithms, it is much more efficient to perform filtering locally on a surface for algorithms such as texture mapping. In order to perform this type of filtering, one must not only trace the ray passing through the pixel, but also have some approximation of the distance to neighboring rays hitting the surface (i.e., a ray's footprint). In this paper, we present a fast, simple, robust scheme for tracking such a quantity based on ray differentials, derivatives of the ray with respect to the image plane. CR Categories and Subject Descriptors: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism -- color, shading, shadowing, and texture; raytracing. 1 INTRODUCTION Ray tracing [18] is an image generation technique that is able to accurately model many phenomena which are difficult or impossible to produce with a traditional graphics pip...

Sphere tracing is a new technique for rendering implicit surfaces using geometric distance. Distance-based models are common in computer-aided geometric design and in the modeling of articulated figures. Given a function returning the distance to an object, sphere tracing marches along the ray toward its first intersection in steps guaranteed not to penetrate the implicit surface. Sphere tracing is particularly adept at rendering pathological surfaces. Creased and rough implicit surfaces are defined by functions with discontinuous or undefined derivatives. Current root finding techniques such as L-G surfaces and interval analysis require periodic evaluation of the derivative, and their behavior is dependent on the behavior of the derivative. Sphere tracing requires only a bound on the magnitude of the derivative, robustly avoiding problems Manuscript, July 1994. Recommended for publication: The Visual Computer. 5-70 where the derivative jumps or vanishes. This robustness and scope ...

This paper presents a new technique for rendering caustics on non-Lambertian surfaces. The method is based on an extension of the photon map which removes previous restrictions limiting the usage to Lambertian surfaces. We add information about the incoming direction to the photons and this allows us to combine the photon map with arbitrary reflectance functions. Furthermore we introduce balancing of the photon map which not only reduces the memory requirements but also significantly reduces the rendering time. We have used the method to render caustics on surfaces with reflectance functions varying from Lambertian to glossy specular. Keywords: Caustics, Photon Map, Ray Tracing, Rendering. 1 Introduction Caustics provides some of the most spectacular patterns of light in nature. Caustics are formed when light reflected from or transmitted through a specular surfaces strikes a diffuse surface. An example is the caustic formed as light shines through a glass of wine onto a table. In ...

We present an extension to existing techniques to provide for more accurate resolution of specular to diffuse transfer within a global illumination framework. In particular this new model is adaptive with a view to capturing high frequency phenomena such as caustic curves in sharp detail and yet allowing for low frequency detail without compromising noise levels and aliasing artefacts. A 2-pass ray-tracing algorithm is used, with an adaptive light-pass followed by a standard eye-pass. During the light-pass, rays are traced from the light sources (essentially sampling the wavefront radiating from the sources), each carrying a fraction of the total power per wavelength of the source. The interactions of these rays with diffuse surfaces are recorded in `illumination-maps', as first proposed by Arvo [Arvo86]. The key to reconstructing the intensity gradients due to this light-pass lies in the construction of the illumination maps. We record the power carried by the ray as a `splat' of ener...

Classical ray-tracing algorithms compute radiance returning to the eye along one or more sample rays through each pixel of an image. The output of a ray-tracing algorithm, although potentially photorealistic, is a two-dimensional quantity -- an image array of radiance values -- and is not directly useful from any viewpoint other than the one for which it was computed. This paper

Figure 1: Real-time renderings of complex refractive objects – (left) glass with red wine casting a colorful caustic, 24.8 fps. (middle) Amberlike bunny with black embeddings showing anisotropic scattering and volume caustics in the surrounding smoke and its interior, 13.0 fps. (right) Rounded cube composed of three differently colored and differently refracting kinds of glass showing scattering effects and caustics in its interior, 6.4 fps. We present a new method for real-time rendering of sophisticated lighting effects in and around refractive objects. It enables us to realistically display refractive objects with complex material properties, such as arbitrarily varying refractive index, inhomogeneous attenuation, as well as spatially-varying anisotropic scattering and reflectance properties. User-controlled changes of lighting positions only require a few seconds of update time. Our method is based on a set of ordinary differential equations derived from the eikonal equation, the main postulate of geometric optics. This set of equations allows for fast casting of bent light rays with the complexity of a particle tracer. Based on this concept, we also propose an efficient light propagation technique using adaptive wavefront tracing. Efficient GPU implementations for our algorithmic concepts enable us to render a combination of visual effects that were previously not reproducible in real-time.