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64
Metropolis Light Transport
 Computer Graphics (SIGGRAPH '97 Proceedings
, 1997
"... 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). Eac ..."
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Cited by 212 (1 self)
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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 ...
Curvaturebased transfer functions for direct volume rendering: Methods and applications
 In Proceedings of IEEE Visualization 2003
, 2003
"... Figure 1: Volume renderings of a 64 3 synthetic volume with four different curvature measures. Left to right: first principal curvature κ ..."
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Cited by 157 (10 self)
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Figure 1: Volume renderings of a 64 3 synthetic volume with four different curvature measures. Left to right: first principal curvature κ
Guaranteeing the Topology of an Implicit Surface Polygonization for Interactive Modeling
, 1997
"... 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 efficie ..."
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Cited by 112 (9 self)
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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 topologicallyguaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.
Tracing Ray Differentials
, 1999
"... 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 filteri ..."
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Cited by 88 (0 self)
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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]: ThreeDimensional 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: A Geometric Method for the Antialiased Ray Tracing of Implicit Surfaces
 The Visual Computer
, 1994
"... Sphere tracing is a new technique for rendering implicit surfaces using geometric distance. Distancebased models are common in computeraided geometric design and in the modeling of articulated figures. Given a function returning the distance to an object, sphere tracing marches along the ray towar ..."
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Cited by 80 (2 self)
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Sphere tracing is a new technique for rendering implicit surfaces using geometric distance. Distancebased models are common in computeraided 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 LG 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. 570 where the derivative jumps or vanishes. This robustness and scope ...
Interval Methods for MultiPoint Collisions between TimeDependent Curved Surfaces
 Computer Graphics
, 1993
"... We present an efficient and robust algorithm for finding points of collision between timedependent 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 un ..."
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Cited by 69 (0 self)
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We present an efficient and robust algorithm for finding points of collision between timedependent 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 multipoint 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...
Rendering Caustics on NonLambertian Surfaces
 Computer Graphics Forum
, 1996
"... This paper presents a new technique for rendering caustics on nonLambertian 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 u ..."
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Cited by 42 (3 self)
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This paper presents a new technique for rendering caustics on nonLambertian 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 ...
Eikonal rendering: efficient light transport in refractive objects
 ACM Transactions on Graphics
, 2007
"... Figure 1: Realtime 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 ..."
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Cited by 40 (6 self)
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Figure 1: Realtime 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 realtime 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 spatiallyvarying anisotropic scattering and reflectance properties. Usercontrolled 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 realtime.
A comprehensive theory of volumetric radiance estimation using photon points and beams
 ACM Transactions on Graphics
, 2011
"... We present two contributions to the area of volumetric rendering. We develop a novel, comprehensive theory of volumetric radiance estimation that leads to several new insights and includes all previously published estimates as special cases. This theory allows for estimating inscattered radiance at ..."
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Cited by 37 (14 self)
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We present two contributions to the area of volumetric rendering. We develop a novel, comprehensive theory of volumetric radiance estimation that leads to several new insights and includes all previously published estimates as special cases. This theory allows for estimating inscattered radiance at a point, or accumulated radiance along a camera ray, with the standard photon particle representation used in previous work. Furthermore, we generalize these operations to include a more compact, and more expressive intermediate representation of lighting in participating media, which we call “photon beams. ” The combination of these representations and their respective query operations results in a collection of nine distinct volumetric radiance estimates. Our second contribution is a more efficient rendering method for participating media based on photon beams. Even when shooting and storing less photons and using less computation time, our method significantly reduces both bias (blur) and variance in volumetric radiance estimation. This enables us to render sharp lighting details (e.g. volume caustics) using just tens of thousands of photon beams, instead of the millions to billions of photon points required with previous methods.
Theory and Application of Specular Path Perturbation
, 2000
"... In this paper we apply perturbation methods to the problem of computing specular reflections in curved surfaces. The key idea is to generate families of closely related optical paths by expanding a given path into a highdimensional Taylor series. Our path perturbation method is based on closedform ..."
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Cited by 35 (3 self)
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In this paper we apply perturbation methods to the problem of computing specular reflections in curved surfaces. The key idea is to generate families of closely related optical paths by expanding a given path into a highdimensional Taylor series. Our path perturbation method is based on closedform expressions for linear and higherorder approximations of ray paths, which are derived using Fermat's Variation Principle and the Implicit Function Theorem. The perturbation formula presented here holds for general multiplebounce reflection paths and provides a mathematical foundation for exploiting path coherence in ray tracing acceleration techniques and incremental rendering. To illustrate its use, we describe an algorithm for fast approximation of specular reflections on curved surfaces; the resulting images are of high accuracy and nearly indistinguishable from ray traced images. Keywords: perturbation theory, implicit surfaces, optics, ray tracing, specular reflection 1 1 Introduct...