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40
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 150 (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 108 (7 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 efficiently durin ..."
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Cited by 98 (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.
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 63 (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...
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 60 (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 ...
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 59 (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...
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 36 (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 ...
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 27 (2 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...
Adaptive Splatting for Specular to Diffuse Light Transport
 Proceedings of the 5th Eurographics Workshop on Rendering
, 1994
"... 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 all ..."
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Cited by 24 (2 self)
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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 2pass raytracing algorithm is used, with an adaptive lightpass followed by a standard eyepass. During the lightpass, 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 ‘illuminationmaps’, as first proposed by Arvo [Arvo86]. The key to reconstructing the intensity gradients due to this lightpass lies in the construction of the illumination maps. We record the power carried by the ray as a ‘splat ’ of energy flux, deposited on the surface using a gaussian distribution kernel. The kernel of the splat is adaptively scaled according to an estimation of the wavefront divergence or convergence, thus resolving sharp intensity gradients in regions of high wavefront convergence and smooth gradients in areas of divergence. The 2nd pass eyetrace modulates the surface’s radiance according to the power stored in the illumination map in order to include the specular to diffuse light modelled during the first pass. 2.
Conservative Radiance Interpolants for Ray Tracing
, 1996
"... Classical raytracing algorithms compute radiance returning to the eye along one or more sample rays through each pixel of an image. The output of a raytracing algorithm, although potentially photorealistic, is a twodimensional quantity  an image array of radiance values  and is not directly ..."
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Cited by 18 (5 self)
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Classical raytracing algorithms compute radiance returning to the eye along one or more sample rays through each pixel of an image. The output of a raytracing algorithm, although potentially photorealistic, is a twodimensional 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