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40
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
The Raxel Imaging Model and RayBased Calibration
, 2005
"... An imaging model provides a mathematical description of correspondence between points in a scene and in an image. The dominant imaging model, perspective projection, has long been used to describe traditional cameras as well as the human eye. We propose an imaging model which is flexible enough to r ..."
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Cited by 18 (3 self)
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An imaging model provides a mathematical description of correspondence between points in a scene and in an image. The dominant imaging model, perspective projection, has long been used to describe traditional cameras as well as the human eye. We propose an imaging model which is flexible enough to represent an arbitrary imaging system. For example using this model we can describe systems using fisheye lenses or compound insect eyes, which violate the assumptions of perspective projection. By relaxing the requirements of perspective projection, we give imaging system designers greater freedom to explore systems which meet other requirements such as compact size and wide field of view. We formulate our model by noting that all imaging systems perform a mapping from incoming scene rays to photosensitive elements on the image detector. This mapping can be conveniently described using a set of virtual sensing elements called raxels. Raxels include geometric, radiometric and optical properties. We present a novel ray based calibration method that uses structured light patterns to extract the raxel parameters of an arbitrary imaging system. Experimental results for perspective as well as nonperspective imaging systems are included.
Single Scattering in Refractive Media with Triangle Mesh Boundaries
 PUBLISHED IN THE ACM SIGGRAPH 2009 CONFERENCE PROCEEDINGS
, 2009
"... 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 loworder scattering. Refraction through a complex boundary allows a single external ..."
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Cited by 17 (2 self)
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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 loworder 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 halfvector 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.
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 15 (8 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.
A Vector Approach for Global Illumination in Ray Tracing
, 1998
"... This paper presents a method taking global illumination into account in a ray tracing environment. A vector approach is introduced, which allows to deal with all the types of light paths and the directional properties of materials. Three types of vectors are defined: Direct Light Vectors associate ..."
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Cited by 12 (5 self)
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This paper presents a method taking global illumination into account in a ray tracing environment. A vector approach is introduced, which allows to deal with all the types of light paths and the directional properties of materials. Three types of vectors are defined: Direct Light Vectors associated to light sources, Indirect Light Vectors which correspond to light having been diffusely reflected at least once and Caustic Light Vectors which are associated to light rays emitted by sources and reflected and/or transmitted by specular surfaces. These vectors are estimated at a small number of points in the scene. A weighted interpolation between known values allows to reconstruct these vectors for the other points, with the help of a gradient computation for the indirect component. This approach also allows to take uniform area light sources (spherical, rectangular and circular) into account for all the types of vectors. Computed images are thus more accurate and no discretizing of the geometry of the scene is needed. 1.
Hierarchical Caustic Maps
, 2007
"... Interactive applications typically rely on local models for lighting, occasionally augmented by GPUfriendly methods for approximating global illumination. Caustic mapping approximates the specular focusing of light using a lightspace image, akin to a shadow map, which is projected onto the scene d ..."
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Cited by 12 (2 self)
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Interactive applications typically rely on local models for lighting, occasionally augmented by GPUfriendly methods for approximating global illumination. Caustic mapping approximates the specular focusing of light using a lightspace image, akin to a shadow map, which is projected onto the scene during final rendering. Unfortunately, existing caustic map implementations must choose between quality and speed. Quickly generated maps use few photons and look extremely blurry, while sharper maps created from millions of photons only render at a few frames per second. This paper introduces a number of hierarchical enhancements to caustic mapping that allow realtime rendering with high quality caustic maps, even when using maps from multiple light sources. These techniques utilize the geometry processing stage of recent GPUs to avoid processing every photon and to render a pyramidal caustic map that allows photon splats of varying diameters without the increased costs inherent in rasterizing large splats. 1
Line Space Gathering for Single Scattering in Large Scenes
"... We present an efficient technique to render single scattering in large scenes with reflective and refractive objects and homogeneous participating media. Efficiency is obtained by evaluating the final radiance along a viewing ray directly from the lighting rays passing near to it, and by rapidly ide ..."
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Cited by 10 (1 self)
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We present an efficient technique to render single scattering in large scenes with reflective and refractive objects and homogeneous participating media. Efficiency is obtained by evaluating the final radiance along a viewing ray directly from the lighting rays passing near to it, and by rapidly identifying such lighting rays in the scene. To facilitate the search for nearby lighting rays, we convert lighting rays and viewing rays into 6D points and planes according to their Plücker coordinates and coefficients, respectively. In this 6D line space, the problem of closest lines search becomes one of closest points to a plane query, which we significantly accelerate using a spatial hierarchy of the 6D points. This approach to lighting ray gathering supports complex light paths with multiple reflections and refractions, and avoids the use of a volume representation, which is expensive for largescale scenes. This method also utilizes far fewer lighting rays than the number of photons needed in traditional volumetric photon mapping, and does not discretize viewing rays into numerous steps for ray marching. With this approach, results similar to volumetric photon mapping are obtained efficiently in terms of both storage and computation.
Perturbation Methods for Interactive Specular Reflections
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2000
"... We describe a new approach for interactively approximating specular reflections in arbitrary curved surfaces. The technique is applicable to any smooth implicitlydefined reflecting surface that is equipped with a ray intersection procedure; it is also extremely e#cient as it employs local perturbati ..."
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Cited by 8 (1 self)
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We describe a new approach for interactively approximating specular reflections in arbitrary curved surfaces. The technique is applicable to any smooth implicitlydefined reflecting surface that is equipped with a ray intersection procedure; it is also extremely e#cient as it employs local perturbations to interpolate point samples analytically. After ray tracing a sparse set of reflection paths with respect to a given vantage point and static reflecting surfaces, the algorithm rapidly approximates reflections of arbitrary points in 3space by expressing them as perturbations of nearby points with known reflections. The reflection of each new point is approximated to secondorder accuracy by applying a closedform perturbation formula to one or more nearby reflection paths. This formula is derived from the Taylor expansion of a reflection path and is based on first and secondorder path derivatives. After preprocessing, the approach is fast enough to compute reflections of tessellated di#use objects in arbitrary curved surfaces at interactive rates using standard graphics hardware. The resulting images are nearly indistinguishable from ray traced images that take several orders of magnitude longer to generate.
Adaptive Representation of Specular Light Flux
, 2000
"... Caustics produce beautiful and intriguing illumination patterns. However, their complex behavior make them difficult to simulate accurately in all but the simplest configurations. To capture their appearance, we present an adaptive approach based upon light beams. The coherence between light rays fo ..."
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Cited by 7 (0 self)
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Caustics produce beautiful and intriguing illumination patterns. However, their complex behavior make them difficult to simulate accurately in all but the simplest configurations. To capture their appearance, we present an adaptive approach based upon light beams. The coherence between light rays forming a light beam greatly reduces the number of samples required for precise illumination reconstruction. The light beams characterize the distribution of light due to interactions with specular surfaces (specular light flux) in 3D space, thus allowing for the treatment of illumination within singlescattering participating media. The hierarchical structure enclosing the light beams possesses inherent properties to detect efficiently every light beam reaching any 3D point, to adapt itself according to illumination effects in the final image, and to reduce memory consumption via caching.
Interactive caustics using local precomputed irradiance
 In Proc. of Pacific Graphics
, 2004
"... Bright patterns of light focused via reflective or refractive objects onto matte surfaces are called “caustics”. We present a method for rendering dynamic scenes with moving caustics at interactive rates. This technique requires some simplifying assumptions about caustic behavior allowing us to cons ..."
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Cited by 7 (1 self)
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Bright patterns of light focused via reflective or refractive objects onto matte surfaces are called “caustics”. We present a method for rendering dynamic scenes with moving caustics at interactive rates. This technique requires some simplifying assumptions about caustic behavior allowing us to consider it a local spatial property which we sample in a preprocessing stage. Storing the caustic locally limits caustic rendering to a simple lookup. We examine a number of ways to represent this data, allowing us to trade between accuracy, storage, run time, and precomputation time. 1.