Greg Smith
2 Contents
1 Global Illumination: A Survey
4.1.3 Metropolis Light Transport
4.2.1 Radiosity on graphics hardware (2004)
4.2.2 Dynamic Ambient Occlusion and Indirect Lighting (2005)
4.2.3 Voxel-based global illumination (2011)
4.3.1 A ray tracing solution for diffuse interreflection
4.3.2 Interactive global illumination in dynamic scenes
4.3.4 The RADIANCE light simulation and rendering system
4.4.1 Progressive Photon Mapping (2008)
4.4.2 Simulating Photon Mapping for Real-time Applications (2004)
4.4.3 Low latency photon mapping using block hashing (2002)
4.4.4 Interactive global illumination using selective photon tracing (2002)
4.4.5 Photon mapping of programmable graphics hardware (2003)
4.4.6 Interactive screen-space accurate photon tracing on GPUs (2006)
4.4.7 Real-time KD-tree construction on graphics hardware (2008)
4.4.8 An efficient GPU-based approach for interactive global illumination (2009)
4.4.9 Hardware-accelerated global illumination by image space photon mapping (2009)
4.4.10 Interactive global photon mapping (2009)
4.4.11 Multi-image based photon tracing for interactive global illumination of dynamic scenes (2010)
4.4.12 Parallel progressive photon mapping on GPUs (2010)
4.5.1 Instant Radiosity (1997)
4.5.2 Bidirectional Instant Radiosity (2006)
4.5.3 Reflective Shadow Maps (2005)
4.5.4 Incremental Instant Radiosity for Real-Time Indirect Illumination (2007)
4.5.5 Splatting Indirect Illumination (2006)
4.5.6 Imperfect Shadow Maps for Efficient Computation of Indirect Illumination (2008)
4.5.8 Real-time indirect illumination with clustered visibility
4.6.1 Tensor clustering for rendering many-light animations (2008)
4.6.2 Virtual spherical lights for many-light rendering of glossy scenes (2009)
4.6.3 Lightcuts: a scalable approach to illumination (2005)
4.6.4 Matrix row-column sampling for the many-light problem (2007)
4.7.1 Point Based Approximate Color Bleeding (2008)
4.7.2 Micro-Rendering for Scalable, Parallel Final Gathering (2009)
4.7.3 Importance point projection for GPU-based final gathering (2011)
4.8 Precomputed Radiance Transfer
4.8.2 Fast arbitrary BRDF shading for low-frequency lighting using spherical harmonics (2002)
4.8.3 All frequency shadows using non-linear wavelet lighting approximation (2003)
4.8.4 Triple product wavelet integrals for all-frequency relighting (2004)
4.8.5 Spherical harmonic gradients for mid-range illumination (2004)
4.8.6 All frequency precomputed radiance transfer for glossy objects (2004)
4.8.7 All-frequency relighting of glossy objects (2006)
4.8.8 Normal mapping for precomputed radiance transfer (2006)
4.8.10 The irradiance volume (1998)
4.8.11 Ambient occlusion fields (2005)
4.8.12 Matrix radiance transfer (2003)
4.9.1 Global illumination with radiance regression functions
Radiance is the radiant flux per unit projected area per unit solid angle.
is
the radiant flux emitted, reflected or transmitted.
is
the solid angle.
is
the projected area.
The outgoing radiance at a surface location in direction is calculated as the sum of emitted radiance and reflected radiance .
The reflected radiance is measured using the rendering equation:
is
the incident light direction.
is
the surface normal at position x.
is
the incident radiance at point in
the direction .
is
the BRDF. The BRDF is a four-dimensional function that defines how light is
reflected at a surface. The function returns the ratio of reflected radiance
exiting along to
the irradiance incident on the surface from direction .
As radiation travels through a participating medium it undergoes three kinds of phenomena: absorption, scattering and emission.
The transport equation describes the variation of radiance at a point in direction . The transport equation takes into account radiance added due to in-scattering and radiance lost due to absorption and out-scattering. The incident radiance at a point is the sum of the reduced incident radiance and media radiance .
is
the scattering albedo.
is
the reduced incident radiance. The reduced incident radiance is modeled using
beer’s law.
is
the medium radiance, which is the radiance due to the contribution of the
source radiance within the medium.
is
the scattering phase function.
The rendering equation can be solved using Monte Carlo techniques. To do so, a high number of directional samples are produced, the rendering function is evaluated for every sample and the average of all results converges to the true solution. To evaluate a sample, the incoming light from one direction has to be computed. This is usually done using ray tracing: a ray is sent in the direction and the light emitted from the first hit point is computed, potentially, again by computing a solution of the rendering equation at this location.
The final gathering method reconstructs the incoming radiance values over the hemisphere for each point visible though the pixel read though through the stored radiance solution. Radiance at each point can be estimated using photon density. Final gathering aims to reduce photon artifacts.
Bidirectional ray tracing generates paths starting at the light sources and the surface point simultaneously and connects both paths in the middle to find a contribution to the light transport between the light source and the point for which a radiance value needs to be computed.
The algorithm has the availability of two different path generators when computing a Monte Carlo estimate for the flux through a certain pixel.
Metropolis light transport is a stochastic ray tracing technique where the overall strategy is to sample paths with probability proportional to the image contribution function. To do this, we generate a sequence of paths where each patch is obtained by a random mutation to the path . The mutations can have almost any desired form, and typically involve adding, deleting or replacing a small number of vertices on the current path.
The metropolis framework gives a recipe for determining the acceptance probability for each mutation such that in the limit the sampled paths are distributed according to the image contribution function.
The underlying idea is to discretize the scene’s surfaces into finite surface elements, often called patches, and then compute the light transport between them.
For every patch one need to store the radiosity value for diffuse surfaces, or the directional distribution of incoming and outgoing light in the non-diffuse case, the light transport amounts to solving a linear system of equations once the form factors, which denote the amount of light transport between two patches, are known.
Here is presented a technique for computing radiosity, including an adaptive subdivision of the model. The implementation that is equivalent to conventional patch orientated radiosity on a uniformly subdivided domain. This system stores the radiosity and the residual as textures on the modeling polygons. The scene polygon with the highest total residual energy is chosen as the next shooter. We use the hemicube method to sample visibility from the current shooter. We divide the shooter into m subsections and proximate their areas with oriented discs.
If an element is visible from the shooter, then the next step is to compute the intensity that it receives. We use the disc approximation to a differential area-to-area form factor equation between two elements I and j.
This method subdivides the scene geometry hierarchically into a quadtree with the radiosity data stored at the leaf nodes.
To render a texture quadtree, we traverse it recursively. When a leaf node is reached, a quadrilateral is rendered with the node’s radiosity texture. We display all scene polygons textured with the adaptive radiosity solution.
This paper introduces a new technique for computing diffuse light transport and show how it can be used to compute global illumination for animates scenes. This technique works by treating polygon meshes as a set of surface elements that can emit, transmit or reflect light and that can shadow each other.
We define polygon meshes as disk-shaped elements, one element created for each vertex. Elements defined by position, normal and area.
Ambient occlusion provides soft shadows by darkening surfaces that are partially visible to the environment. It involves calculating the accessibility value, which is the percentage of the hemisphere above each surface point not occluded by geometry. We also calculate the direction of least occlusion (bent normal).
We calculate the accessibility values for each vertex in a multipass algorithm that removes multiple shadowing effects.
We compute the bent normal by first multiplying the normalized vector between elemenets and the form factor. Then we subtract this result from the original element.
We calculate the occlusion result be rendering the result to a texture. The shader calculates the amount of shadow received at each element and writes it to the alpha component of the pixel. Bent normal is also rendered. We calculate the amount of light transferred from one surface element to another using the geometric disk-to-disk form factor. We run one pass of this for our radiance-transfer shader to calculate the max amount of reflected or emitted light that can reach any element. Then we run a shadow pass that subtracts from the total light at each element based on how much light reaches the shadowing elements.
This paper introduces Voxel-based Global Illumination (VGI), a scalable technique that ranges from real-time near-field illumination to interactive global illumination solutions. It introduces a new atlas-based boundary voxelization algorithm and an extension to a fast ray-voxel intersection test.
We render the complete object to a single atlas texture image in one rendering pass. World-space positions have to be written to the atlas and during that process arbitrary other data can be stored as well. All valid entries in the texture atlas are inserted into the grid storing the voxel data using point rendering. The voxelization camera’s frustum defines the region that is voxelized. A vertex is generated for each valid texel of the atlas texture.
Irradiance caching is an effective technique for accelerating the computation of indirect illumination in diffuse scenes. Irradiance caching exploits the insight that the irradiance at diffuse surfaces varies smoothly in most scenes. Irradiance is cached in a data structure an when possible, these cached values are interpolated to approximate irradiance at nearby surfaces.
Irradiance gradients are used to determine when cached values can be interpolated to produce reasonably accurate results. The translation and rotation gradient estimate how irradiance changes with position and direction. An error estimate, based on the split-sphere model is used to determine which samples can be used for interpolation. The error at a point due to a cached sample at location is given:
is
the mean harmonic distance of objects visible from the cached sample .
and
are
the normals at and
the sample respectively.
Irradiance at point is interpolated using the cached irradiance values of nearby samples using the weight for the ith sample.
The interpolated irradiance at point p is then
The cached samples are stored in an octree constructed over the scene. This data structure permits the decoupling of geometry for illumination values. When the irradiance at a point must be computed, the octree is searched to find “nearby” cached samples that are accurate enough to be used to approximate the irradiance.
An efficient ray tracing method is presented for calculating interreflections between surfaces with both diffuse and specular components. A monte carlo technique computes the indirect contributions to illuminance at locations chosen by rendering process. The indirect illuminance values are averaged over surfaces in place of a constant “ambient” term.
Ray tracing computes multiple reflections by recursion. At each level, the calculation proceeds as follows:
1. Intersect the ray with scene geometry.
2. Compute direct contributions from light sources.
3. Compute specular contributions from reflection surfaces.
4. Compute diffuse contributions from reflecting surfaces.
Indirect illumination values are cached in the following manner.
If one or more values is stored near this point, use stored value(s). Else, compute and store values at this point.
Illuminance is defined on a surface as the integral of luminance over the projected hemisphere.
In the primary method of calculating indirect illuminance, the integral is approximated with a discrete set of sample rays that do not intersect light sources. A uniform segmented monte carlo distribution is derived by standard transformation methods.
is
the polar angle
is
the azimuthal angle
is
the luminance from direction
, are
uniform random numbers between 0 and 1.
is
the total number of samples.
The secondary method either approximates illuminance by averaging between primary values or determines that a new primary value is needed. Our method uses an estimate of the change in illumination over a surface based on scene geometry. The inverse of this serves as the weight for each primary value during averaging.
The inverse of the estimated error is used in a weighted average approximation of illuminance.
is
the computed illuminance at .
is the harmonic mean distance to objects visible from .
a is a user selected constant.
The approximate illuminance , is given by the weighted mean to all adjacent illuminance values. The constant a is directly related to the maximum approximation error.
Sections of the scene that do not contribute to the image, directly or indirectly are not examined. Areas where the indirect illumination varies rapidly will have a higher concentration of values. Flat ears without nearby influences will have only a few values.
Illuminance
storage:
Each illuminance is stored in the octree node containing its position and
having a size greater than twice but not more than four time the appropriate
“valid domain”. Each node in the octree will contain a list of illuminance
values and a pointer to eight children. This algorithm will not only pick up
the nodes containing p, but will also search nodes having boundaries within
half the cube size of p. In this way, all lists that might have an illuminance
value whose valid domain contains p will be examined.
This paper presents a system for interactive computation of global illumination in dynamic scenes. Our system uses a novel scheme for caching the results of a high quality pixel-based renderer such as bidirectional path tracer.
They have designed a novel scheme for caching high quality samples generated by pixel-based rendering algorithms such as path tracing and then interpolating between these samples using graphics hardware. The shading cache is a hierarchical subdivision mesh attached to each primitive in the scene, with lazily evaluated shading values at the mesh vertices. It is refined by choosing locations in the image plane that require more accuracy. The selection of these locations is made using a priority map, which capture the likelihood of error due to interpolation, view-dependence and object motion.
This paper also introduces a novel flood filling operator for efficiently capturing the high frequency detail in the images to supplement the priority based sampling. Finally the graphics hardware is used to efficiently interpolate between the shading samples.
During initialization, the mesh for each geometric primitive is set to be a single un-subdivided patch. The shading values for these patches are not pre-computed, but evaluated lazily when required for generating a good image. When a patch is selected for update, we either evaluate the shading values for its vertices or subdivide the patch into four children and evaluate the shading values for their vertices.
The information from a hemispherical sampling of the luminous environment is interpreted in a new way to predict the change in irradiance as a function of position and surface orientation.
Specular contributions are computed with separate rays in appropriate directions. Once the direct and specular contributions have been removed from the integral, the indirect diffuse contribution is computed using a Monte Carlo sampling of the hemisphere.
In meshless caching scheme, the location of the computed indirect irradiance is determined by the proximity and curvature of the surfaces and does not fall on a regular grid, so a weighted sum is used in place of a more standard bilinear interpolation.
Indirect
Irradiance Calculation
Indirect illumination
is calculated using a fixed number of samples in a uniformly weighted,
stratified Monte Carlo sampling.
is the indirect radiance in the direction
, are uniformly distributed random variables in the range [0,1), MN is the total number of samples.
Irradiance samples, consisting of a point, normal vector and an irradiance value, are stored in an octree for later interpolation.
Gradient
Calculation
We compute a rotational
gradient and a translational gradient.
Rotational
is the base plane unit vector in the direction
Translational
to compute the
translational irradiance gradients we consider how the projected solid angle of
each MN hemisphere cells is affected by a translation of the hemisphere center.
To determine how irradiance changes with translation in this tangent plane, we sum the marginal changes for each cell.
The change in irradiance with respect to translation for each cell wall is simply the length of the cell wall multiplied by the rate of motion of the wall with respect to motion in a specified direction.
is
the unit vector in the direction.
is
the unit vector int the direction
is
the polar angle at the previous boundary
is
the polar angle at the next boundary
is
the azimuthal angle at the previous boundary
is
the intersection distance cell (j,k)
Irradiance interpolation
is
the test point position.
is
the surface normal at the test point.
is
the irradiance value at sample i.
is
the position of sample i.
is
the surface normal at sample i.
is
the harmonic mean distance to object visible from .
is
the set of valid irradiance values.
This paper describes a physically-based rendering system tailored to demands of lighting design and architecture. The simulation uses a light-backwards ray-tracing method with extensions to efficiently solve the rendering equation under most conditions.
Radiance uses a ray-tracing in recursive evaluation of the rendering equation. Indirect lighting changes gradually over surfaces. It should be possible to spread out this influence over many pixels to obtain a result that is smooth and accurate at a modest sampling cost. The original method for computing and using cached irradiance values has been enhanced using gradient information.
The basic idea is to perform a full evaluation of the rendering equation for indirect diffuse contributions only as needed, caching and interpolating these values over each surface. We are free to adjust the density of out calculation point in response to the illumination environment.
To compute the indirect irradiance at a point in our scene, we send a few hundred rays that are uniformly distributed over the projected hemisphere. If any of our rays hits a light source we disregard it since the direct contribution is computed separately. The sampling process is applied recursively for multiple reflections. We have developed a numerical approximation to the irradiance gradient based on hemisphere samples. Knowing the gradient in addition to the value of a function, we can use a higher order interpolation method.
We reduced the number of shadow rays with a prioritized list of potential source contributions at each evaluation of the rendering equation. The largest potential contributions are tested for shadows first, and we stop testing when the remainder of the source list is below some fraction of unoccluded contributions.
Photon Mapping is a two pass global illumination method.
The photon maps are constructed by emitting a large number of photons from the light sources in the scene. Each photon is traced through the scene using a method similar to path tracing. Every time a photon hits a surface it is stored within the photon map and Russian roulette is used to determine whether the photon is absorbed or reflected. The new direction of a reflected photon is computed using the BRDF of the surface.
We use two
photon maps:
Caustic photon map: The caustic photon map is used only to store photons
corresponding to caustics and is created by emitting photons towards the
specular objects in the scene and storing these as they hit diffuse surfaces.
Caustics are rendered by visualizing a radiance estimate based on the caustics
photon map directly.
Global Photon Map: The global photon map is used as a rough approximation of the light/flux within the scene and is created by emitting photons towards all objects. It is not visualized directly and therefore it does not require the same precision as the caustic photon map.
The photons are stored in a balanced kd-tree.
To compute the radiance , leaving an intersection point x at a surface with BRDF , we locate the N photons with the shortest distance to x. Based on the assumption that each photon p represents flux arriving at x from direction we can integrate the information into the rendering equation.
Caustics are evaluated using the information in the caustics photon map. The radiance estimated based on the caustics photon map is visualized directly and this is the reason why the number of photons in the caustics photon map must be high.
Soft indirect illumination is incoming light which has been reflected diffusely at least once since it left the light source. This light is then reflected diffusely by the surface and consequently the resulting illumination is very “soft”. The approximate evaluation of this integral is the radiance estimate based on the global photon map.
The main idea in progressive photon mapping is to reorganize the standard photon mapping algorithm based on the conditions of consistency, in order to compute a global illumination solution with arbitrary accuracy without storing the full photon map in memory.
Progressive photon mapping is a multi-pass algorithm in which the first pass is ray tracing and all subsequent passes use photon tracing.
Ray Tracing
Pass:
Use standard ray tracing to find all the surfaces in the scene visible through
each pixel in the image. Each ray path includes all specular bounces until the
first non-specular surface seen. In scenes with large number of specular
surfaces the length of ray paths can be limited by Russian roulette.
For each ray path we store all hit points along the path where the surface has a non-specular component in the BRDF. We store data points in the struct hitpoint.
Photon
Tracing Passes:
The photon tracing step
is used to accumulate photon power at the hit points found in the ray tracing
pass. It can be divided into multiple passes where each pass consists of
tracing a given number of photons into the scene in order to build a photon
map.
After each photon tracing pass we loop through all hit points (from the ray tracing pass) and find the photons within the radius of each hit point. We use the newly added photons to refine the estimate of the illumination.
Once the contribution of the photons have been recorded they are no longer needed, and we can discard all photons and proceed with a new photon tracing pass. This continues until enough photons have been accumulated and the final image quality is sufficient.
:
Number of photons within a radius after a photon trace.
:
Reduced radius
: Total Flux Received.
: Adjusted flux
: Radiance Evaluation
This paper introduces a method for simulating photon mapping. It exploits the main idea behind photon mapping namely that the different elements in global illumination can be calculated separately (direct, specular, caustics and indirect)
Photons are intelligently selected to be re-emitted. Photons from light sources are grouped together where each photon in each group has similar starting directions. Each photon is enumerated in each group. One photon is emitted from each group every frame. The path of each photon is stored, and if the new path diverges from the previous path, all photons from the group will be marked for redistribution.
The photons are stored as photon-hits on the surfaces along the path of the traced photon. The complete path of each photon is also stored. Each surface also has pointers to photon-hits that have hit that particular surface.
To approximate global illumination we compute the irradiance using N-nearest neighbor query of the photons. The radiance of the surface is stored in reconstruction texture maps applied to the surface.
Typical KNN photon mapping algorithm use spatial partitioning. Here, we present a neighborhood-preserving hashing algorithm that is low-latency and has sub-linear access time.
Our algorithm uses hash functions to categorise photons by their positions. Then a kNN query proceeds by deciding which hash bucket is matched to the query point and retrieving the photons contained inside the hash bucket for analysis.
This method exploits temporal coherence of illumination by tracing photons selectively to the scene regions that require illumination update.
Photon tracing is based on Quasi-Monte Carlo sampling with the multi-dimensional Halton sequence. The main problem is to identify each invalid photon and to replace it by the corresponding photon, which is traced for the current scene configuration. We show how the periodicity property of this sequence, allows for immediate identification of photons that have similar paths in the scene. Thus, for any invalid photon, it is easy to identify indices of all similar photons in Z that are likely to be invalid as well.
This paper presents a modified photon mapping algorithms capable of running on GPUs. The implementation uses photon tracing to distribute the photons on the GPU. Photons are stored in a grid based photon map, constructed on the GPU. A KNN method is also described.
This paper presents a new method to directly render caustics on complex objects. The algorithm is based on the rasterization of photon paths in texture maps. Intersection events are then resolved on a per-fragment basis using layered depth images.
This method provides an effective means to resolve inter-object light transfer as well as several refractions at complex and dynamic polygonal objects.
Photon rays are traced in screen-space on programmable graphics hardware. This is done by rendering line primitives with respect to the current view. To be able to resolve intersection events at arbitrary position along these lines they are rasterized into texture maps. Intersections between photon rays and objects in the scene can now be detected using layered depth maps and simple fragment operations. By rendering oriented point sprites at the receiver pixels in screen-space we account for the energy transport through beams of light. The use of energy splats significantly minimizes the number of photons that have to be traced.
The paper presents an algorithms for constructing kd-trees on GPUs. Specifically the algorithm builds tree nodes in breadth-first search order to fully exploit the fine-grained parallelism of modern GPUs at all stages of kd-tree construction.
This paper presents a GPU-based method for interactive global illumination that integrates complex effects such as multi-bounce indirect lighting, glossy reflections, caustics, and arbitrary specular paths. Our method builds upon scattered data sampling and interpolation on the GPU.
It starts with raytraced shading points and partitions them into coherent shading clusters using adaptive seeding followed by k-means. At each cluster center we apply final gather to evaluate its incident irradiance using GPU-based photon mapping. We approximate the entire photon tree as a compact illumination cut, this reducing the final gather cost for each ray. The sampled irradiance values are then interpolated at all shading points to produced rendering. Our method exploits the spatial coherence of illumination to reduce sampling cost. We sample sparsely and the distribution of sample points conforms with the underlying illumination changes. Therefore our method is both fast and preserves high rendering quality.
ISPM is a screen-space algorithm which takes two steps of the photon mapping algorithm, the initial bounce and the photon gathering. The initial bounce is calculated for each light and stored in a bounce map. Photon gathering is done by splatting the final photon volumes to produce indirect lighting.
The first step of ISPM is the render light GBuffers – a GBuffer for each light. Each Light GBuffer describes the different BSDF properties of the surfaces at each pixel in light space.
The initial photon bounce is made by rasterizing a bounce map for each emitter in the scene. A fragment shader is used to emit a photon through each pixel center. The pixels are projected onto a sphere around the emitter. When the photon is emitted, the first bounce is calculated using the light GBuffers. The GBuffer contain the necessary information for where the photon will hit the surface and the properties of the surface.
Overview of the algorithm:
· For each light: render the light GBuffers and render the light bounce map.
· Render the direct lighting.
· Render subsampled eye GBuffer.
· Extract and trace the photon from the bounce map.
· Render the indirect lighting by splatting the photons.
· Upsample the indirect lighting and combine it with the direct lighting.
· Add color correction, post effects and display the image.
This paper presents a photon mapping technique capable of computing high quality global illumination at interactive frame rates. By extending the concept of photon differentials to efficiently handle diffuse reflections, we generate footprints at all photon hit points.
The final image is computed by ray tracing with indirect illumination retrieved from the photon map. By combining these with a highly parallel BVH build and density estimation based on photon footprints.
In this paper the image space approach is extended by using multiple environment maps for photon mapping computation to achieve interactive global illumination of dynamic complex scenes.
The key contribution is a new stochastic spatial hashing scheme that achieves a data-parallel construction of a photon map and an efficient range query of a photon map on GPUs. This method provides a very simple way to map computation of progressive photon mapping into data parallel computation. The new hashing scheme achieves about the same performance as the state of the art method in this implementation, but with a significantly simpler algorithm.
In a typical CPU implementation of spatial hashing, each hash entry keeps a list of elements when a hashing collision occurs. This solution is to stochastically store a single photon instead of storing a list of photons at each hash entry. More precisely, given n photons that would be mapped to the same hash entry, we select on photon according to the uniform probability p(x).
Instant Radiosity is a separate class of algorithms similar to photon mapping but is based on gathering rather than density estimation. Instant Radiosity is a two pass technique: In the first pass, photons are emitted and bounced inside the scene. The second pass, each photon is treated as a virtual point light (VPL) that emits light into the scene.
Radiance is calculated using a discrete density of virtual light sources. Radiance is calculated using quasi-Monte Carlo integration and photon transport is done using quasi-random walk.
The goal of bidirectional instant radiosity is to find a relevant set of virtual light sources (VPL’s). Instead of generating VPL’s only from light sources, they are also generated from the camera. The end of such path gives the location of a VPL which can bring light to the camera after one bounce.
A reflective shadow map is an extension of a standard shadow map, where every pixel is considered an incident light source. We render the scene from the perspective of the light source. In a reflective shadow map, with every pixel, we additionally store the light reflected off the hit surface.
This method is a variant on instant radiosity. In this method hardware shadow mapping is employed for determining visibility between the VPLs and the visible surfaces of the scene. Another method is introduced of reusing VPLs so that their shadow maps need not be computed every frame. The goal is VPL management is to keep the distribution of VPLs as close to ideal by removing and adding new VPLs within an allotted budget.
The same geometry causing indirect illumination is captured by an extended shadow map. Instead of iterating over all image pixels and gathering the indirect light from the RSM, we select a subset of RSM pixels, and distribute their light to the image pixels, using a splat in screen space.
Indirect illumination mostly consists of smooth gradiations. We exploit this by approximating visibility for indirect illumination with imperfect shadow maps. Low resolution shadow maps rendered from a crude point-based representation of the scene.
Many LoD’s is a GPU approach to efficiently compute many LoD’s from a bounding volume hierarchy. The scene geometry is subdivided into hierarchal bounding volumes. The algorithm computes a multi-cut in a BVH corresponding to the many LoDs from a large number of viewpoints, using a fine-grained parallelism.
This paper introduces virtual area lights (VALs). Instead of using traditional VPL-based instant radiosity algorithm, we cluster the VPLs into a small number of VALs. Visibility between these few VALs and the scene is computed with a very fast soft shadowing technique instead of using hard shadows for a large number of VPLs.
To compute the global illumination at a point x, instant radiosity approximates the reflected radiance in direction with a set of N VPLs each carrying a radiant flux as
is the distance between VPL I and receiver, and are the angles between VPL I and receiver normal and the transmission direction. is the brdf and is the binary visibility.
To accelerate the visibility computation we group the N VPLs into a much lower number of M clusters (VPLs)
Using a mapping function C : [1…N] -> [1…M] which maps VPL i to the corresponding virtual area light C(i).
To approximate the visibility of the M virtual area lights, any soft shadow algorithm can be used. This paper selects convolution soft shadow maps. The basic idea is to compute a soft shadow with percentage closer filtering.
Many-light approaches are a variant of IR that abstracts the way VPLs are produced. Instead, they are just called ‘lights’. Indirect light and complex direct light such as local area lights or natural illumination from captured environment maps can be supported in one elegant framework.
This paper presents a tensor formulation of the animated many-light problems, where each element of the tensor expresses the contribution of one light to one pixel in one frame. We sparsely sample rows and columns of the tensor, and introduce a clustering algorithm to select a small number of representative lights to efficiently approximate the animation.
Here, a new virtual light type is presented, the virtual spherical light, with the following desirable properties:
The point-wise evaluations of traditional VPLs are replaced by integration over non-zero solid angle, eliminating the spikes caused by narrow glossy BRDF lobes and the geometry term.
Since the VSL acts as a point light in visibility computations, fast GPU shadow mapping can be exploited. The VSL contribution depends only on values local to the surface point and light location, so its estimation becomes a purely numerical kernel ideally suited to evaluation in a GPU shader.
The VSL
approximation:
The contribution of a VSL to a surface sample is
:
sample position
:
photon location
:
surface normal
:
photon normal
:
power of the light
:
vpl sphere radius
The visibility of the VSL is defined to be the visibility between the sample position and the photon location . The indication function is replaced by an additional cosine factor.
A light tree is a binary tree where the leaves are individual lights and the interior nodes are light clusters containing the lights below them in the tree.
A cut through the tree is a set of nodes such that every path from the root of the tree to a leaf will contain exactly on node from the light cut. Thus each cut corresponds to a valid partitioning of the lights into clusters.
To choose a lightcut, we start with a very coarse cut (root of the tree) and progressivelt refine it until out criterion is met.
Each refinement step considers the node in the current cut with the largest error bound. If its error bound is greater than out error ratio times the current total illumination estimate we remove it from the cut, replace it with its two children from the light tree, compute their cluster estimates and error bounds, and update out estimate of the total radiance.
Each tree is built using a greedy, bottom-up-approach by progressively combining pairs of light and/or clusters.
We view the many-light problems as a large matrix of sample-light interactions; the final image is the sum of matrix columns. The key observation is that the inherent structure of the transfer matrix can be revealed by sampling just a small number of rows and columns.
Point based Global Illumination shares some ideas with many-lights approach but also has some fundamental differences e.g. the way visibility is treated. In works in three passes.
In the first pass, the scene surface is approximated using lit surfels (points) on which hierarchy is computed. The points also cover unlit surfaces. Every interior node in this hierarchy stores bounds for the light and the geometry it contains. Next the points are updated. Third, for every pixel, the points are rasterized into a small framebuffer for every pixel.
First a sufel representation of the directly illuminated geometry is created in a precomputation phase and stored in a point cloud. A surfel in a disk-shaped surface element i.e. a point with a normal, radius and color. The surfels are organized in an octree. The illumination from the surfels in each octree node is approximated using spherical harmonics.
To compute the global illumination at a surface point, we add the illumination from all surfels using three degrees of accuracy. Overlapping surfels are ray traced, other nearby surfels are approximated as disks, and distant surfels are accounted for by evaluating the spherical harmonic representation of clusters.
The input to the method is a point cloud of surfels with direct illumination values. The method first organizes the surfels into an octree and computes data for each octree node. Then for each receiving point, the octree is traversed. Then for each receiving point, the octree is traversed, the color contributions of surfels and clusters are rasterized and the color bleeding is computed as a weighted sum of the rasterized pixels.
This method is based on parallel final gathering. At each final gathering location we perform micro-rendering. We traverse and rasterize a hierarchical point-based scene representation into an importance-warped micro-buffer which allows for BRDF importance sampling. The final reflected radiance is computed at each gathering location using the micro-buffers and is then stored in image space.
Micro-rendering method is based on a hierarchical point-based representation of the scene.
For rendering, this hierarchy is traversed starting from the root node: each node’s bounding sphere is projected into micro screen space to compare its size to a given threshold.
The point-based representation of the scene is generated in an offline preprocessing step
In this paper, we present a new method for GPU-based final gathering of virtual point lights. We adopt a single point cloud to represent directly illuminated scene geometry. We project and splat these points into each pixel’s microbuffer, which stores the occluded incoming radiance field.
We create a point cloud sampled from a scene with directly illuminated radiance. Each point is associated with a position, normal, delta surface area and radiance. We sue poisson disk surface sampling to generate points on scene surfaces.
Our goal is to project point to each pixel’s microbuffer which stores the depth and color of the closest projected point. The microbuffer is essentially a small environment map observed at a pixel representing its incoming radiance field.
To improve efficiency, we draw samples stochastically from the point cloud using importance sampling.
Once a point is selected, we project it to the microbuffer, and splat its color if the center of the splat succeeds a depth test. To project we map the line-of-sight direction to the microbuffer using hemi-octahedral mapping.
PRT methods assume that the scene’s geometry is fixed, only lights and views can change. Parts of the light transport can be precomputed enabling real-time rendering of complex light transport effects.
As a preprocess, a global illumination simulator is run over the model that captures how its shadows and scatters light onto itself. The result is recorded as a dense set of vectors (diffuse case) or matrices (glossy case) over the model. At run time incident radiance is projected to the SH basis. The model’s field of transfer vectors or matrices is then applied to the lighting’s coefficient vector. If the object is diffuse, a transfer vector at each point on the object is dotted with the lighting’s coefficients to produce correctly self-scattering shading. If the object is glossy, a transfer matrix is applied to the lighting coefficients to produce the coefficients of a spherical function, representing self-scattering incident radiance at each point. This function is convolved with the object’s BRDF and then evaluated at the view dependent reflection direction to produce the final shading.
Radiance self-transfer encapsulated how an object shadows and scatters light into itself. To represent it, we first parameterize incident lighting point denoted , using the SH basis. Incident lighting is therefore represented as a vector of n2 coefficients . We sample the lighting dynamically and sparsely near the surface, perhaps at only a single point. The assumption is that lighting variation over not due to its own presence is small. We also precompute and store densely over transfer vectors or matrices.
A transfer vector is useful for diffuse surfaces and represent a linear transformation on the lighting vector producing scalar exit radiance, denoted , via inner product.
A transfer matrix is used for glossy surfaces and represents a linear transformation on the lighting vector which produces projection coefficients for and entire spherical function of transferred radiance .
Unshadowed diffuse transfer:
Defined as the scalar function
Producing exit
radiance which is invariant with view angle for diffuse surfaces.
is
the object’s albedo.
is
the cosine weight.
is
the incident radiance.
Shadowed diffuse transfer adds an additional visibility function
We decompose the integral into two functions, using an SH-projection of and the transfer function:
Interreflected diffuse transfer
is the radiance from itself in the direction .
Glossy Transfer
Self transfer for glossy objects can be defined similarity, but generalizes the kernel function to depend on a (view-dependent) reflection direction R rather than a (fixed) normal N. We model glossy reflections as the kernel where a scalar defines the “glossiness” of the specular response.
We can then define the analogous three glossy transfer functions for the unshadowed, shadowed and interreflected cases.
Transfer can be represented as a matrix rather than a vector. For example, glossy shadowed transfer is
Because the SH basis is orthonormal, a scalar function defined over can be projected into its coefficients via the integral:
Orthonormality of the SH basis provides the useful property that given two functions and over , their projections satisfy
An important limitation of precomputed transfer is that material properties of influencing interreflections in and (like albedo or glossiness) must be “baked in” to the preprocessed transfer and can’t be changed at run-time.
As preprocess, we perform a global illumination simulation over an object using the SH basis over the infinite sphere as emitters. Its novelty lies in how it parameterizes the lighting and collects the resulting integrated transfers. The simulation is parameterized by an n-th order SH projection of the unknown sphere of incident light L: by n2 unknown coefficients . The infinitely-distant sphere will be replaced at run-time by the actual incident radiance field around , .
To capture the sphere of directions at sample points , we generate a large (10k-30k), quasi-random set of directions , .
In this first pass, for each , we cast shadow rays in the hemisphere about ’s normal , using the hierarchy to cull directions outside the hemisphere. Self-occluded directions and bins are tagged so that we can perform further interreflection passes on them.
For diffuse surfaces, at each point we further compute the transfer vector by SH-projecting . For glossy surfaces, we compute the transfer matrix by SH-projecting . The result represents the radiance collected at , parameterized by .
Diffuse:
Glossy:
Transfer integration over [shadow pass, iteration 0]
The superscript 0 refers to the iteration number. The vector or matrix at each point is initialized to 0 before the shadow pass, which then sums over all at every .
Later interreflection passes traverse the bins having the occlusion bit set during the shadow pass. Instead of shadow rays, they shoot rays that return transfer from exiting illumination on .
Diffuse:
Glossy:
Transfer integration over [interreflection passes, iteration b]
Since stores incident radiance, it must be convolved with ’s BRDF at to obtain exiting radiance in the direction, yielding a summation over k. si the k-th convolution coefficient. The “reflect” operator simply reflects its first vector argument with respect to its second. Interreflection passes are repeated until the total energy of a given pass falls below a threshold.
Run-time rendering of Radiance Transfer
We now have a model capturing radiance transfer at many point over its surface, represented as vector or matrices. Rendering requires the following step at run-time.
1. Compute incident lighting at one or more sample points near in terms of the SH basis.
2. Rotate these to ’s coordinate frame and blend them to produce a field of incident lighting over .
3. Perform a linear transformation at each point on to obtain exit radiance. This requires a dot product with for diffuse surfaces or a matrix-vector multiplication with for glossy surfaces.
4. Glossy surfaces need a final step in which the radiance vector resulting from step 3 is convolved with ’s BRDF at , and then evaluating at the view-dependent reflection direction R.
A good set of sample points can be obtained using the ICP (iterated closest point) algorithm.
Self-transfer
for Volumetric Models
Self-transfer on
volumetric data uses the same framework as surfaces. Our simple simulator
currently works only for diffuse volumes. For shadowed transfer without
interreflection, we gather energy from the emitter to every voxel of the volume, attenuated by its path
through the volume. To include interreflections, we traverse every voxel and
forward-scatter its transfer along random directions. The transfer is deposited
to all voxels until exiting the volume.
Rendering is performed in the traditional way: by drawing slices through the 3D volume in back to front order using alpha blending to account for transparency.
Radiance
Neighborhood-Transfer
At run-time, an
arbitrary receiver can
be placed in this volume to capture shadows, reflections, and caustics cast by onto without knowing in advance. ’s neighborhood volume must store a
transfer matrix rather than a vector. Our current implementation precomputes
the transfer matrix at each point within a simple 3D grid surrounding . At run-time, we perform the matrix
transform at each point in the volume and upload the result to the graphics
hardware. The result is a volume texture containing coefficients of transferred
radiance, which is applied to .
To shade a point , we need to compute the lighting integral given by
Where is the outgoing radiance for viewing direction , is the incident illumination function, which we represent in the SH basis via
Where are the SH basis functions. By representing the lighting function in the SH basis, the lighting integral then reduces to the simple dot product.
At each point to be shaded, having view factor and local coordinate frame mapping ’s normal to the positive z axis and two chose tangent vectors to the x and y axes we:
1. Rotate lighting coefficients to frame to obtain rotated coefficients .
2. Rotate view vector to local frame to obtain .
3. Lookup BRDF coefficients at yielding
In the simplest case, the global incident lighting coefficients can be constant for all points over an object. This is analogous to using an environment map representing light at infinity. For finite lighting, we can use an incident lighting field which interpolated lighting sampled at various points around the object.
This paper presents a method, based on pre-computed light transport, for real-time rendering of objects under all-frequency, time-varying illumination represented as a high-resolution environment map. The main contribution is to approximate the environment map in a wavelet basis, keeping only the largest term.
Consider direct illumination from an environment map:
is the sample location of a vertex, or a pixel in the image, is the viewing direction, indexes incident direction, is the environment map, is the (binary) visibility function, is the BRDF.
In the image relighting case, depends only on , so the combined transport is given by
Which is easier to write simply in matrix notation,
is the light transport matrix, and are column vectors for computed radiance and incident illumination.
We first compute transport matrix in the ray lighting basis of cubemap pixel lights. We project each row of the raw matrix (corresponding to the dot-product transfer of light from onto a single output location ) onto a wavelet basis. Our transform is 2D Haar over each cubemap face.
We dither and quantize the matrix elements to 6, 7 or 8 bits, depending on the desired level of fidelity and discard all zero coefficients.
We use a very small number of matrix columns to relight each frame. We relight the scene by performing matrix multiplication with the equation: where is sparse because of non-linear approximation, and is sparse because of wavelet encoding.
We propose a new mathematical and computational analysis of pre-computed light transport. We use factored forms, separately pre-computing and representing visibility and material properties. Rendering requires computing triple product integrals at each vertex, involving the lighting, visibility and BRDF.
Factored
representations:
We focus on factored
representations, where visibility and materials (BRDF) are pre-computed and
represented separately in an appropriate basis.
Triple
Product Integral Representations:
Triple product
integrals must be computed in relighting from factored forms. At each vertex,
we must compute an integral of three factors: the lighting, visibility and
BRDF, each of which is represented in basis functions such as spherical
harmonics or wavelets.
Triple
product integral computation:
direct lighting:
is the reflected light, position , outgoing direction , is lighting, is incident direction, is brdf, is binary visibility, is the surface normal.
Basis
Function Expansions:
In analogy with the coupling coefficient for doubling product integrals, we also treat the tripling coefficients for triple product integrals.
There is no simple general formula for tripling coefficients. For spherical harmonics, the correspond to Clebsch-Gordon coefficients.
Unlike double product integrals, which simply reduce to a dot product of coefficients, we see that triple product integrals are substantially more complicated to estimate.
Haar
Tripling Coefficients:
The integral of three
2D Haar basis functions, which we label the tripling coefficients for
those three basis elements is non zero if and only if one of the following
cases hold:
1. All three one of the scaling function. In this case
2. All three occupy the same wavelet square and all are different wavelet types where the square is at level .
3. Two are identical wavelets, and the third is either the scaling function or a wavelet that overlaps at a strictly coarser level.
This techniques alleviates costly sampling of incident radiance using a first-order Taylor expansion of the spherical-harmonic lighting coefficients around a point. Here is proposed an interpolation scheme based on these gradients.
Projecting the incident radiance into spherical harmonics is done by integrating against the SH basis functions
Rendering an object using the SH gradient involves the following steps:
First we pick a single sample locations (usually the centroid of an object) and render a cube map containing exit radiances of the surrounding objects/emitters. We also read the depth buffer and the emitter normal.
We compute the gradients analytically using the cube map.
At each vertex of the object, we now compute the estimated coefficients:
These coefficients are then used to compute the final excitant radiance using the dot-product between the coefficients and the cosine weighted coefficient vector.
This paper combines three ideas from previous work: BRDF factorization, all frequency precomputed radiance transfer using Haar wavelets and Principal Component Analysis for precomputed radiance transfer compression.
Our lighting basis uses Haar wavelets over blocks, called segments, of a cube map. Quantizing or truncation near-zero coefficients then provides a simple way to approximate the lighting that preserves the most important context.
Shading at a point p with view vector v is given by an integral over the hemisphere H of lighting direction s in the local frame.
is the transferred incident radiance function. It is the radiance from the source lighting that arrives at p after including transport effects like self-shadowing from the object.
also rotates the lighting from a global to a local frame.
The BRDF product function is defined as where is the BRDF and is the cosine factor normal component of the incident radiance direction s.
We factor f via
Where and are m-dimensional vector functions purely of view direction and light direction respectively.
Any linear basis for source lighting, such as the spherical harmonic basis, the haar wavelet basis over cube map facer or ever a directional basis, represents radiance via
Where is the ith lighting basis function is its coefficient.
In this lighting basis, the PRT signal becomes a transfer matrix at each point, , a component of which is given by
Where is a scalar spherical function representing radiance from the jth lighting basis function,. ’s row represent contribution to one component of transferred incident radiance corresponding to . Its column represent the response to one lighting basis function, .
The shading result is given simply by
is the m-dimensional row vector formed by transposing the column-vector BRDF factor , is the transfer matrix at p, and is the vector of lighting coefficients.
To factor the BRDF product function , we begin by forming a matrix whose components are with view samples, and light samples . The viewing and lighting directions are parameterized using the parabolic map. We then perform the singular value decomposition on the matrix and set all but the largest m singular values to zero.
PRT
computation
We outline our
precomputation of the PRT signal .
Currently, out implementation only handles direct shadowing effects and ignores
inter-reflection.
At each mesh vertex p, we first compute a visibility map, at directional samples which returns 0 is p is shadowed in the direction and 1 if unshadowed.
From the visibility map, we then compute a “raw” transfer matrix signal, which integrates against the BRDF basis function
is the cone of direction within one cubemap texel of the direction , is the bilinear basis function on the cubemap centered at the sample and rotates the direction from the global frame to the local frame.
We then compress using principal component analysis over each transfer segment. We apply the Haar wavelet transform to the representative matrices in each cluster and quantize them into 16 bits of precision, followed by a lossless sparsity coding.
PRT Rendering
1. Project the time-varying lighting environment onto the cubemap and then into the Haar basis over each segment to obtain the lighting vector .
2. For each transfer segment, transform the lighting through each cluster’s representatives to obtain
3. At each vertex, reconstruct the transferred radiance vector using a weighted combination of the .
4.
Compute the local
view direction and
return the dot product of with .
We present a technique for interactive rendering of glossy objects in complex and dynamic lighting environments that capture interreflections and all-frequency shadows. Our system is based on precomputed radiance transfer and separable BRDF approximation.
The current mathematical framework of out technique requires a BRDF parameterization in incident and view dependent directions. To factorize, we typically apply a separable decomposition, which approximates a 4D BRDF , as the sum of products of 2D functions ’s and ’s.
Where is the incident direction is the view direction, and K is the number of approximation terms. The factorization typically computed using singular value decomposition (SVD).
The outgoing radiance at a surface location x in view direction is represented in compact matrix notation as
is the light vector, <> is the inner product, is called the view –dependent k-vector, which is produced by texture lookups of into all BRDF view maps. is the precomputed transport matrix, the rows of which are the transport function. The multiplication of with produces a k-vector which we call the light dependent k-vector.
We use a multi-pass gathering approach that is straight forward adaptation of the jabobi iterations well known in radiosity. We call the direction illumination step in 0th path, which computes a set of direct transport vectors. In classic radiosity, global illumination is computed one step at a time: the 0th pass computes outgoing radiance for every surface location due to indirect illumination; each following pass computes bounced outgoing radiance for every surface location by gathering reflected radiance from all other surface locations. Our method is different in that for every surface location we gather transport vector, instead of radiance values, from all other surface locations. The gathering process produces a new set of transport vectors, which we call the bounced transport vectors.
This paper presents several techniques that effectively combine normal mapping and precomputed radiance transfer for rigid objects. In particular, it investigates representing the convolved radiance function in various bases and borrowing concepts from the separable decomposition of BRDF’s.
Any point on the surface of an object a transfer matrix represents how distant lighting expressed in same lighting basis (spherical harmonics for this work) maps to transferred incident radiance. If the object has complex normal variation, the incident radiance is a smooth function, while the outgoing radiance has more variations. Decoupling normal variation from incident radiance makes practical rendering objects with complex surface variation.
In brief, this paper makes the following contributions:
A novel representation for PRT data and radiance functions based on SRBFs is introduced, which allows a compact data representation and real-time rendering of complex objects under high-frequency lighting environments.
A new technique for analyzing multi-dimensional data is proposed, which iteratively re-classifies cluster members to search for a locally optimal solution.
A new approach for modeling area light sources, such as high dynamic range (HDR) environment maps, with scattered SRBFs is also presented, which may be promising for other problems, including the importance sampling of spherical functions.
The irradiance volume represents a volumetric approximation of the irradiance function. The volume is built in an environment as a pre-process, and can then be used by and application to quickly approximate the irradiance at locations within the environment.
If we compute the irradiance for all possible orientations of a small patch, we can plot these irradiances as a radial function. We call this the irradiance distribution function at the point.
An irradiance distribution function can be computed at every point in space, yielding a 5-D function. This function represents the irradiance of a hypothetical differential surface oriented at any location and direction within space .
Suppose we have a volumetric approximation to , within the space enclosed by an environment. This approximation is what we call the irradiance volume, and the key assumption is that we can approximate accurately enough that the visual artifacts of are not severe. The simplest way to approximate a function is to evaluate it at a finite set of point and use interpolation techniques.
The irradiance volume is compute as follows:
1. Subdivide the bounding box of the scene into a regular grid.
2. For any grid cells that contain geometry, subdivide into a finer grid.
3. At each vertex in the grid, approximate the irradiance distribution function.
The irradiance distribution function at a point is approximated using the following procedure:
1. Given a directional sampling resolution, choose a set of directions over the sphere of directions in which to sample radiance.
2. In each direction chosen, determine and store the radiance.
3. Using the stored radiance, compute the irradiance distribution function.
At each grid vertex in the volume, the radiance is sampled in a pre-computed set of directions, . Each radiance value is stored in an array and is used to compute the irradiance distribution at that point once the sampling is finished.
The irradiance in a given direction is computed for hypothetical surface whose normal vector points in that direction. Given a directional set of radiance samples , taken at a point, x, in space, the irradiance in direction is calculated using the formula:
Where is the radiance seen in the direction from point , is the solid angle of the bin associated with and is the number of bins.
Here three distinct data structures are used: samples, cells and grids. Samples contain directional irradiance values corresponding to a particular point in the environment. A cell represents a box in space bounded by eight samples, one at each of its corners. A grid is a three-dimensional array of cells. Each cell may also contain another grid, forming a bilevel structure.
Given a point, , and a direction, , querying the irradiance from the volume requires the following steps:
1. Calculate which cell in the first-level grid contains .
2. If the cell contains a grid, calculate which cell in the second-level grid contains .
3. Find which data value in the cell’s samples corresponding to .
4. Given the position of within the cell and the eight values from the surrounding samples. Interpolate to get the irradiance.
We present a novel real-time technique for computing inter-object ambient occlusion. For each occluding object, we precompute a field in the surrounding space that encodes an approximation of the occlusion caused by the object. This volumetric information is then used at run-time for quickly determining the shadow cost on the receiving object.
We approximate the occluder by a spherical cap when computing the ambient occlusion on the receiving surfaces.
Main contributions:
· A spherical cap approximation for fast computation of ambient occlusion.
· A radial parameterization of space and simple models for the subtended solid angle and the average direction of occlusion in order to compactly store the data
· A practical method for combining occluders.
To quickly determine ambient occlusion at an arbitrary point in space around an occlude, we approximate the visibility of the occlude with a spherical cap.
We define as the visibility function of a cap from position towards direction . has a value of 1 when falls within the cap and 0 otherwise. The direction of the cap is the average direction of occlusion.
We approximate the solid angle:
In order to fit the above model to data, the coefficients , and have to be determined for each direction.
Here is presented a new method: matrix radiance transfer. This paper generalizes the previous radiance transfer methods to work with a matrix representation of the BRDF and optimize exit radiance computation by expressing the exit radiance in a new, directionally locally supported basis set. Instead of spherical harmonics, we compress our radiance transfer matrices through principal component analysis.
A radiance regression function (RRF) represents a non-linear mapping from local and contextual attributes of surface points, such as position, viewing direction, and lighting conditions, to their indirect illumination values.
We model the RRF as multilayer acyclic feed-forward neural network, which provides a close functional approximation of the indirect illumination and can be efficiently evaluated at run time.
The indirect illumination can be approximated using a regression function. We define the radiance regression function at surface point to be which represents a map from the total number of parameters to R3.
The training data we use consists of a set of N input-output pairs that sample the indirect illumination . , . is the input vector and is the corresponding output vector. The radiance regression function is determined by minimizing the least squares error.
We use a neural network with 2 hidden layers. The training set is constructed by sampling light positions and viewpoints, and tracing rays from the viewpoint towards points in the scene to determine their indirect illumination. The number of training samples is roughly ten times the number of weights in w.
After training the neural network, the indirect illumination of each scene point can be rendered under different lighting and view conditions.
|
Author(s) |
Title |
Year |
Citation |
Index |
|
Photon Mapping |
|
|
|
|
|
Ma and McCool |
Low latency photon mapping using block hashing. |
2002 |
Ma, Vincent CH, and Michael D. McCool. "Low latency photon mapping using block hashing." Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware. Eurographics Association, 2002. |
[1] |
|
Dmitriev et al. |
Interactive global illumination using selective photon tracing. |
2002 |
Dmitriev, Kirill, et al. "Interactive global illumination using selective photon tracing." Rendering Techniques 2002 (2002): 100-113. |
[2] |
|
Purcell et al. |
Photon mapping on programmable graphics hardware. |
2003 |
Purcell, Timothy J., et al. "Photon mapping on programmable graphics hardware." Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware. Eurographics Association, 2003. |
[3] |
|
Kruger et al. |
Interactive screen-space accurate photon tracing on GPUs. |
2006 |
Krüger, Jens H., Kai Bürger, and Rüdiger Westermann. "Interactive Screen-Space Accurate Photon Tracing on GPUs." Rendering Techniques 2006 (2006): 17th. |
[4] |
|
Zhou et al. |
Real-time KD-tree construction on graphics hardware. |
2008 |
Zhou, Kun, et al. "Real-time kd-tree construction on graphics hardware." ACM Transactions on Graphics (TOG) 27.5 (2008): 126. |
[5] |
|
Wang et al. |
An efficient GPU-based approach for interactive global illumination. |
2009 |
Wang, Rui, et al. "An efficient GPU-based approach for interactive global illumination." ACM Transactions on Graphics (TOG) 28.3 (2009): 91. |
[6] |
|
McGuire et al. |
Hardware-accelerated global illumination by image space photon mapping. |
2009 |
McGuire, Morgan, and David Luebke. "Hardware-accelerated global illumination by image space photon mapping." Proceedings of the Conference on High Performance Graphics 2009. ACM, 2009. |
[7] |
|
Fabianowski and Dingliana |
Interactive global photon mapping. |
2009 |
Fabianowski, Bartosz, and John Dingliana. "Interactive global photon mapping." Computer Graphics Forum. Vol. 28. No. 4. Blackwell Publishing Ltd, 2009. |
[8] |
|
Yao et al. |
Multi-image based photon tracing for interactive global illumination of dynamic scenes. |
2010 |
Yao, Chunhui, et al. "Multi‐Image Based Photon Tracing for Interactive Global Illumination of Dynamic Scenes." Computer Graphics Forum. Vol. 29. No. 4. Blackwell Publishing Ltd, 2010. |
[9] |
|
Hachisuka and Jensen |
Parallel progressive photon mapping on GPUs. |
2010 |
Hachisuka, Toshiya, and Henrik Wann Jensen. "Parallel progressive photon mapping on GPUs." ACM SIGGRAPH ASIA 2010 Sketches. ACM, 2010. |
[10] |
|
Many Lights |
|
|
|
|
|
Hasan et al. |
Tensor clustering for rendering many-light animations. |
2008 |
Hašan, Miloš, et al. "Tensor Clustering for Rendering Many‐Light Animations." Computer Graphics Forum. Vol. 27. No. 4. Blackwell Publishing Ltd, 2008. |
[11] |
|
HKWB09 |
Virtual spherical lights for many-light rendering of glossy scenes. |
2009 |
Hašan, Miloš, et al. "Virtual spherical lights for many-light rendering of glossy scenes." ACM Transactions on Graphics (TOG). Vol. 28. No. 5. ACM, 2009. |
[12] |
|
Walter et al. |
Lightcuts: a scalable approach to illumination |
2005 |
Walter, Bruce, et al. "Lightcuts: a scalable approach to illumination." ACM Transactions on Graphics (TOG). Vol. 24. No. 3. ACM, 2005. |
[13] |
|
Hasan et al |
Matrix row-column sampling for the many-light problem. |
2007 |
Hašan, Miloš, Fabio Pellacini, and Kavita Bala. "Matrix row-column sampling for the many-light problem." ACM Transactions on Graphics (TOG). Vol. 26. No. 3. ACM, 2007. |
[14] |
|
Instant Radiosity |
|
|
|
|
|
Keller |
Instant Radiosity |
1997 |
Keller, Alexander. "Instant radiosity." Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 1997. |
[15] |
|
Dachsbacher and Stamminger |
Reflective Shadow Maps |
2005 |
Dachsbacher, Carsten, and Marc Stamminger. "Reflective shadow maps." Proceedings of the 2005 symposium on Interactive 3D graphics and games. ACM, 2005. |
[16] |
|
Dachsbacher and Stamminger |
Splatting Indirect Illumination |
2006 |
Dachsbacher, Carsten, and Marc Stamminger. "Splatting indirect illumination." Proceedings of the 2006 symposium on Interactive 3D graphics and games. ACM, 2006. |
[17] |
|
SIMP06a |
Bidirectional instant radiosity |
2006 |
Segovia, Benjamin, et al. "Bidirectional Instant Radiosity." Rendering Techniques. 2006. |
[18] |
|
Laine et al. |
Incremental instant radiosity for real-time indirect illumination |
2007 |
Laine, Samuli, et al. "Incremental instant radiosity for real-time indirect illumination." Proceedings of the 18th Eurographics conference on Rendering Techniques. Eurographics Association, 2007. |
[19] |
|
Ritschel et al. |
Imperfect shadow maps for efficient computation of indirect illumination |
2008 |
Ritschel, Tobias, et al. "Imperfect shadow maps for efficient computation of indirect illumination." ACM Transactions on Graphics (TOG) 27.5 (2008): 129. |
[20] |
|
Dong et al. |
Real-time indirect illumination with clustered visibility. |
2009 |
Dong, Zhao, et al. "Real-time Indirect Illumination with Clustered Visibility." VMV. Vol. 9. 2009. |
[21] |
|
Novak et al. |
Screen-space bias compensation for interactive high-quality global illumination with virtual point lights |
2011 |
Novák, Jan, Thomas Engelhardt, and Carsten Dachsbacher. "Screen-space bias compensation for interactive high-quality global illumination with virtual point lights." Symposium on Interactive 3D Graphics and Games. ACM, 2011. |
[22] |
|
Ritschel et al. |
Making imperfect shadow maps view-adaptive: high quality global illumination in large dynamic scenes. |
2011 |
Ritschel, Tobias, et al. "Making Imperfect Shadow Maps View‐Adaptive: High‐Quality Global Illumination in Large Dynamic Scenes." Computer Graphics Forum. Vol. 30. No. 8. Blackwell Publishing Ltd, 2011. |
[23] |
|
Hollander et al. |
ManyLoDs: Parallel many-view level-of-detail selection for real-time global illumination. |
2011 |
Hollander, Matthias, et al. "ManyLoDs: Parallel Many‐View Level‐of‐Detail Selection for Real‐Time Global Illumination." Computer Graphics Forum. Vol. 30. No. 4. Blackwell Publishing Ltd, 2011. |
[24] |
|
Finite Elements |
|
|
|
|
|
Coombe et al. |
Radiosity on graphics hardware |
2004 |
Coombe, Greg, Mark J. Harris, and Anselmo Lastra. "Radiosity on graphics hardware." Proceedings of Graphics Interface 2004. Canadian Human-Computer Communications Society, 2004. |
[25] |
|
Bunnell et al. |
Dynamic Ambient Occlusion and Indirect Lighting. |
2005 |
Bunnell, Michael. "Dynamic ambient occlusion and indirect lighting." Gpu gems 2.2 (2005): 223-233. |
[26] |
|
Dong et al. |
Interactive global illumination using implicit visibility |
2007 |
Dong, Zhao, et al. "Interactive global illumination using implicit visibility." Computer Graphics and Applications, 2007. PG'07. 15th Pacific Conference on. IEEE, 2007. |
[27] |
|
Dachsbacher et al. |
Implicit visibility and antiradiance for interactive global illumination |
2007 |
Dachsbacher, Carsten, et al. "Implicit visibility and antiradiance for interactive global illumination." ACM Transactions on Graphics (TOG). Vol. 26. No. 3. ACM, 2007. |
[28] |
|
Meyer et al. |
Data-parallel hierarchical link creation for radiosity. |
2009 |
Meyer, Quirin, et al. "Data-Parallel Hierarchical Link Creation for Radiosity." EGPGV. 2009. |
[29] |
|
Thiedemann et al. |
Voxel-based global illumination |
2011 |
Thiedemann, Sinje, et al. "Voxel-based global illumination." Symposium on Interactive 3D Graphics and Games. ACM, 2011. |
[30] |
|
Point Based |
|
|
|
|
|
Christensen |
Point-Based approximate color bleeding. |
2008 |
Christensen, Per. "Point-based approximate color bleeding." Pixar Technical Notes 2.5 (2008): 6. |
[31] |
|
Ritschel et al. |
Micro-rendering for scalable, parallel final gathering. |
2009 |
Ritschel, Tobias, et al. "Micro-rendering for scalable, parallel final gathering." ACM Transactions on Graphics (TOG) 28.5 (2009): 132. |
[32] |
|
Hollander et al. |
ManyLoDs: Parallel many-view level-of-detail selection for real-time global illumination. |
2011 |
Hollander, Matthias, et al. "ManyLoDs: Parallel Many‐View Level‐of‐Detail Selection for Real‐Time Global Illumination." Computer Graphics Forum. Vol. 30. No. 4. Blackwell Publishing Ltd, 2011. |
[33] |
|
Maletz and Wang |
Importance point projection for GPU-based final gathering. |
2011 |
Maletz, David, and Rui Wang. "Importance Point Projection for GPU‐based Final Gathering." Computer Graphics Forum. Vol. 30. No. 4. Blackwell Publishing Ltd, 2011. |
[34] |
|
Precomputed Radiance Transfer |
|
|
|
|
|
Sloan et al. |
Precomputed radiance transfer for real-time rendering in dynamic low-frequency lighting environments |
2002 |
Sloan, Peter-Pike, Jan Kautz, and John Snyder. "Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments." ACM Transactions on Graphics (TOG). Vol. 21. No. 3. ACM, 2002. |
[35] |
|
Kautz et al. |
Fast arbitrary BRDF shading for low-frequency lighting using spherical harmonics |
2002 |
Kautz, Jan, John Snyder, and Peter-Pike J. Sloan. "Fast Arbitrary BRDF Shading for Low-Frequency Lighting Using Spherical Harmonics." Rendering Techniques 2 (2002): 291-296. |
[36] |
|
Ng et al. |
All frequency shadows using non-linear wavelet lighting approximation |
2003 |
Ng, Ren, Ravi Ramamoorthi, and Pat Hanrahan. "All-frequency shadows using non-linear wavelet lighting approximation." ACM Transactions on Graphics (TOG). Vol. 22. No. 3. ACM, 2003. |
[37] |
|
Ng et al. |
Triple product wavelet integrals for all-frequency relighting. |
2004 |
Ng, Ren, Ravi Ramamoorthi, and Pat Hanrahan. "Triple product wavelet integrals for all-frequency relighting." ACM Transactions on Graphics (TOG) 23.3 (2004): 477-487. |
[38] |
|
Annen et al. |
Spherical harmonic gradients for mid-range illumination. |
2004 |
Annen, Thomas, et al. "Spherical harmonic Gradients for Mid-Range Illumination." Rendering Techniques. 2004. |
[39] |
|
Liu et al. |
All frequency precomputed radiance transfer for glossy objects. |
2004 |
Liu, Xinguo, et al. "All-Frequency Precomputed Radiance Transfer for Glossy Objects." Rendering Techniques 2004 (2004). |
[40] |
|
Wang et al. |
All-frequency relighting of glossy objects |
2006 |
Wang, Rui, John Tran, and David Luebke. "All-frequency relighting of glossy objects." ACM Transactions on Graphics (TOG) 25.2 (2006): 293-318. |
[41] |
|
Sloan et al. |
Normal mapping for precomputed radiance transfer. |
2006 |
Sloan, Peter-Pike. "Normal mapping for precomputed radiance transfer." Proceedings of the 2006 symposium on Interactive 3D graphics and games. ACM, 2006. |
[42] |
|
Tsai and Shih |
All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation. |
2006 |
Tsai, Yu-Ting, and Zen-Chung Shih. "All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation." ACM Transactions on Graphics (TOG) 25.3 (2006): 967-976. |
[43] |
|
Green et al. |
view-dependent precomputed light transport using nonlinear Gaussian function approximations. |
2006 |
Green, Paul, et al. "View-dependent precomputed light transport using nonlinear gaussian function approximations." Proceedings of the 2006 symposium on Interactive 3D graphics and games. ACM, 2006. |
[44] |
|
Green et al. |
Efficient reflectance and visibility approximations for environment map rendering. |
2007 |
Green, Paul, Jan Kautz, and Frédo Durand. "Efficient reflectance and visibility approximations for environment map rendering." Computer Graphics Forum. Vol. 26. No. 3. Blackwell Publishing Ltd, 2007. |
[45] |
|
Akerlund et al. |
Precomputed visibility cuts for interactive relighting with dynamic BRDFs. |
2007 |
Akerlund, Oskar, Mattias Unger, and Rui Wang. "Precomputed visibility cuts for interactive relighting with dynamic BRDFs." Computer Graphics and Applications, 2007. PG'07. 15th Pacific Conference on. IEEE, 2007. |
[46] |
|
Sun and Ramamoorthi |
Interactive relighting of dynamic refractive objects. |
2007 |
Sun, Xin, et al. "Interactive relighting of dynamic refractive objects." ACM Transactions on Graphics (TOG). Vol. 27. No. 3. ACM, 2008. |
[47] |
|
Xu et al. |
Spherical piecewise constant basis functions for all-frequency precomputed radiance transfer. |
2008 |
Xu, Kun, et al. "Spherical piecewise constant basis functions for all-frequency precomputed radiance transfer." IEEE Transactions on Visualization and Computer Graphics 14.2 (2008): 454-467. |
[48] |
|
Lehtinen et al. |
Meshless finite elements for hierarchical global illumination. |
2008 |
Lehtinen, Jaakko, et al. "Meshless finite elements for hierarchical global illumination." (2007). |
[49] |
|
Sun et al. |
Affine double and triple product wavelet integrals for rendering. |
2009 |
Sun, Bo, and Ravi Ramamoorthi. "Affine double-and triple-product wavelet integrals for rendering." ACM Transactions on Graphics (TOG) 28.2 (2009): 14. |
[50] |
|
Ritschel et al. |
Interactive illumination with coherent shadow maps. |
2007 |
Ritschel, Tobias, et al. "Interactive illumination with coherent shadow maps." Proceedings of the 18th Eurographics conference on Rendering Techniques. Eurographics Association, 2007. |
[51] |
|
Ritschel et al. |
Interactive global illumination based on coherent surface shadow maps. |
2008 |
Ritschel, Tobias, et al. "Interactive global illumination based on coherent surface shadow maps." Proceedings of Graphics Interface 2008. Canadian Information Processing Society, 2008. |
[52] |
|
Greger et al. |
The irradiance volume. |
1998 |
Greger, Gene, et al. "The irradiance volume." IEEE Computer Graphics and Applications 18.2 (1998): 32-43. |
[53] |
|
Kontkanen et Laine |
Ambient occlusion fields. |
2005 |
Kontkanen, Janne, and Samuli Laine. "Ambient occlusion fields." Proceedings of the 2005 symposium on Interactive 3D graphics and games. ACM, 2005. |
[54] |
|
Kontkanen et Aila |
Ambient occlusion for animated characters. |
2006 |
Kontkanen, Janne, and Timo Aila. "Ambient Occlusion for Animated Characters." Rendering techniques. 2006. |
[55] |
|
Green et al. |
View-dependent precomputed light transport using nonlinear Gaussian function approximations. |
2006 |
Green, Paul, et al. "View-dependent precomputed light transport using nonlinear gaussian function approximations." Proceedings of the 2006 symposium on Interactive 3D graphics and games. ACM, 2006. |
[56] |
|
Green et al. |
Efficient reflectance and visibility approximations for environment map rendering. |
2007 |
Green, Paul, Jan Kautz, and Frédo Durand. "Efficient reflectance and visibility approximations for environment map rendering." Computer Graphics Forum. Vol. 26. No. 3. Blackwell Publishing Ltd, 2007. |
[57] |
|
Tsai et al. |
All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation. |
2006 |
Tsai, Yu-Ting, and Zen-Chung Shih. "All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation." ACM Transactions on Graphics (TOG) 25.3 (2006): 967-976. |
[58] |
|
Sun et al. |
Interactive relighting with dynamic BRDFs. |
2007 |
Sun, Xin, et al. "Interactive relighting with dynamic BRDFs." ACM Transactions on Graphics (TOG) 26.3 (2007): 27. |
[59] |
|
Sun et al. |
Interactive relighting of dynamic refractive objects. |
2008 |
Sun, Xin, et al. "Interactive relighting of dynamic refractive objects." ACM Transactions on Graphics (TOG). Vol. 27. No. 3. ACM, 2008. |
[60] |
|
Xu et al. |
Spherical piecewise constant basis functions for all-frequency precomputed radiance transfer. |
2008 |
Xu, Kun, et al. "Spherical piecewise constant basis functions for all-frequency precomputed radiance transfer." IEEE Transactions on Visualization and Computer Graphics 14.2 (2008): 454-467. |
[61] |
|
Lehtinen et al. |
Meshless finite elements for hierarchical global illumination. |
2008 |
Lehtinen, Jaakko, et al. "Meshless finite elements for hierarchical global illumination." (2007). |
[62] |
|
Sloan et al. |
Clustered principal components for precomputed radiance transfer. |
2003 |
Sloan, Peter-Pike, et al. "Clustered principal components for precomputed radiance transfer." ACM Transactions on Graphics (TOG) 22.3 (2003): 382-391. |
[63] |
|
Lehtinen et al. |
Matrix radiance transfer. |
2003 |
Lehtinen, Jaakko, and Jan Kautz. "Matrix radiance transfer." Proceedings of the 2003 symposium on Interactive 3D graphics. ACM, 2003. |
[64] |
|
Wang et al. |
Precomputed radiance transfer for real-time indirect lighting using a spectral mesh basis. |
2007 |
Wang, Rui, Jiajun Zhu, and Greg Humphreys. "Precomputed radiance transfer for real-time indirect lighting using a spectral mesh basis." Proceedings of the 18th Eurographics conference on Rendering Techniques. Eurographics Association, 2007. |
[65] |
|
Wang et al. |
All-frequency interactive relighting of translucent objects with single and multiple scattering. |
2005 |
Wang, Rui, John Tran, and David Luebke. "All-frequency interactive relighting of translucent objects with single and multiple scattering." ACM Transactions on Graphics (TOG) 24.3 (2005): 1202-1207. |
[66] |
|
Annen et al. |
Spherical harmonic gradients for mid-range illumination. |
2005 |
Annen, Thomas, et al. "Spherical harmonic Gradients for Mid-Range Illumination." Rendering Techniques. 2004. |
[67] |
|
Sloan et al. |
Image-based proxy accumulation for real-time soft global illumination. |
2007 |
Sloan, Peter-Pike, et al. "Image-based proxy accumulation for real-time soft global illumination." Computer Graphics and Applications, 2007. PG'07. 15th Pacific Conference on. IEEE, 2007. |
[68] |
|
Yu et al. |
Perceptual influence of approximate visibility in indirect illumination. |
2009 |
Yu, Insu, et al. "Perceptual influence of approximate visibility in indirect illumination." ACM Transactions on Applied Perception (TAP) 6.4 (2009): 24. |
[69] |
|
Ihrke et al. |
Eikonal rendering. |
2007 |
Ihrke, Ivo, et al. "Eikonal rendering: Efficient light transport in refractive objects." ACM Transactions on Graphics (TOG). Vol. 26. No. 3. ACM, 2007. |
[70] |
|
Sun et al. |
Interactive relighting of dynamic refractive objects. |
2008 |
Sun, Xin, et al. "Interactive relighting of dynamic refractive objects." ACM Transactions on Graphics (TOG). Vol. 27. No. 3. ACM, 2008. |
[71] |
|
Irradiance Caching |
|
|
|
|
|
Ward et al. |
A ray tracing solution for diffuse interreflection. |
1988 |
Ward, Gregory J., Francis M. Rubinstein, and Robert D. Clear. "A ray tracing solution for diffuse interreflection." ACM SIGGRAPH Computer Graphics 22.4 (1988): 85-92. |
[72] |
|
Tole et al. |
Interactive global illumination in dynamic scenes. |
2002 |
Tole, Parag, et al. "Interactive global illumination in dynamic scenes." ACM Transactions on Graphics (TOG). Vol. 21. No. 3. ACM, 2002. |
[73] |
|
ward et al. |
Irradiance Gradients |
1992 |
Ward, Gregory J., and Paul Heckbert. "Irradiance gradients." Third Eurographics Workshop on Rendering. Vol. 8598. 1992. |
[74] |
|
Ward et al. |
The RADIANCE Light Simulation and Rendering System |
1994 |
Ward, Gregory J. "The RADIANCE lighting simulation and rendering system." Proceedings of the 21st annual conference on Computer graphics and interactive techniques. ACM, 1994. |
[75] |
|
Deep Learning |
|
|
|
|
|
Ren et al. |
Global illumination with radiance regression functions |
2013 |
Ren, Peiran, et al. "Global illumination with radiance regression functions." ACM Transactions on Graphics (TOG) 32.4 (2013): 130. |
[76] |


Back
Technical
calculator 009
Jan 6
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Random Maori Proverbs 007
Nov 20
JavaScript language 006
Nov 2
Problem Solving 005
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JavaScript basics 004
Oct 9
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May 15
Html Css Dom 002
May 15
Html Css Dom 001
May 15


N-Gram collections with corresponding statistics (frequencies or probabilities) for n-grams in order range.
N-Gram collections with corresponding statistics (frequencies or probabilities) for n-grams with given order.
N-Gram collections with corresponding statistics (frequencies or probabilities).
N-gram frequencies collections functionality.
N-gram probabilities collections functionality.
N-gram statistics collections functionality.


I took my first dose of clonazepam because I ran out of oxy and hydrocodone. It was late night, about 1am and I had absolutely nothing to do the next day. I knew almost nothing about klonopin (clonazepam) when I took it, but I have a ready supply because my parent takes it regularly and gets a 3 month supply at a time. I took two 2mg pills around 1pm and after about 30 minutes, nothing really happened. So I figured this was a waste. No big deal I will get on the computer and research some other recreational drugs.
Well about 2pm the screen started wobbling back and forth, and as soon as I stood up, I fell directly onto my bed. I am a small guy 150lbs, so I'm not sure what doseage I would reccomend, but 4mg put me on my back. I layed down under my covers in the dark (that's the way I like to enjoy my hydrocodone highs) and from then on it turned into a pleasant feeling of carelessness.
Once I got used to the feeling I could get up and walk, but speech was slurred. I couldn't really care less about what anyone else who might have been around me said or thought. I was in my own world. It was great. I wouldn't recommend drinking alcohol or mixing clonazepam with other drugs, I think the effect would be too intense. The only negative effect of this drugs, if you can call it that, is that the next day asfter I took it, I slept until 6:30pm and had to be woken up at that time. This drug knocked me out for the long haul!
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


{# Be aware that we need these extra new lines here or marked will not realise that the
- thus breaking the HTML #}


Full Name is required
Birth Date is required
Address is required
City is required
State is required
Postcode is required
Country is required


| Watch | Price | Actions | ||||
|---|---|---|---|---|---|---|
Rolex Submariner |
$100.00 |
|
||||
Rolex Submariner |
$100.00 |
|
||||
Rolex Submariner |
$100.00 |
|
||||
| Continue Shopping | Total: $10.00 |


{% extends "common/base/base.html" %} {% block content %} {% load bootstrap4 %} Edit Playlist Delete Playlist {% endblock %}


Ever feel lost waiting for the long lines, the slow traffic, the never ending frisking? No longer... Cherry & some dude named Jon have invented the most magical invention of the 21st Century, and with it the world will change...


The orbital theory of climate change first elaborated in the 19 th century 1 was subsequently confirmed to exert a strong control on global climate, as evident from pioneering paleoceanographic studies showing regular orbital obliquity (41,000 yr cycles) and precession (19,000–23,000 yr cycles) in benthic foraminifera δ 18O associated with changing ice volume on the continents 2, 3. The orbital paradigm suggests that Northern Hemisphere Summer Insolation on June 21 at 65°N latitude (hereafter NHSI) controls global climate via variations in ice sheet extent, which in turn exert responses in temperature and atmospheric and oceanic circulation. However, in many continental regions the role of orbital variations in paleoclimate remains poorly known due to the difficulty of obtaining long absolutely dated paleoclimate records. For example, controls on Great Basin paleoclimate have been debated since the classic 19 th century monographs on Pluvial Lakes Lahontan and Bonneville 4– 7 (Fig. 1). Despite this work, a lack of highly resolved records spanning orbital timescales makes it difficult to attribute the past controls on Western North America (WNA) paleoclimate and to facilitate future projections.
Phasing relationships for insolation and Great Basin Paleoclimate. ( A) Is 65°N June 21 insolation; ( B) is Leviathan chronology and band-pass filter; U-series ages are shown in blue for Leviathan chronology. Yellow and blue backgrounds are marine isotope stages 1–6. Circles are ages of peaks and troughs in band-pass filtered data. Stars indicate TII and inceptions (see text).
An exception is the well-dated 175,000 yr-long 8 speleothem oxygen isotope record from caves in Nevada, based on records from Leviathan, Pinnacle, and Lehman Caves 8, 9. Several features of the Leviathan chronology suggest that it is a reliable proxy for Great Basin climate variations: it is securely dated with 65 high-precision U-series ages; the stalagmites grew in near-surface vadose zone caves <100 m from the land surface in areas of rapid infiltration of winter precipitation, ensuring a short response time to atmospheric climate changes, the predominant source of aquifer recharge; and modern stalagmite calcite forms in isotopic equilibrium with cave drip waters 8. Further, the δ 18O time series showed a strong NHSI control on continental paleoclimate, with climate lagging insolation by a few thousand years. However, the origin and quantification of this lag has not been completed, hampering our ability to identify plausible forcing mechanisms. Here, we investigate the orbital-scale phasing relationships between Nevada paleoclimate and insolation forcing over the past 175,000 years, and highlight several key features of the δ 18O time series that support a fast climate response to precessional-scale forcing in the Great Basin of western North America.


| 接口 | 说明 |
|---|---|
| Navigator |
Handler class for responding on navigation requests.
|
| 类 | 说明 |
|---|---|
| ActiveProcessDefinitionNavigator | |
| DatabaseNavigator | |
| DefaultNavigator | |
| DeploymentNavigator | |
| GroupNavigator | |
| JobNavigator | |
| ManagementNavigator | |
| MyProcessesNavigator | |
| NavigationFragmentChangeListener |
FragmentChangedListener that is responsible to navigating the application to the right
page depending on the URI fragment.
|
| NavigatorManager | |
| ProcessInstanceNavigator | |
| ProcessModelNavigator | |
| ProcessNavigator | |
| ReportNavigator | |
| SavedReportNavigator | |
| SuspendedProcessDefinitionNavigator | |
| TaskNavigator | |
| UriFragment |
Class containing parts of an uri-fragment (eg: "task", "inbox", "123") and
parameters based on the URL's query string.
|
| UserNavigator |
Copyright © 2017 Alfresco. All rights reserved.


About the author
VeraPish is a web app developed by myself (Óscar Iglesias) in the context of an Universitary Information Security Master of Science End of Degree project at UNIR in Spain.
I am an Electrical engineer working for many years in telecommunication operators. Lately, as a Cybersecurity Product Manager in Vodafone Spain. You can check my LinkedIn profile in here.
Perfectly aware of the fact that I am not an outstanding developer, but I thought companies could take advantage of this web application easily. Also perhaps someone else wants to build anything much better on top of that, so I decided to license it as MIT (free to use and modify).
Will be more than happy to hear from you in case you use my contribution or leverage on it somehow, through any of the above commented channels.
Enjoy it and take care!
Óscar Iglesias.


Program Leaders
-
Launch Director
Shailesh Murali -
BlackMagic Lead
Jonathan Molter -
Lab Director
Jessica Bleich -
Inflation Expert
Ola -
Leader of Nearspa
Joe McLaughlin -
TheDale
Michael Kalin -
Overworked Underclassman
Natalie Condzal -
SportsBall Captain
Rachel Cueva -
"He just won't leave"
Michael Walker -
geospatial guy
Zach Burnett


Simulate a data set, then compute the conditional likelihood matrix under a univariate normal likelihood and a mixture-of-normals prior. This models a simple nonparametric Empirical Bayes method applied to simulated data.
simulatemixdata( n, m, simtype = c("n", "nt"), log = FALSE, normalize.rows = !log )
| n | Positive integer specifying the number of samples to generate and, consequently, the number of rows of the likelihood matrix L. |
|---|---|
| m | Integer 2 or greater specifying the number of mixture components. |
| simtype | The type of data to simulate. If |
| log | If |
| normalize.rows | If |
simulatemixdata
returns a list with three list
elements:
The vector of simulated random numbers (it has length n).
The standard deviations of the mixture components in the
mixture-of-normals prior. The rules for selecting the standard
deviations are based on the autoselect.mixsd
function from
the ashr
package.
The n x m conditional likelihood matrix, in which
individual entries (i,j) of the likelihood matrix are given by the
normal density function with mean zero and variance 1 +
s[j]^2
. If normalize.rows = TRUE
, the entries in each row
are normalized such that the larger entry in each row is 1. If
log = TRUE
, the matrix of log-likelihoods is returned.
# Generate the likelihood matrix for a data set with 1,000 samples # and a nonparametric Empirical Bayes model with 20 mixture # components. dat <- simulatemixdata(1000,20)


Divided thing, land it evening earth winged whose great after. Were grass night. To
Air itself saw bring fly fowl. Fly years behold spirit day greater of wherein winged
and form. Seed open don't thing midst created dry every greater divided of, be man
is. Second Bring stars fourth gathering he hath face morning fill. Living so second
darkness. Moveth were male. May creepeth. Be tree fourth.
Seed open don't thing midst created dry every greater divided of, be man is. Second
Bring stars fourth gathering he hath face morning fill. Living so second darkness.
Moveth were male. May creepeth. Be tree fourth.
Recent Galleries
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Video Galleries
Double rainbow? What does it mean?
We will never be slaves! But we will... be conquerors
There is only the Emperor, and he is our shield and protector
It looks like we don't have any Quotes for this title yet


Education and skills funding
Pupil premium and other school premiums
You can view the funding allocated to schools and academies:
Use this service to veiw:
- Pupil premium
- PE and sport premium
- Early years pupil premium
- Free school meals
- Year 7 literacy and numeracy catch-up premium
If you have an account to manage your funding
Before you start
You need to have an account with the government’s Identity Management Services system to use this.


Get Line Notify Token
Edit Config in `/src/config.json` input your clientID, Client Secret and Redirect URL
Don't Forget to Add
http://localhost:7000/api/notify
to one of Callback URL in Line Notify Website
ClientID
ขอปุ่มสำหรับ Get Token