Photo-realistic Rendering and Global Illumination in Computer Graphics Spring 2012 Hybrid Algorithms K. H. Ko School of Mechatronics Gwangju Institute of Science and Technology

2 Instant Radiosity The key idea of instant radiosity is to replace indirect diffuse illumination in a scene by direct diffuse illumination from a set of point sources. The point sources are placed at the locations where a number of simulated photon trajectories hit the surfaces of objects.

3 Instant Radiosity

First, a small number of photon trajectories is traced.  Point light sources are placed at the locations where these trajectories hit object surfaces.  The direct illumination due to these point light sources (Images 1 to 20) is accumulated.  Image A shows the result of accumulating the Images 1 to 10, with light source points at the origin of the simulated trajectories, on the extended light source.  This results in direct illumination due to the extended light source. Accumulating Images 11 to 20, corresponding to the other places visited by the photon trajectories, adds indirect diffuse illumination (Image B). 4

Instant Radiosity It can be viewed as a kind of bidirectional path tracing.  The eye paths are only one segment long, or are allowed to scatter specularly only.  On the other hand, more than one light path is combined with each eye-path vertex. The same set of light paths is used for all eye paths. 5

Instant Radiosity The main advantage of instant radiosity is in the so-called positively correlated sampling for all pixels.  Because the same light paths are used for all pixels, images computed with instant radiosity look smoother and lack the typical noisy artifacts of (bidirectional) path tracing. 6

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The shadow rays traced between eye-path vertices and the light-path vertices are highly coherent, similar to eye rays traced in ray casting.  They can be traced significantly faster than in (bidirectional) path tracing. 8

Instant Radiosity One potential problem is in the singularity of the kernel of the radiosity equation, which needs to be evaluated between each light-path and eye-path vertex. When the distance r xy tends to zero, G(x,y) becomes very large. 9

Instant Radiosity As a solution, a small constant can be added to the denominator, similar to certain classic integration schemes for point-to-patch form factors in radiosity. Doing so introduces a small, but hardly noticeable, bias. 10

Lightcuts and Multidimensional Lightcuts Even with all the advances in Monte Carlo sampling, rendering complex scenes that include a large number of light sources, and effects such as motion blur, depth of field, and participating media, remains challenging. Most existing techniques are too slow (and noisy) in the face of such complexity. Lightcuts and multidimensional lightcuts are scalable rendering algorithms for high complexity scenes. 11

Lightcuts Background  Rendering scenes with a large number of complex light sources is a challenge. Convergence of Monte Carlo sampling for direct illumination is often two slow for such scenes. Hybrid algorithms like instant radiosity convert indirect illumination into direct from a set of indirect lights.  The performance of such algorithms depends linearly on the number of lights created. This linear performance often limits the complexity of scenes and illumination that these approaches can handle. 12

Lightcuts Lightcuts introduce a scalable solution for computing illumination from many point lights.  The rendering cost is sublinear in the number of point lights, thus enabling rendering from an extremely large number of light sources.  This sublinear performance can be exploited to render difficult illumination problems simulated as illumination from many point lights. Area light, sun/sky models, high dynamic range (HDR) environment maps, and indirect illumination using instant radiosity, and point lights, can be unified into one common framework. Apart from quality, this unification allows performance gains because bright illumination from one source can mask errors in approximating other illumination. 13

Lightcuts Lightcuts achieve scalability by constructing a light tree over all light sources.  The light tree clusters lights in a binary tree where the leaves are individual lights and the interior nodes are light clusters containing the lights below them in the tree.  Each tree note has a representative light that approximates the contribution of all the lights in the node’s cluster. 14

Lightcuts Lightcuts achieve sublinear performance by using tree nodes when possible to approximate the contribution of a group of lights without having to evaluate each light individually. When rendering the image, for each eye ray, a cut through the light tree is found.  A cut is a set of nodes such that every path from the root of the tree to a leaf contains exactly one node from the cut.  Only representatives on the cut are evaluated to shade the eye ray.  The cut corresponds to a valid partitioning of the lights into clusters, such that evaluation of the cut approximates the shading of the eye ray. 15

Lightcuts 16

Lightcuts Given a set of point light sources, the radiance caused by their illumination at a surface point is a product of each light’s material, geometry, visibility, and intensity terms, summed over all the lights: Σ i M i G i V i I i. The cluster with representative j, that corresponds to these lights can be used to approximate the radiance of the cluster: M i G i V i Σ i I i.  The sum of the light intensities in the cluster is precomputed and stored in the cluster node, and the material, geometry, and visibility term are evaluated only for the representative light j. 17

Lightcuts The goal of finding the cut is to compute a cut that approximates the original image well. Cuts that use nodes higher up in the tree are more efficient because they use more clustering.  However, they could also introduce more error. The cut selection algorithm starts at the root for each eye ray.  The cut is progressively refined to meet the error criterion.  The algorithm uses both the cluster’s approximate contribution and error bound to determine when refinement is necessary. 18

Multidimensional Lightcuts Monte Carlo rendering is powerful enough to handle a wide range of effects, including motion blur, depth of field, and participating media.  These effects can all be cast into the rendering equation as integrals over different domains. Motion blur is an integration of radiance over time. Participating media is an integration along the ray in the medium. Depth of field is integration over the lens aperture. Spatial anti-aliasing is integration over the area of a pixel. 19

Multidimensional Lightcuts This multidimensional integral can be solved by sampling using standard Monte Carlo technique.  The pixel integral is converted into a set of points, and radiance is evaluated at each point and averaged. The problem is that a large number of points are often required for good approximations, which quickly becomes very expensive especially when the illumination is also complex. Multidimensional lightcuts build on lightcuts to develop a unified, scalable, point-based rendering algorithm for rapidly and accurately approximating such multidimensional integrals. The key insight is that instead of evaluating each point to high accuracy, it is possible to achieve scalable performance by considering the pixel as a whole. 20

Multidimensional Lightcuts Multidimensional lightcuts first discretize the illumination sources into a set of point lights L, using the techniques of lightcuts. Then, for each pixel, they generate a set of gather points G, by tracing rays from the eye or camera.  These gather points are appropriately distributed in time, volume, aperture, and pixel area. The total pixel value is then: M, G, and I are the material, geometry, and intensity. V ji is the visibility term that checks that points i and j exist at the same time instant. S j is the strength of a gather point. 21

Multidimensional Lightcuts Multidimensional lightcuts use an implicit construction of a hierarchy over the space of gather-light pairs. Separate hierarchies over the gather points and the light points are constructed:  The gather tree and light tree. The Cartesian product graph of the gather tree and light tree is then an implicit hierarchy on the set of all gather-light pairs where leaf nodes correspond to individual gather-light pairs. The implicit construction allows computation using a hierarchy of gather-light pairs without actually having to explicitly construct the full hierarchy. 22

Multidimensional Lightcuts 23

Multidimensional Lightcuts A cut partitions the set of gather-light pairs into clusters  The goal is to adaptively select a cut that will result in an accurate approximation of the pixel.  A cut in the product graph is a set of nodes such that the set of all paths from the root to a leaf will always contain exactly one node from the cut. This condition guarantees that the cut corresponds to a valid partitioning of gather-light pairs. This algorithm discretizes time into a fixed set of T time instants for any frame. The strengths S and intensities I of the gather and light points are then time vectors. A representative (g,l) approximates shading L c = M gl G gl V gl (S c ·I c ), where the material, geometry, and visibility terms are evaluated at the representative (g,l), g and l are required to exist at the same time instant. S c and I C are the sum of the strength and intensity vectors for all the gather and light points in the corresponding gather and light clusters. 24

Multidimensional Lightcuts The rendering algorithm then starts at the root of both the gather and light trees and refines the cut based on the error of nodes on the cut.  Finding the cut in the product graph requires bounding the error introduced by the representatives on the cut.  A perceptual threshold based on Weber’s law is used to determine when an approximation on the cut is good enough. 25

Multidimensional Lightcuts The Roulette Wheel demonstrates motion blur. The split image shows the static wheel on the left and the wheel spinning on the right. Tableau demonstrates depth of field. The Kitchen demonstrates participating media. 26