Academic literature on the topic 'Specular light paths'

Complex visual effects such as caustics are often produced by light paths containing multiple consecutive specular vertices (dubbed specular chains) , which pose a challenge to unbiased estimation in Monte Carlo rendering. In this work, we study the light transport behavior within a sub-path that is comprised of a specular chain and two non-specular separators. We show that the specular manifolds formed by all the sub-paths could be exploited to provide coherence among sub-paths. By reconstructing continuous energy distributions from historical and coherent sub-paths, seed chains can be generated in the context of importance sampling and converge to admissible chains through manifold walks. We verify that importance sampling the seed chain in the continuous space reaches the goal of importance sampling the discrete admissible specular chain. Based on these observations and theoretical analyses, a progressive pipeline, manifold path guiding , is designed and implemented to importance sample challenging paths featuring long specular chains. To our best knowledge, this is the first general framework for importance sampling discrete specular chains in regular Monte Carlo rendering. Extensive experiments demonstrate that our method outperforms state-of-the-art unbiased solutions with up to 40 × variance reduction, especially in typical scenes containing long specular chains and complex visibility.

Robust light transport algorithms, particularly bidirectional path tracing (BDPT), face significant challenges when dealing with specular or highly glossy involved paths. BDPT constructs the full path by connecting sub-paths traced individually from the light source and camera. However, it remains difficult to sample by connecting vertices on specular and glossy surfaces with narrow-lobed BSDF, as it poses severe constraints on sampling in the feasible direction. To address this issue, we propose a novel approach, called proxy sampling , that enables efficient sub-path connection of these challenging paths. When a low-contribution specular/glossy connection occurs, we drop out the problematic neighboring vertex next to this specular/glossy vertex from the original path, then retrace an alternative sub-path as a proxy to complement this incomplete path. This newly constructed complete path ensures that the connection adheres to the constraint of the narrow lobe within the BSDF of the specular/glossy surface. Unbiased reciprocal estimation is the key to our method to obtain a probability density function (PDF) reciprocal to ensure unbiased rendering. We derive the reciprocal estimation method and provide an efficiency-optimized setting for efficient sampling and connection. Our method provides a robust tool for substituting problematic paths with favorable alternatives while ensuring unbiasedness. We validate this approach in the probabilistic connections BDPT for addressing specular-involved difficult paths. Experimental results have proved the effectiveness and efficiency of our approach, showcasing high-performance rendering capabilities across diverse settings.

Finding valid light paths that involve specular vertices in Monte Carlo rendering requires solving many non-linear, transcendental equations in high-dimensional space. Existing approaches heavily rely on Newton iterations in path space, which are limited to obtaining at most a single solution each time and easily diverge when initialized with improper seeds. We propose specular polynomials , a Newton iteration-free methodology for finding a complete set of admissible specular paths connecting two arbitrary endpoints in a scene. The core is a reformulation of specular constraints into polynomial systems, which makes it possible to reduce the task to a univariate root-finding problem. We first derive bivariate systems utilizing rational coordinate mapping between the coordinates of consecutive vertices. Subsequently, we adopt the hidden variable resultant method for variable elimination, converting the problem into finding zeros of the determinant of univariate matrix polynomials. This can be effectively solved through Laplacian expansion for one bounce and a bisection solver for more bounces. Our solution is generic, completely deterministic, accurate for the case of one bounce, and GPU-friendly. We develop efficient CPU and GPU implementations and apply them to challenging glints and caustic rendering. Experiments on various scenarios demonstrate the superiority of specular polynomial-based solutions compared to Newton iteration-based counterparts. Our implementation is available at https://github.com/mollnn/spoly.

We introduce virtual blue noise lighting, a rendering pipeline for estimating indirect illumination with a blue noise distribution of virtual lights. Our pipeline is designed for virtual lights with non-uniform emission profiles that are more expensive to store, but required for properly and efficiently handling specular transport. Unlike the typical virtual light placement approaches that traverse light paths from the original light sources, we generate them starting from the camera. This avoids two important problems: wasted memory and computation with fully-occluded virtual lights, and excessive virtual light density around high-probability light paths. In addition, we introduce a parallel and adaptive sample elimination strategy to achieve a blue noise distribution of virtual lights with varying density. This addresses the third problem of virtual light placement by ensuring that they are not placed too close to each other, providing better coverage of the (indirectly) visible surfaces and further improving the quality of the final lighting estimation. For computing the virtual light emission profiles, we present a photon splitting technique that allows efficiently using a large number of photons, as it does not require storing them. During lighting estimation, our method allows using both global power-based and local BSDF important sampling techniques, combined via multiple importance sampling. In addition, we present an adaptive path extension method that avoids sampling nearby virtual lights for reducing the estimation error. We show that our method significantly outperforms path tracing and prior work in virtual lights in terms of both performance and image quality, producing a fast but biased estimate of global illumination.

Feature lines visualize the shape and structure of 3D objects, and are an essential component of many non-photorealistic rendering styles. Existing feature line rendering methods, however, are only able to render feature lines in limited contexts, such as on immediately visible surfaces or in specular reflections. We present a novel, path-based method for feature line rendering that allows for the accurate rendering of feature lines in the presence of complex physical phenomena such as glossy reflection, depth-of-field, and dispersion. Our key insight is that feature lines can be modeled as view-dependent light sources. These light sources can be sampled as a part of ordinary paths , and seamlessly integrate into existing physically-based rendering methods. We illustrate the effectiveness of our method in several real-world rendering scenarios with a variety of different physical phenomena.

In order to improve the effect of urban landscape design, this paper combines big data technology with digital technology. For scenes and solutions containing SDS paths, a processing method similar to photon graphs is used and added to the calculation of two-way optical path tracking. In the processing scene, this paper uses the two-way optical path tracking method to perform specular reflection or refraction from the subpath starting from the light source and then store information such as the light energy of the points on the diffuse reflection surface or the directional reflection surface. Moreover, this paper combines the actual needs of urban landscape design to construct an urban landscape design system based on big data technology and digital technology. Finally, this paper designs experiments to carry out urban landscape simulation and design effect evaluation. From the test results, it can be seen that the system designed in this paper basically meets the needs of urban landscape planning and design.

As scenes become ever more complex and real-time applications embrace ray tracing, path sampling algorithms that maximize quality at low sample counts become vital. Recent resampling algorithms building on Talbot et al.'s [2005] resampled importance sampling (RIS) reuse paths spatiotemporally to render surprisingly complex light transport with a few samples per pixel. These reservoir-based spatiotemporal importance resamplers (ReSTIR) and their underlying RIS theory make various assumptions, including sample independence. But sample reuse introduces correlation , so ReSTIR-style iterative reuse loses most convergence guarantees that RIS theoretically provides. We introduce generalized resampled importance sampling (GRIS) to extend the theory, allowing RIS on correlated samples, with unknown PDFs and taken from varied domains. This solidifies the theoretical foundation, allowing us to derive variance bounds and convergence conditions in ReSTIR-based samplers. It also guides practical algorithm design and enables advanced path reuse between pixels via complex shift mappings. We show a path-traced resampler (ReSTIR PT) running interactively on complex scenes, capturing many-bounce diffuse and specular lighting while shading just one path per pixel. With our new theoretical foundation, we can also modify the algorithm to guarantee convergence for offline renderers.

AbstractMulti‐bounce, pure specular light paths produce complex lighting effects, such as caustics and sparkle highlights, which are challenging to render due to their sparse and diverse nature. We introduce a learning‐based method for the efficient rendering of pure specular light transport. The key idea is training a neural network to model the distribution of all specular light paths between pairs of endpoints for one specular object. To achieve this, for each object, our method models the distribution of sparse and diverse specular light paths between two endpoints using smooth 2D maps of ray directions from one endpoint and represents these maps with a 2D convolutional network. We design a training scheme to efficiently sample specular light paths from the scene and train the network. Once trained, our method predicts specular light paths for a given pair of endpoints using the network and employs root‐finding‐based algorithms for rendering the specular light transport. Experimental results demonstrate that our method generates high‐quality results, supports dynamic lighting and moving objects within the scene, and significantly enhances the rendering speed of existing techniques.

AbstractCaustics are complex optical effects caused by the light being concentrated in a small area due to reflection or refraction on surfaces with low roughness, typically under a sharp light source. Rendering caustic effects is challenging for Monte Carlo‐based approaches, due to the difficulties of sampling the specular paths. One effective solution is using the specular manifold to locate these valid specular paths. Unfortunately, it needs many iterations to find these paths, leading to a long rendering time. To address this issue, our key insight is that the specular paths tend to be similar for neighboring shading points. To this end, we propose to reuse the specular paths spatially. More specifically, we generate some specular path samples with a low sample rate and then reuse these specular path samples as the initialization for specular manifold walk among neighboring shading points. In this way, much fewer specular path‐searching iterations are performed, due to the efficient initialization close to the final solution. Furthermore, this reuse strategy can be extended for dynamic scenes in a temporal manner, such as light moving or specular geometry deformation. Our method outperforms current state‐of‐the‐art methods and can handle multiple bounces of light and various scenes.

Au cours des vingt dernières années, la restitution numérique d'édifices anciens ayant disparu ou s'étant dégradés est devenue un outil essentiel pour les historiens, tant dans leurs recherches que pour la transmission auprès du public. De nombreux projets de restitution, de la Renaissance au XVIIIe siècle font intervenir en grandes quantités des objets en verres soufflés au sein de fenêtres ou de dispositifs d'éclairages. Ces verres, produits de manière artisanale, se caractérisent par une surface déformée, la présence de bulles, ainsi que par un indice de réfraction variable produit par le mélange de plusieurs pâtes de verre de compositions différentes. Lorsque des verres de cette époque sont utilisés dans des fenêtres ou dans des dispositifs d'éclairage comme des lanternes, ils produisent des effets lumineux complexes encore mal supportés par les méthodes de simulation physique d'éclairage. Dans cette thèse, nous étudions dans un premier temps la modélisation des objets en verre ancien utilisés dans les vitres et les lanternes. L'emploi de fonctions de distance signée permet de représenter les irrégularités de surface et les bulles présentes dans les panneaux de verre soufflé. Des méthodes de tracé de sphères non linéaires permettent de simuler les trajectoires courbes des rayons lumineux se propageant dans un verre hétérogène. Ces outils constituent un modèle direct général pour la simulation des rayons lumineux en interaction avec des objets en verres irréguliers, permettant leur intégration dans des méthodes de simulation physique d'éclairage de tracé de chemins. Un modèle phénoménologique permet par la suite de générer des données d'entrée plausibles permettant de représenter des verres soufflés produits par les techniques du manchon et de la cive. Par un procédé similaire aux techniques de composition de vitraux, une méthode d'assemblage permet de représenter des objets complexes constitués de facettes de verre comme des fenêtres, des lanternes ou des vitraux. Nous poursuivons notre étude par l'estimation de l'éclairage produit par une source de lumière au travers d'une vitre irrégulière possédant un indice de réfraction variable. Nous caractérisons les chemins lumineux admissibles entre deux points de l'espace comme ceux dont le chemin optique est stationnaire (principe de Fermat). Trouver l'ensemble des chemins admissibles revient à résoudre un problème d'optimisation visant à trouver tous les points stationnaires d'une fonction de plusieurs variables. Nous résolvons ce problème de façon itérative par une méthode de Newton. Cette technique s'intègre aux méthodes stochastiques de tracé de chemins, omniprésentes dans le domaine de la synthèse d'image photoréaliste. Notre méthode se compare favorablement à l'état de l'art en matière de vitesse de convergence et d'exploration de l'espace des chemins admissibles. Contrairement à l'état de l'art utilisant des contraintes d'orientation pour définir des chemins admissibles, l'emploi du principe de Fermat permet de gérer des vitres dont l'indice de réfraction est variable. Nous exploitons des résultats de sismologie théorique portant sur le tracé de rayons paraxiaux dans un milieu hétérogène pour généraliser la méthode précédente aux vitres complexes présentant des déformations de surface et des variations d'indice de réfraction. Enfin, nous adaptons notre modèle de simulation directe au rendu temps réel rastérisé. La déformation des tampons de rendu permettra alors un rendu approché des effets de réfraction au travers du verre dans l'espace de l'image. Nous pré-calculons l'éclairage complexe produit par des lanternes et l'enregistrons dans des perceptrons multicouches à l'aide d'un encodage paramétrique multirésolution. Cette approche permet une reconstruction en temps réel du champ lumineux proche des dispositifs d'éclairage complexes rencontrés dans des projets de restitutions
Over the last twenty years, the virtual restoration of ancient environments that have disappeared or deteriorated has become an essential tool for historians, both as part of their research and for communicating their results to the public. Many restitution projects from Renaissance to 18th century include hand-blown glass objects, either for window works or in various types of lighting devices. These glass objects, made by hand, are characterized by their irregular surface, the presence of bubbles and by a continuously varying index of refraction caused by the mixing of several glass pastes of different compositions. When they are used in windows or in lanterns, these irregularities produce complex lighting effects that are still challenging to compute using photorealistic light simulation techniques. In this thesis, we first study the geometric representation of old glass objects as used in windows and lanterns. We used signed distance functions to implicitly define the characteristic irregular surface and bubbles of old glass. Non-linear sphere tracing allows the simulation of the curved trajectory of light rays inside heterogeneous glass. These tools constitute a general model for the simulation of light transport through these irregular objects, allowing their integration into photorealistic light simulation algorithms such as path tracing. A phenomenological model is then used to generate plausible input data for modeling crown and cylinder blown glass. We introduce a method based on texture coordinates to easily create and render complex objects made of individual flat pieces of glass cut from multiple glass panels, as tipically seen in stained-glass windows. We then propose a method for estimating the complex transmitted lighting produced by a light source through an irregular and heterogeneous glass panel. We characterize the set of admissible light paths existing between two points of space as the set of stationary optical paths (Fermat's principle). Finding all the admissible paths resorts to solving a non-linear optimization problem consisting in finding all the stationary points of a function of several variables, for which we use Newton's method and results from theoretical seismology. This technique integrates seamlessly into stochastic methods like path tracing, ubiquitous in photorealistic image synthesis. Our method compares favorably to state-of-thè-art methods in terms of speed of convergence and exploration of the path space. Contrarily to the state-of-the-art, our use of Fermat's principle allows us to generalize our work to transparent media with continuously varying index of refraction. Finally, we adapt our old glass window model to real time rasterized rendering. Direct ray tracing through objects made of flat pieces of glass is realized using a sphere tracing algorithm. We use traced rays and geometry buffers to warp a rasterized rendering of the scene and reproduce in screen space the refraction effects created by a glass window. We pre-compute the complex light field produced by a luminaire made of old glass and encode it inside a small size, fully connected neural network backed by a multiresolution grid encoding. This allows the real time reconstruction of the incident lighting produced by a complex luminaire, as encountered in restitution projects where the most of the lighting is provided by complex lighting devices such as lanterns

Light beam tracing is an e cient rendering algorithm for simulating caustics, the envelopes of light that are scattered from shiny curved surfaces and focussed into lines or spots of concentrated light. Light beam tracing is e cient for rendering caustics because the algorithm is able to exploit the coherency of the transport paths within an envelope of light. However, light beam tracing rendering algorithms found in the literature only support mirror-like specular surface interactions. Therefore, there is motive for extending light beam tracing to include more realistic roughened specular and other glossy surfaces while maintaining the e ciency of the rendering algorithm. This thesis rst o ers a conjecture on how to extend light beam tracing to include glossy surface interactions. The glossy bidirectional re ectance distribution function (BRDF) that is required to support the conjecture is then derived and shown to be physically plausible. Following from the conjecture a new extension to light beam tracing that allows glossy surface interactions for more realistic rendering of caustics is formulated. Gauss' divergence theorem is used to replace the irradiance surface integral of the lighting equation with a more e cient boundary line integral. This solution is also shown to be reusable for all-frequency interactions although more work is required to complete the derivations. Finally, multi-bounce glossy light beam tracing is demonstrated which further extends the application domain of glossy light beam tracing. The new rendering algorithm is shown to be a good alternative for rendering single-bounce and multi-bounce caustics due to specular as well as glossy surfaces. The expectation is that the irradiance solution would also in future be useful for more general applications.
Thesis (PhD)--University of Pretoria, 2015.
tm2015
Computer Science
PhD
Unrestricted

POINTS (Precision Optical INTerferometry in Space) is a proposed dual astrometric interferometer with a nominal measurement accuracy of 5 microarcseconds for pairs of stars approximately 90 degrees apart. Each interferometer measures the arc-second-scale offset of its optical axis from a target star, and a metrology system, described by Phillips and Reasenberg (in this Digest), measures the approximately 90 degree angle between the two interferometers. To achieve the nominal accuracy will require monitoring the positions of the critical optical elements to a few picometer (pm). Even with the most stable materials and active temperature control, the larger optical elements, especially the 25 cm primaries, will experience thermal distortions much larger than this limit. In one subsystem, required in both interferometers, a novel technique called full aperture metrology is used to measure the appropriate average optical path length and correct for any changes. Laser light is injected into the interferometer at the primary beamsplitter and follows the starlight paths, but in the reverse direction, illuminating the active area of each optical element back to the primary mirrors. Most of the metrology light is sent out toward the target stars, but shallow phase-contrast zone plates on the primaries focus a few percent of the metrology light to axial points near the specular foci of the mirrors. The two metrology beams are collimated by athermal lenses and interfere at an auxiliary beamsplitter. The phase of the interference measures the path length difference between the two arms of the interferometer and is used to drive a null servo.

Variando con el paso del día y del año, la luz del Sol y del cielo modula, visual y energéticamente, los territorios, las ciudades y los edificios. ¿Cómo sintetizar y manejar en el proyecto estas informaciones donde se mezcla el azar de las nubes pasajeras con la regularidad astronómica de los trayectos solares? En cuanto a las herramientas de simulación, el mayor avance de estos últimos años se ha producido en los programas de renderización, con los cuales nos vemos forzados a construir la iluminación de una escena a partir de distintos componentes, cada uno de los cuales requiriendo su propia algorítmica: luz directa del Sol, obertura al cielo, reflexión difusa y especular de Sol y cielo. Veremos primero que la mejor manera de entrar estos componentes en una lógica de diseño (y ya no solamente de análisis) consiste en aprovechar las propiedades geométricas de diferentes proyecciones: estereográfica, equivalente, ortogonal, gnomónica, isócrona,… Recordaremos también que el componente aparentemente más sencillo – los trayectos solares – nos conduce ya a un problema de cinco dimensiones. Con el ejemplo del programa “Heliodon 2”, [Beckers & Masset, 2009], indicaremos las formas de diseñar con la doble geometría del Sol y del cielo. Por el crecimiento y la necesaria densificación de nuestras ciudades, nuevos problemas se hacen sensibles: el derecho de todos a ver el cielo, el ahorro energético, la captación y distribución de la energía solar – la ciudad se considera entonces como fuente de energía, y ya no solamente como lugar de consumo –, el control del impacto mutuo entre la ciudad y la atmósfera. Con este último tema, nos encontramos frente a lo que los físicos llaman un “problema multiescala”; es decir: un mismo fenómeno, como el de la isla de calor, es el producto de innumerables contribuciones, las cuales se han de estudiar conjuntamente y de forma simultánea a escalas tan distintas que ya no las gobiernan las mismas ecuaciones. Habrá que aprender a construir edificios pensando en la ciudad, ciudades pensando en el territorio, y concebir el mismo territorio a partir de las ciudades, cuyos buenos o malos procederes modelan hasta los campos más distantes, y el planeta entero. By their continuous transformations along the day and the year, Sun and sky light are modeling, visually and energetically, the cities and buildings. How this information can be synthesized and used in the project, considering together the random occurrence of the passing clouds and the astronomical regularity of the sun paths? Regarding to the simulation tools, the main progress in late years has been produced in the render software, that force the users to separate the different components of light in any construction of an illuminated scene, using the opportune algorithms for direct Sun light, sky aperture, diffuse and specular reflections of Sun and sky. It will be first shown how the best mode of introducing these components into a design logic consists in taking advantage of the geometrical properties of different projections, as the stereographic, equivalent, orthographic, gnomonic or isochronal ones. It will be also remembered that the apparently simplest problem – Sun paths – conduces the architect to a five dimensions problem. With the example of “Heliodon 2” software, [Beckers & Masset, 2009], it will be shown how to design with the double geometry of Sun paths and sky light. Due to the growth and necessary densification of our cities, new problems are appearing: the right for everybody to see the sky, the energies economy, the solar energy collect and distribution – cities are then considered as energy sources and not only as consummation places –, the control of the mutual impact between the city and the atmosphere. With this last theme, we are in front of a “multiscale problem”, as say the physics when a unique problem, as the urban heat island, is the product of innumerable contributions that have to be studied together and simultaneously in so different scales that they are not governed yet by the same equations. We must listen to build architectures thinking on the city, cities thinking on the territory, and to conceive the territory itself from the cities, because our good or bad urban ideas model the most distant countries, and the entire planet.

The path to high resolution leads to shorter wavelengths. In the extreme ultraviolet (EUV) spectral region, imaging systems are possible using normal incidence reflective optics. As the diffraction limit is reduced, the errors in the optical surfaces often limit performance. Figure errors with a spatial period ranging from the size of the mirror down to about a tenth of the mirror size limit the resolution. Finish errors or roughness on a shorter length scale leads to non-specular scattering. Scattering will reduce the throughput of an optical system by removing light from the image. In addition, light scattered within the field of view (flare) can reduce the contrast of the image. For a lithographic imaging system this will reduce the process latitude. As the wavelength of light is reduced, the total integrated scatter increases as 1/λ2, which places a much more stringent demand on optical finish.

A new method of monitoring layer thickness during thin film deposition is presented. A beam of linearly polarized light of fixed azimuth strikes the film at oblique incidence. The reflected light is intercepted by a fixed arrangement of two partially specularly reflecting photodetectors with nonparallel surfaces. As the layer is deposited, the ratio of the detector currents varies as a periodic, linear sawtooth function of film thickness. Precalibration of the two-detector arrangement provides a plot of the expected path of the ratio. The thickness of the growing film is monitored continuously by comparing the measured ratio to its predetermined value. An example of the application of the CRUST-M is given for the deposition of common dielectric films on Si. The resolution is ~1 Å for monitoring the oxidation of Si.