Disclaimer: This is a pure garbage article, which is a supplement to the previous two articles. I just sorted it out for my own review. All titles can be redirected to the paper homepage. Special terms are given in Chinese and English as much as possible. If there are any mistakes, please point them out. Thank you very much.

original:https://zhuanlan.zhihu.com/p/830617613

Table of contents

1. [Xia 2023] A Practical Wave Optics Reflection Model for Hair and Fur
2. [Xia 2023] Iridescent Water Droplets Beyond Mie Scattering
3. [Aakash 2023] Accelerating Hair Rendering by Learning High-Order Scattered Radiance
4. [Kneiphof and Klein 2024] Real-Time Rendering of Glints in the Presence of Area Lights
5. [Huang 2024] Real-time Level-of-detail Strand-based Hair Rendering
6. [Xing 2024] A Tiny Example-Based Procedural Model for Real-Time Glinty Appearance Rendering
7. [Zhu 2022] Practical Level-of-Detail Aggregation of Fur Appearance
8. [Clausen 2024] Importance of multi-modal data for predictive rendering
9. [Shlomi 2024] A Free-Space Diffraction BSDF
10. [Kaminaka 2024] Efficient and Accurate Physically Based Rendering of Periodic Multilayer Structures with Iridescence
11. [Yu 2023] A Full-Wave Reference Simulator for Computing Surface Reflectance
12. [Shlomi 2022] Towards Practical Physical-Optics Rendering
13. [Huang 2022] A Microfacet-based Hair Scattering Model
14. [Shlomi 2021] A Generic Framework for Physical Light Transport
15. [Shlomi 2024] A Generalized Ray Formulation For Wave-Optics Rendering
16. [Shlomi 2021] Physical Light-Matter Interaction in Hermite-Gauss Space
17. [GUILLÉN 2020] A general framework for pearlescent materials
18. [Werner 2017] Scratch iridescence: Wave-optical rendering of diffractive surface structure
19. [Fourneau 2024] Interactive Exploration of Vivid Material Iridescence using Bragg Mirrors
20. [Chen 2020] Rendering Near-Field Speckle Statistics in Scattering Media
21. [Kajiya and Kay 1989] Kajiya-Kay Model
22. [Marschner 2003] Light Scattering from Human Hair Fibers
23. [Benamira 2021] A Combined Scattering and Diffraction Model for Elliptical Hair Rendering
24. [Zinke 2008] Dual Scattering Approximation for Fast Multiple Scattering in Hair

[Xia 2023] A Practical Wave Optics Reflection Model for Hair and Fur

Wave optics, hair rendering, surface electromagnetics, far-field scattering

Wave optics is used to render hair. The surface electromagnetic field is calculated to obtain the scattered field, and then noise is added to simulate the Glints effect.

I found that the authors of this series are all very good-looking. (crossed out)

1. Background

Hair rendering has been mainly based on ray tracing technology, which cannot handle wave optics effects, such as strong forward scattering and subtle color changes on the hair surface. Previous research [Xia et al. 2020] demonstrated that diffraction effects play a key role in the color and scattering direction of fibers. However, this study did not consider surface roughness and the microstructure of the fiber epidermis (such as tilted keratin scales).

2. Motivation

In order to make up for the lack of treatment of diffraction and forward scattering (such as Glints phenomenon) in the existing light optics model.

Although full-wave simulations can produce very detailed scattering data, the computational effort is still too high and must be accelerated or simplified in some way to achieve hair or fur rendering in large-scale scenes.

We wanted to develop a model that could efficiently handle various fiber geometry variations.

3. Methods

Hair modeling is based on scanning electron microscope (SEM) images of hair.

Use "WAVE SIMULATION WITH 3D FIBER MICROGEOMETRY" to calculate the reflection and diffraction of rough fiber surfaces. That is, PO.

Speckle theory is introduced to analyze the statistical characteristics of the scattering pattern, and noise is used to accelerate it.

[Xia 2023] Iridescent Water Droplets Beyond Mie Scattering

Wave optics, iridescence effect, Quetelet scattering model of water droplets on water surface

Combining Mie scattering, Quetelet scattering (light interference) and dynamic changes of water droplets, the rainbow-like color effect of water droplets on the water surface and in the steam is realistically rendered, surpassing the traditional single Mie scattering model.

1. Background

Iridescence is common in nature, especially in water droplets, fog and steam. It can generally be explained by Mie scattering. Mie scattering describes the scattering effect that occurs when light encounters spherical particles of the same wavelength. It is one of the important theories currently used to simulate natural phenomena such as water droplets, clouds, rain and fog.

However, while Mie scattering can explain the optical properties of isolated water droplets, it cannot fully explain phenomena such as the iridescence of water droplets on the surface of water and the complex rainbow patterns in vapor. Phenomena depend not only on how individual particles scatter light, but also on surface reflections, interference effects, and dynamic changes in particle size.

2. Motivation

Mie scattering can only deal with isolated light scattering phenomena and cannot explain more complex optical interference effects.

Accurately simulating these natural phenomena can greatly improve the realism and look and feel of image rendering.

Existing computer optical models and rendering methods are mostly limited to Mie scattering and cannot explain the interaction of light in a multi-particle environment, such as light interference and reflection between water droplets or between water droplets and surfaces.

3. Methods

The "Quetelet scattering model on water" is used to explain the rainbow effect produced by water droplets floating on the water surface. By building an empirical model, thermal imaging technology is used to relate temperature to the size and height of water droplets. Quetelet scattering phase function and BRDF (bidirectional reflectance distribution function) are used to render particle groups and water surfaces.

A water droplet growth and evaporation model was developed to simulate the dynamic changes of water droplets in steam. Combined with Mie scattering, water droplets of non-uniform size were used to simulate the rainbow color changes in steam. In order to improve rendering efficiency, an acceleration algorithm based on motion blur was used, which increased the calculation speed by 10 times compared with traditional methods.

[Aakash 2023] Accelerating Hair Rendering by Learning High-Order Scattered Radiance

Hair rendering, MLP, accelerated hair scattering

The method of learning hair higher-order scattered radiance online combined with a small multilayer perceptron (MLP) significantly accelerates hair rendering in a path tracing framework, reducing computation time and introducing only a small amount of bias.

1. Background

The multiple scattering of hair is very complex, especially in the path tracing process, because it is necessary to simulate the multiple scattering of light between hairs, which makes it difficult to converge.

2. Motivation

Develop a method to improve computational efficiency while maintaining high-quality simulation of multiple scattering effects.

In the existing technology, some methods make simplifying assumptions about the scene or lighting. This paper hopes to propose a general method that does not make any assumptions about the scene.

3. Methods

A small multilayer perceptron (MLP) is used to learn higher-order scattered radiance online. This MLP network learns the scattering properties of hair in real time during the rendering process, without relying on pre-computed tables or simulations.

The MLP is integrated into the path tracing framework to infer and compute higher-order diffuse radiation contributions.

The renderer's bias and speedup can be adjusted in real time to find the optimal balance between computational efficiency and rendering quality.

[Kneiphof and Klein 2024] Real-Time Rendering of Glints in the Presence of Area Lights

Accelerated area light source Glints, microsurface models, real-time rendering

Rendering glints under area lights is done in real time by combining Linearly Transformed Cosines (LTC) with a microsurface count model based on the binomial distribution.

1. Background

Many real-world materials (such as metals, gemstones, etc.) have a glittering appearance, which is caused by the reflection of micro-surfaces. However, glitter is a discrete phenomenon, and the computational complexity of wave optics simulation is too large.

Previous studies have mostly focused on using infinitesimal point light sources to render flash effects, which is a reasonable simplification for distant light sources like the sun, but in reality most light sources are essentially area light sources. Existing technologies have not been able to effectively handle flash rendering under area light sources.

2. Motivation

Glint rendering under area lights. Area lights (such as the light shining into a room through a window) are a common type of light, and how to efficiently render glint effects under such lights is an unsolved problem. We hope to develop a method that can accurately render glint effects under area lights while meeting the needs of real-time rendering.

It is hoped that it can be easily integrated into existing real-time rendering frameworks without introducing significant additional overhead to existing area light shading methods.

3. Methods

Glint reflection probability estimation computes the probability that a microfacet is correctly oriented to reflect light from a light source to an observer, using Linearly Transformed Cosines (LTC) for large sources and a locally constant approximation for small sources.

The number of reflective microsurfaces is counted using a binomial distribution-based counting model.

Integration with existing frameworks.

[Huang 2024] Real-time Level-of-detail Strand-based Hair Rendering

Hair rendering, LoD, based on hair strands, BCSDF

An innovative real-time strand-based hair rendering framework is proposed, which ensures the consistent appearance of hair at different view distances and achieves significant rendering acceleration through seamless level-of-detail (LoD) transition.

1. Background

Strand-based hair rendering is becoming increasingly popular in film, television and game production for its realistic appearance, but it is computationally very expensive, especially at long viewing distances.

The current LoD method is prone to noticeable discontinuities in the transition from hair strands to cards, resulting in inconsistent appearance.

2. Motivation

Solve discontinuity in dynamics and appearance. Existing solutions for converting hair strands to hair cards have significant differences in appearance and animation performance. The goal of this paper is to achieve seamless LoD transition from far to near, eliminating appearance changes during transition while maintaining computational efficiency.

3. Methods

Encapsulates multiple hair strands within an elliptical volume using an elliptical thick hair model. The shape and overall structure of the hair cluster is maintained at different LoDs, providing a consistent look as the view distance changes.

The elliptical bidirectional curve scattering distribution function (BCSDF) simulates single and multiple scattering phenomena within hair clusters and is suitable for hair distribution scenarios ranging from sparse to dense and from static to dynamic.

Dynamic LoD adjustment and hair width calculation.

[Xing 2024] A Tiny Example-Based Procedural Model for Real-Time Glinty Appearance Rendering

Glints, material self-similarity

A model based on tiny example microstructures that renders glinty effects in real time, significantly reducing memory usage and computational overhead while maintaining the realism of high-frequency reflection details.

1. Background

The shimmering details produced by complex microstructures can significantly improve the realism of renderings, especially on materials such as metals and gemstones. These details usually require high-resolution normal maps to define each micro-geometry, but such methods have high memory requirements and are not suitable for real-time rendering applications.

2. Motivation

Reduce memory and computational overhead.

Leveraging material self-similarity: Many materials have independent structural features and self-similarity, and small samples are used to implicitly represent complex microstructures, thereby reducing memory requirements.

3. Methods

A tiny example-based procedural model based on the microstructure of a small sample can generate complex sparkle details by reusing a small number of samples based on the self-similarity of the material.

Precomputed Normal Distribution Functions (NDFs) Precompute and store small samples of normal distribution functions (NDFs) using 4D Gaussians. Stored in multi-scale NDF maps and called by simple texture sampling at rendering time.

A tiny example-based NDF evaluation method combines texture sampling with a small example NDF evaluation method to quickly generate the shiny appearance of complex surfaces.

[Zhu 2022] Practical Level-of-Detail Aggregation of Fur Appearance

Hair rendering, simplified hair count, neural networks

A practical hair appearance aggregation model that significantly accelerates hair rendering while maintaining realistic visual effects by reducing the number of geometric hairs and combining multiple scattering of light, using neural networks to achieve real-time dynamic simplification.

1. Background

If there are too many hairs, the light scattering and reflection of each hair will greatly increase the calculation amount, especially when simulating multiple light scattering.

Most existing simplification methods improve rendering efficiency by reducing the number of hairs, but this method has great limitations. This method can cause the hair to look too rough or dry, and the reflection and scattering effects of light are not realistic.

2. Motivation

Reducing geometric complexity.

Improving rendering efficiency.

3. Methods

An aggregated fur appearance model is proposed, which uses a thick cylinder to represent the optical behavior of a group of hair clusters. By analyzing the optical properties of individual hairs (such as the incident angle of light), the model can accurately reflect the aggregated appearance of hair clusters.

A lightweight neural network is used to map the optical properties of individual hairs to parameters in the aggregate model.

A dynamic level-of-detail scheme based on view distance and number of light bounces is proposed to dynamically simplify the geometric structure of hair.

[Clausen 2024] Importance of multi-modal data for predictive rendering

Predictive rendering, spectral rendering, microsurface geometry

Multi-modal data is important for predictive rendering, especially in accurately modeling material reflection behavior. By combining spectral, spatial information and micro-geometric details, the realism and computational efficiency of reflection models can be improved.

1. Background

The need for predictive rendering aims to accurately simulate the appearance of materials.

Most current databases on material reflection behavior are limited to a single dimension, usually covering only the spectral domain or the spatial domain, and lack descriptions of microgeometry details.

2. Motivation

In order to address data limitations, multimodal data can not only better simulate the reflection of materials under different lighting conditions, but also reveal the influence of the microscopic geometry of the material surface on light scattering.

Multimodal reflectance data can help develop more realistic and efficient reflectance models.

3. Methods

Building a multi-modal reflection database, including spectral data, spatial distribution data and microgeometry details of the material.

Simulating microgeometry of the microgeometry of a material surface.

Integrating spectral and spatial domains.

[Shlomi 2024] A Free-Space Diffraction BSDF

Wave optics, electromagnetic computing, free space diffraction, importance sampling, PT integration,

A bidirectional scattering distribution function (BSDF) based on free-space diffraction can efficiently simulate the diffraction phenomenon of light around the edges of objects in complex scenes through ray tracing without the need for geometric preprocessing, and is particularly suitable for path tracing technology.

1. Background

Free-space diffraction is an optical phenomenon in which light is diffracted when it encounters an edge or corner of an object, bending some of its energy into the shadowed area. This phenomenon is important for modeling the propagation of light waves, especially at long wavelengths, such as radar, WiFi, and cellular signals.

The limitations of traditional methods such as the Geometric Theory of Diffraction (GTD) and the Unified Theory of Diffraction (UTD) are the extremely high computational complexity caused by the need to deal with light rays that interfere with each other, especially in complex geometric scenes. Existing methods rely on scene simplification and specific geometric structures and cannot effectively handle complex three-dimensional scenes.

2. Motivation

Addressing diffraction rendering in complex scenes. Existing diffraction simulation methods are difficult to scale and make compatible with path tracing techniques.

Existing diffraction methods often rely on complex nonlinear interference calculations, while path tracing uses linear rendering equations. This paper hopes to design a free-space diffraction BSDF that works efficiently within the path tracing framework without requiring major modifications to the path tracer.

3. Methods

The Fraunhofer diffraction edge model is based on Fraunhofer diffraction. Near the intersection of light and geometric objects, the relevant edges are identified and the diffraction effects are calculated. When the light hits the object, the BSDF of free space diffraction is constructed through geometric analysis to quantify how the light propagates around the geometric object and how much energy is diffracted.

The importance sampling strategy evaluates the geometric edges around the points where the ray interacts with the object and samples and traces the diffracted rays.

Seamless integration in path tracing

[Kaminaka 2024] Efficient and Accurate Physically Based Rendering of Periodic Multilayer Structures with Iridescence

Multi-layer oil film rendering, iridescence effect, wave optics

A multi-layer interference rendering method. It can express the iridescence effect of periodic multi-layer structures. By introducing the Huxley method from biology, it can achieve efficient calculation independent of the number of layers.

1. Background

Thin-film interference is an optical phenomenon caused by the wave properties of light waves, which produces iridescence when the viewing angle or illumination angle changes. It usually appears in single-layer or multi-layer structures in nature, such as butterfly wings, beetle shells and dielectric mirrors.

The limitations of existing methods such as recursive calculation method and transfer matrix method (TMM) are that the computational complexity increases significantly with the number of layers. Simplified methods ignore multiple reflections in thin films.

2. Motivation

Improving efficiency for multilayer structures.

Applied to physical rendering of complex materials.

3. Methods

A multilayer interference model based on Huxley's approach is proposed. It can efficiently calculate the reflection and transmission coefficients in periodic multilayer structures and supports multiple materials and absorption effects.

Based on BRDF implementation. Implemented as a BRDF (Bidirectional Reflectance Distribution Function), it can be integrated into traditional rendering systems such as PBRT-v3.

[Yu 2023] A Full-Wave Reference Simulator for Computing Surface Reflectance

Wave optics, full-wave simulation

Full-wave simulator based on the boundary element method (BEM) that can calculate light scattering on rough surfaces with high accuracy. It is used to evaluate and improve approximate reflection models in computer graphics, especially when multiple scattering, interference and diffraction effects are significant.

1. Background

Surface reflection models are usually based on geometric optics, which assumes that light propagates in the form of rays. For scenes where surface features are comparable to the wavelength of light, geometric optics models cannot accurately capture wave effects such as diffraction and interference.

Based on wave optics approximations, such as Beckmann-Kirchhoff theory and Harvey-Shack model, they still produce errors under multiple scattering and complex geometric structures.

2. Motivation

Since existing reflection models have different accuracy in different situations, there is a lack of reliable benchmarks to verify their accuracy. The goal of this paper is to develop a simulator based on full-wave theory to minimize approximations and achieve high-precision surface reflection calculations through numerical discretization, thereby providing a reference tool that can be used to evaluate the accuracy of various reflection models.

Addressing multiple scattering and wave effects.

3. Methods

Boundary Element Method (BEM), accelerated by Adaptive Integral Method (AIM).

The simulator's full-wave simulation completely solves Maxwell's equations and can accurately simulate wave phenomena such as light propagation, interference, and scattering.

And it can efficiently calculate BRDF (efficient BRDF computation).

[Shlomi 2022] Towards Practical Physical-Optics Rendering

Wave optics, PLT

We propose an efficient Physical Light Transport (PLT) framework that exploits the principles of partially coherent light and wave optics to achieve accurate rendering of interference, diffraction, and polarization effects in complex scenes through an improved rendering algorithm, bringing its performance close to that of classic “physically based” rendering methods.

1. Background

Most existing rendering methods ignore the wave characteristics of light, especially in complex scenes, which makes it impossible to render physical phenomena such as interference and diffraction of light, which are particularly important on certain materials (such as iridescent coatings, optical discs, etc.). To solve this problem, a rendering framework based on Maxwell's electromagnetic theory is proposed.

Although PLT provides a theoretical full-wave model that can simulate the coherence, interference and diffraction of light, existing methods are very computationally difficult.

2. Motivation

Simplifying the physical light transport model.

Introducing new coherence-aware materials and developing material models that can perceive light coherence will improve the usability of PLT in practical scenarios.

3. Methods

Restricting the coherence shape of light, through thermodynamic derivation, proves that this approximation is reasonable under most natural light sources.

An extended Stokes-Mueller calculus is used to combine the radiation, polarization and coherence properties of light as new rendering primitives. The generalized Stokes parameters can fully quantify all properties of light and accurately simulate complex optical phenomena caused by these properties, such as interference and diffraction.

Wave BSDF and importance sampling.

New coherence-aware material models take full advantage of the coherence properties of light to expand the scope of application of PLT.

[Huang 2022] A Microfacet-based Hair Scattering Model

Hair rendering, scattering lobes, BCSDF

The first hair scattering model based on microsurface theory is proposed to accurately describe the scattering behavior of hair, including non-separable scattering lobe structure, elliptical cross section, efficient importance sampling and forward scattering spot (glint-like) effect.

1. Background

Complexity of hair rendering. Most existing hair scattering models simplify the mathematical calculations through separable scattering lobes, which are fast but not ground truth.

Most hair scattering models are based on geometric simplification, treating hair as smooth cylinders, which leads to deviations in scattering behavior.

2. Motivation

Introducing a physically-plausible microfacet model more accurately describes the scattering behavior of hair: the surface microscopic roughness, the tilted scale structure, and the non-separable scattering lobe shapes.

Improving sampling efficiency and physical accuracy.

3. Methods

The hair modeling is combined with microfacet theory, and GGX or Beckmann normal distribution is applied to describe the microscopic roughness of the surface. And it is non-separable lobes.

The bidirectional curve scattering distribution function (BCSDF) describes the complex interaction of light on the hair surface.

Support for elliptical cross-sections and efficient sampling. Support for elliptical cross-sections for hair.

[Shlomi 2021] A Generic Framework for Physical Light Transport

Wave optics, PLT

The first global light transport framework based on Maxwell's electromagnetic theory that can handle partially coherent light is proposed, which accurately simulates the interference and diffraction effects of light and extends the traditional radiometric-based light transport theory to the field of wave optics.

1. Background

Existing light transport models are usually based on geometric optics and radiometry, which ignore the wave characteristics of light and cannot simulate phenomena such as interference and diffraction. They cannot accurately reproduce wave optical effects such as rainbow effect, grating, thin film interference, light polarization, etc., which is the limitation of classical radiometric light transport models.

Current models can only handle local treatment of wave effects, but cannot account for the transmission and coherence of light in global scenes.

2. Motivation

Achieving global wave-optics consistency in light transport, that is, combining Maxwell's electromagnetic theory.

Combining wave optics with classical geometric optics (integrating wave optics with classical geometric optics) can deal with the wave effect of light and be consistent with classical geometric optics in the short wavelength limit.

3. Methods

Modeling partially-coherent light is divided into two parts: two-point coherence description and light source model. Different from traditional radiance, this paper introduces a "cross-spectral density function" based on the partial coherence of light, which can capture the interference characteristics of light. The physical model of natural light sources is based on the principle of spontaneous radiation in quantum mechanics.

Generalizing the light transport equation. The spectral-density transport equation is used to calculate the interference and diffraction effects of light during propagation. This paper also proves that the framework can be simplified to classical geometric optics in the short wavelength limit, so it can be seamlessly integrated with existing light transport methods.

Diffraction and propagation model.

[Shlomi 2024] A Generalized Ray Formulation For Wave-Optics Rendering

Wave optics, wave sampling theory, bidirectional path tracing

A generalized ray formal model is proposed for wave optics rendering. By solving the sampling problem, weak locality, linearity and completeness are simultaneously established in wave optics. Bidirectional wave optics path tracing and efficient rendering are achieved in complex scenes.

1. Background

The classical model of light transport is based on ray optics, which assumes that light propagates as a point query in a linear manner. However, ray optics cannot capture the wave nature of light and ignores interference and diffraction phenomena, such as the iridescence effect, thin film interference, and diffraction of long-wave radiation.

Although wave optics can accurately describe the interference and diffraction effects of light, traditional sampling and path tracing techniques are difficult to apply due to its nonlinear behavior.

2. Motivation

Solving the sampling problem in wave optics. In order to apply wave optics in bidirectional optical transmission, it is necessary to solve the sampling problem under weak locality.

Develop a novel formalism of wave optics that enables efficient applications in inverse path tracing and bidirectional light transport while maintaining linearity and completeness.

Improving wave-optics rendering efficiency, making the convergence speed of wave-optics rendering close to that of classical ray optics rendering systems.

3. Methods

Introduction of the generalized ray. Perform weak local linear queries. Generalized rays are no longer limited to point queries at a single location, but occupy a small spatial region. They can capture the interference and diffraction effects of light.

Weak locality and linearization. In wave optics, perfect locality and linearization cannot be achieved simultaneously. Therefore, perfect locality is abandoned. Weak locality is adopted to ensure that generalized rays can be linearly superposed.

Backward wave-optical light transport model.

Application in bidirectional path tracing.

[Shlomi 2021] Physical Light-Matter Interaction in Hermite-Gauss Space

Wave optics, PLT

A new framework for light-matter interaction is proposed, which unifies the formulas for scattering and diffraction by decomposing partially coherent light into the Hermite-Gauss space and modeling matter as a locally stationary random process, and enables efficient calculation and description of complex optical phenomena.

1. Background

The light observed in daily life is usually composed of many independent electromagnetic waves. Due to the complexity of partially-coherent light, the coherent properties of partially coherent light, such as reflection on microscopic geometric surfaces, the appearance of coating materials, grating effects, etc., cannot be explained by classical radiosity theory.

The limitations of existing tools only allow for rendering of specific materials and are difficult to generalize.

2. Motivation

Building a general-purpose light-matter interaction framework to efficiently process partially coherent light and simplify the complexity of existing computational tools.

Decomposing light coherence properties, the Hermite-Gauss space is introduced in the hope of decomposing and representing the coherence of light in a computationally feasible way, which is widely applicable to various optical phenomena.

3. Methods

Light transport in Hermite-Gauss space.

Locally-stationary matter model.

Analysis of light-matter interaction.

Unifying light-matter interaction formulae.

[GUILLÉN 2020] A general framework for pearlescent materials

Wave optics, interference pigment optics, inverse rendering

Simulate the optical properties of pearlescent materials, and provide a theoretical basis for the design and reverse rendering of pearlescent materials.

1. Background

Wide Applications of Pearlescent Materials. These materials have unique gloss and color-changing effects and are widely used in packaging, ceramics, printing, cosmetics and other fields.

The complex optical processes of pearlescence are derived from multiple scattering and wave optical interference between pigment flakes. Existing models are difficult to fully describe these complex optical behaviors.

2. Motivation

Building a More Comprehensive Model for Pearlescent Materials. Existing pearlescent material models do not adequately account for the complex structure of pigments and the effects of the manufacturing process. The goal is to expand the range of pearlescent appearances that can be represented by introducing new optical simulation models.

A generic pearlescent material model can also be used in reverse rendering.

3. Methods

An optical model based on interference pigments is proposed, which takes into account the multilayer structure of pigment flakes, the directional correlation of particles, thickness variation and other characteristics.

Systematic Study of Parameter Space, exploring the effects of orientation, thickness, and arrangement of pigment flakes on the material’s appearance.

Inverse Rendering helps interpret light scattering phenomena in the real world.

[Werner 2017] Scratch iridescence: Wave-optical rendering of diffractive surface structure

Wave optics, non-paraxial scalar diffraction theory, iridescence effect, microscopic scratches

A wave optics model based on non-paraxial scalar diffraction theory is used to simulate the iridescence effect on microscopic scratched surfaces, from local spots to smooth reflections at long distances.

1. Background

Optical Effects of Scratches: Under directional lighting (such as sunlight or halogen lamps), these scratched surfaces will show complex iridescent patterns, which are caused by the diffraction of incident light by the scratch structure. This cannot be reproduced in the geometric optics model.

Although existing analytical models are able to reproduce the iridescence effect of some microstructures (such as optical discs), simulation of the optical behavior of locally resolved scratches remains a challenge.

2. Motivation

Provide a Wave-Optical Scratch Rendering Framework, which can accurately simulate the optical effects caused by scratches, including light spots, iridescence and other visual phenomena.

3. Methods

Wave-Optical Model Based on Non-Paraxial Scalar Diffraction Theory: The method in this paper can accurately simulate the diffraction behavior of light on micro-scale surface features at large angles of incidence and reflection.

Vector Graphics Representation of Scratch Surfaces.

Multi-Scale BRDF Model.

Integration and Optimization in Physically-Based Rendering Systems.

[Fourneau 2024] Interactive Exploration of Vivid Material Iridescence using Bragg Mirrors

Wave optics, iridescence effect, Bragg mirror, spectral approximation

Describes the material iridescence effect of 1D photonic crystals (i.e. Bragg mirrors). Simplifies to a single bounce BRDF for fast computation under certain conditions.

1. Background

Iridescence in nature is manifested in organisms, plants or gemstones. It is caused by specific microscopic geometric structures whose size is comparable to the wavelength of visible light. The most prominent example is photonic crystals, which produce structural colors by repeating in one-, two- or three-dimensional structures.

1D photonic crystals, or optical properties of Bragg mirrors. Most existing works use the classic transfer matrix method to calculate the optical effects of multilayer films, but as the number of films increases, the computational complexity increases significantly.

2. Motivation

Simplifying the computation of Bragg mirror reflectance, introducing a more concise, closed-form reflection formula and exploring fast approximation methods in RGB spectral rendering.

Investigating the effects of rough Bragg layers to explore the influence of surface roughness on optical performance.

3. Methods

Introduce the closed-form reflectance formula. Based on Yeh's formula (Yeh88 Formula), do RGB spectral approximation (RGB Spectral Approximation).

Analyze the effect of roughness on optical transmission.

The appearance of a rough Bragg layer is efficiently rendered using the Single-reflection BRDF Model.

[Chen 2020] Rendering Near-Field Speckle Statistics in Scattering Media

MC path integral, importance sampling, memory effect, speckle, biological tissue imaging

Simulating speckle statistics under near-field imaging conditions in scattering media accelerates speckle rendering in biological tissue imaging applications and provides support for speckle-based imaging techniques.

1. Background

When performing deep imaging in biological tissues, imaging becomes very difficult due to multiple scattering of light inside the tissue. When irradiated with coherent light (such as laser), high-frequency speckle patterns are generated inside the tissue. The statistical properties of speckle patterns, especially the memory effect, provide the basis for tissue imaging techniques (such as fluorescence imaging and adaptive optical focusing).

The limitations of existing models are that they mainly focus on far-field imaging, while near-field conditions are ignored.

2. Motivation

Developing a Physically Accurate and Efficient Model for Near-Field Speckle Rendering.

Improving Computational Efficiency of Speckle Simulations. The wave equation solver is too computationally intensive.

3. Methods

Monte Carlo Path Integral Rendering Framework.

Aperture and Phase Function Approximations.

Importance Sampling.

[Kajiya and Kay 1989] Kajiya-Kay Model

The originator of hair, no need to say more

The hair is simplified as a thin and long cylinder, and the light reflection behavior of the hair surface is simulated by extending the Phong model.

1. Background

Based on the concept of Phong lighting model, it is extended into an empirical model suitable for hair rendering.

2. Motivation

Hair has very unique optical properties, such as specular reflection, subsurface scattering, etc., and the emergence of these phenomena is closely related to the geometric shape and surface structure of hair.

3. Methods

The Kajiya-Kay model is based on the idea of the Phong model and is an extension of the Phong model.

Cylindrical Hair Representation.

[Marschner 2003] Light Scattering from Human Hair Fibers

The originator of hair, no need to say more +1

It is able to capture key visual effects that existing Kajiya-Kay models cannot describe, such as multiple highlights and scattering variations associated with fiber axis rotation.

1. Background

Limitations of the Kajiya-Kay Model assumes that hair is only an opaque cylinder, ignoring key phenomena such as internal reflection and transmission.

2. Motivation

Hair is a dielectric material, and especially light-colored hair (such as blonde, brown, and red) has significant translucency. Therefore, there is a need for a More Accurate Hair Scattering Model.

3. Methods

The 3D full hemispherical light scattering of a single hair was measured.

The Transparent Elliptical Cylinder Model is proposed.

Simplified Shading Model.

[Benamira 2021] A Combined Scattering and Diffraction Model for Elliptical Hair Rendering

Wave optics, hair rendering, elliptical hair, diffraction scattering lobe function, no pre-calculation

A new combined scattering and diffraction model that simulates light scattering and diffraction phenomena for hair with an elliptical cross-section without pre-calculation.

1. Background

Still with wave optics as the background, when light interacts with objects whose size is close to the wavelength of light, interference and diffraction effects become significant.

Rendering hair requires considering its geometric properties as well as the wave effects of light. While ray tracing can simulate most scattering phenomena, it falls short when it comes to diffraction in hair.

2. Motivation

Addressing Diffraction and Elliptical Cross-sections. A model combining the wave and ray properties of light is proposed to handle the light diffraction phenomenon of hair without pre-calculation. Supports hair fibers with arbitrary elliptical cross-sections.

3. Methods

The ray part (Ray Interaction with Elliptical Fibers) introduces a complete light transport model, continues the traditional ray model, and handles most scattering effects.

The Wave Diffraction by Elliptical Fibers section introduces a new diffraction scattering lobe function that captures the strong forward scattering effect that occurs when light interacts with hair.

Precomputation-free Approach.

Integration with Modern Ray Tracers.

[Zinke 2008] Dual Scattering Approximation for Fast Multiple Scattering in Hair

Hair rendering, multiple scattering

The "dual scattering" model is widely used in real-time rendering, and there is no need to explain this classic model.

1. Background

In light-colored dense hair, multiple scattering is a key factor in determining the overall hair color.

Existing methods based on path tracing or photon mapping are too slow to render and often ignore the circular cross-section of hair fibers.

2. Motivation

Need for a Physically Accurate and Efficient Multiple Scattering Model.

3. Methods

Dual Scattering Model, global multiscattering and local multiscattering. The global multiscattering part aims to calculate the light that passes through the hair volume and reaches the neighborhood of the target point, while the local multiscattering considers the scattering events within this neighborhood.