Participating media are frequent in real-world scenes

such as milk

fruit juices

oil

or muddy water in river or ocean scenes. Realistic rendering of participating media is one of the important aspects in the rendering domain. Incoming light interacts with these participating media in a more complex manner than surface rendering: it is refracted at the boundary

absorbed

and scattered as it travels inside the medium. These physical phenomena have different contributions to the overall aspect of the material: refraction focuses light in several parts of the medium

creating high-frequency events

or volume caustics. Scattering blurs incoming light

spreading its contribution. Absorption reduces light intensity as it travels inside the medium. In recent years

several algorithms

such as virtual ray lights (VRL)

several extensions to photon mapping culminating with unified points

beams

and paths (UPBP)

and manifold exploration Metropolis light transport(MEMLT)

have been introduced for rendering participating media. All these methods have greatly improved the simulation of participating media but still encounter problems for simulation of materials with a high albedo

where multiple scattering dominates or high-frequency volumetric caustics effects. Another group of work is called diffusion-based methods. These methods are fast and designed to work with materials with a high albedo. However

these methods produce less accurate results

especially for highly anisotropic media

whereas diffusion-theory-based methods use similarity theory for anisotropic media

which leads to increased inaccuracy. In this paper

several efficient rendering methods are introduced for homogeneous participating media rendering. The first is point-based rendering method for participating media. The point-based method is different from the previous two frameworks (Monte Carlo rendering and density estimation). It first distributes several points in the participating media to generate a point cloud

organizes the point cloud into spatial hierarchy

and then uses it to accelerate the single

second

and multiple scattering computation. For multiple scattering simulation

a precomputed multiple scattering distribution representation in infinite media is presented. With further GPU(graphics processing unit) implementation

this method can achieve interactive efficiency and support the editing of materials and light sources for arbitrary homogeneous participating media

from high-scattered media to high-absorbed media and from isotropic media to highly anisotropic media. The first work is an extension of the point-based method from the surface rendering to volume rendering. Different from the two other frameworks

it is deterministic and noise-free. However

this method is biased. Its target application is material editing or light editing or high-quality rendering with a limited time budget. The second is a precomputed model based on multiple reflections. It precomputes multiple scattering distributions in infinite participating media

proposes a more compact representation than the prior works by analyzing the symmetric of the light distribution

and decreases the number of dimensions from four to three. The precomputed model is then applied to various Monte Carlo rendering methods

such as VRL

UPBP

and MEMET. The original algorithms are in charge of low-order scattering

combined with multiple scattering computed using the precomputed model. Results show substantial improvements in convergence speed and memory costs

and a negligible effect on accuracy. This method is especially interesting for materials with a large albedo and a small mean-free-path

where higher-order scattering effects dominate. It has a limited influence but also a limited cost for more transparent materials with a larger mean-free-path. This method can be used for unidirectional rendering algorithms (e.g.

path tracing) and bidirectional algorithms (e.g.

VRL)

but this method has less impressive speedup in unidirectional algorithms because unidirectional rendering algorithms have difficulties in finding a path for participating media with boundaries. The last introduced method is a path guiding method in participating media rendering

which is under the framework of path tracing. In simple terms

the paths become lost in the medium. Path guiding has been proposed for surface rendering to make the convergence faster by guiding the sampling. In this work

a path guiding solution to translucent materials is introduced. It includes two steps

namely

learning and rendering. In the learning step

the radiance distribution in the volume is learned with path tracing

and this 4D distribution is represent with an SD-tree. In the rendering step

this representation is used for sampling the outgoing direction

combining with the phase function sampling by resampled importance sampling. The key insight of resampled importance sampling is about sampling two multiplied high-frequency functions. The proposed method remarkably improves the performance of light transport simulation in participating media

especially for small lights and media with refractive boundaries. This method can handle any homogeneous participating media

from high scattering to low scattering

from high absorption to low absorption

and from isotropic media to highly anisotropic media. Unlike the previous two works

this method is unbiased. However

it can only handle direction sampling with path guiding and leaves the distance sampling with the original method

which can be further improved. The three methods all target the efficient rendering of homogenous participating media but in different methods.