CG: Volumetric Path Tracing Renderer
Introduction
Volumetric path tracing is a Monte Carlo rendering technique that simulates the propagation of light through participating media, such as fog, smoke, or mist. Unlike traditional ray tracing methods, which only account for light interactions at object surfaces, volumetric path tracing models the scattering, absorption, and emission of light inside a participating medium.
In volumetric path tracing, light rays are traced through the participating medium, and at each step, the probability of the ray being scattered or absorbed is calculated based on the properties of the medium, such as its density and scattering coefficient. The ray is then either scattered in a new direction or absorbed, depending on the calculated probability. This process is repeated for many rays, allowing for a statistically accurate simulation of the light propagation through the medium.
Volumetric path tracing is particularly useful for creating realistic simulations of atmospheric effects, such as fog, mist, or smoke, as well as other materials that exhibit volumetric scattering, such as clouds, fire, or water. It can also be used to simulate the behavior of light inside other types of participating media, such as translucent materials or biological tissue.
Approach
The key to developing correct algorithms is to carefully write down the integrals involved and construct the Monte Carlo estimators systematically.
The integral for volumetric rendering describes the process of computing the color of a pixel in an image that is generated by tracing light rays through a three-dimensional participating medium, such as smoke or fog. The integral takes into account the absorption, scattering, and emission of light as it interacts with the medium, and is typically evaluated using Monte Carlo integration.
The integral is constituted by the following factors:
Inscattering: Inscattering refers to the process by which light is scattered by particles within the participating medium and travels in a new direction towards the observer. Inscattering is influenced by the density and distribution of particles within the medium, as well as their scattering properties. Inscattering can give rise to effects such as haze, fog, and god rays, and is an important factor to consider when simulating atmospheric effects in volumetric rendering.
Emission: Emission refers to the process by which a participating medium emits light. This can occur through a variety of mechanisms, such as thermal radiation, fluorescence, or chemiluminescence. Emission can give rise to glowing or luminous effects in the medium, and is an important factor to consider when simulating light sources that are themselves participating media, such as glowing clouds or flames.
Attenuation: Attenuation refers to the process by which light is absorbed or scattered by particles within the participating medium and loses intensity as it travels through the medium. Attenuation is influenced by the density and composition of the medium, as well as the wavelength of the light. Attenuation is an important factor to consider when simulating the appearance of a participating medium over long distances, and can give rise to effects such as color shifts, light falloff, and depth of field.
The integral is evaluated using Monte Carlo integration, which involves randomly sampling directions and positions within the participating medium, and computing the integral over a large number of samples. This allows for a statistically accurate estimation of the radiance at each point in the image, which looks like this:
