PRT computing volume rendering [Supplement]

When considering volume in-scattering, if the volume particles are of the same nature, then our phase function P (W1, W) = 1/(4 * PI) can be expressed using a constant, so we can simplify in-scattering into 1/(4 * PI) in our computation) using ls (W1) * TS (W1) * dw1. in this way, we project TS (W1) to each particle of volume to obtain the sh coefficient TSI. therefore, when we finally calculate in-scattering, we only need to use the LSI of the Ambient Illumination coefficient and TSI of the particle coefficient as the dot to obtain the calculation amount when in-scattering occurs on this particle.

In the two methods mentioned above, the first method is to simplify particles that are not of the same nature. We ignore TS (W1) and consider P (W1, W, in this way, the sh coefficient of all particles in volume is the same for W in the same line of sight. in this way, we get a set of cube maps based on the line of sight W to save the sh coefficient of the particles. In this case, P (W1, W) is a constant. We can consider the TS (W1) of each particle) in this way, each particle can obtain a set of different sh coefficients. The above two methods are aimed at in-scattering. When we finally calculate the outermost layer of points, we use the Monte Carlo Integration Method in the same way. We sample the back face twice, the front face once, and finally calculate the approximate value of the entire point.