BSSRDF importance sampling

Abstract

Figure 1: Simple BSSRDF without (a) and with (b) axis MIS (25 spp). Complex BSSRDF without (c) and with (d) weight MIS (16 spp).Light propagation within translucent materials can be described by a BSSRDF [Jensen et al. 2001]. The main difficulty in integrating this effect lies in the generation of well-distributed samples on the surface within the support of the rapidly decaying BSSRDF profile. Jensen suggested that these points could be importance sampled but did not provide implementation details. More recently, Walter et al. [2012] and Christensen et al. [2012] proposed other sampling methods which can still suffer from excessive variance. P N Rm r P hitFigure 2: Geometric setup for Equation 1.Disk based sampling Our approach uses a disk distribution of samples which we project against the surface geometry using probe rays. We bound the radial term of the BSSRDF with a maximum distance Rm to define a bounding sphere around the shading point P. We cast probe rays against this sphere along an axis V perpendicular to the disk and compute the incoming irradiance at all intersection points we find inside the sphere. The contribution of each point is modulated by:which accounts for the probability of generating the point, the change in differential area measure and the BSSRDF itself. We omit the view-dependent terms here for simplicity. We choose the pdf to be proportional to R d , as for flat surfaces this results in perfect importance sampling. We have developed equations for both cubic and gaussian profiles. For a single planar gaussian defined as R d (r) = (2πv) −1 e −r 2 /2v , we use the following normalized pdf and warping equation to get r ∈ [0, Rm) from a random sample ξ ∈ [0, 1):pdf disk (r) = R d (r) / 1 − e −R 2 m /2v r(ξ) = −2v log 1 − ξ 1 − e −R 2 m /2v

Dual-Matrix Sampling for Scalable Translucent Material Rendering

“…We would like to explore methods for addressing this problem. It is also interesting to combine our method with the imagespace caching approaches [17], or the local BSSRDF sampling approaches [16].…”

“…An alternative for integrating over surface is to generate samples in the surroundings of camera samples on demand [15], [16]. This kind of methods do not require additional memory for storing surface samples, however, at the expense of less intuitive reuse of surface irradiance.…”

Data-Driven Approaches for Sparse Reflectance Modeling and Acquisition

“…We often find the BSSRDF in translucent materials. For modeling and acquisition of BSSRDFs, refer [25,46,47,48,49,50,51].…”

State of the Art in Efficient Translucent Material Rendering with BSSRDF

“…The real light transport in the medium is often longer than $$r=||x_i-x_o||$$. For sample selection, projecting samples onto the real surface [MKB*03b, KKCF13] does not directly satisfy the importance of sampling with PDF. Even machine learning [VKJ19] struggles to obtain a fit PDF.…”