Ralf Habel, Per H. Christensen, Wojciech Jarosz
Abstract:
We present photon beam diffusion, an efficient numerical
method for accurately rendering translucent materials. Our approach
interprets incident light as a continuous beam of photons inside the
material. Numerically integrating diffusion from such extended sources
has long been assumed computationally prohibitive, leading to the
ubiquitous single-depth dipole approximation and the recent analytic
sum-of-Gaussians approach employed by Quantized Diffusion. In this
paper, we show that numerical integration of the extended beam
is not only feasible, but provides increased speed, flexibility,
numerical stability, and ease of implementation, while retaining the
benefits of previous approaches. We leverage the improved diffusion
model, but propose an efficient and numerically stable Monte Carlo
integration scheme that gives equivalent results using only 3-5
samples instead of 20-60 Gaussians as in previous work. Our method
can account for finite and multi-layer materials, and additionally
supports directional incident effects at surfaces. We also propose a
novel diffuse exact single-scattering term which can be integrated in
tandem with the multi-scattering approximation. Our numerical approach
furthermore allows us to easily correct inaccuracies of the diffusion
model and even combine it with more general Monte Carlo rendering
algorithms. We provide practical details necessary for efficient
implementation, and demonstrate the versatility of our technique by
incorporating it on top of several rendering algorithms in both
research and production rendering systems.
Paper (PDF)
Additional materials: [PBD_matlab_v1.03.zip], [supplemental-theory.pdf]
Published in Computer Graphics Forum (Proceedings of the Eurographics Symposium on Rendering 2013), volume 32, number 4. Eurographics / Blackwell Publishers, June 2013. (Zaragoza, Spain, June 19-21.). Equation 13 amended July 2013.