Spherical Fibonacci Point Sets for Illumination Integrals

Abstract

Quasi-Monte Carlo (QMC) methods exhibit a faster convergence rate than that of classic Monte Carlo methods. This feature has made QMC prevalent in image synthesis, where it is frequently used for approximating the value of spherical integrals (e.g., illumination integral). The common approach for generating QMC sampling patterns for spherical integration is to resort to unit square low discrepancy sequences and map them to the hemisphere. However such an approach is suboptimal as these sequences do not account for the spherical topology and their discrepancy properties on the unit square are impaired by the spherical projection. In this article we present a strategy for producing high quality QMC sampling patterns for spherical integration by resorting to spherical Fibonacci point sets. We show that these patterns, when applied to illumination integrals, are very simple to generate and consistently outperform existing approaches, both in terms of Root Mean Square Error (RMSE) and image quality. Furthermore, only a single pattern is required to produce an image, thanks to a scrambling scheme performed directly in the spherical domain.

The Structures of Secretory and Dimeric Immunoglobulin A

“…The SIgA and dIgA structures revealed bent and tilted relationships between two IgA monomers, which are supported by stabilizing interactions that are likely to limit flexibility between the two IgA Fcs. Seeking to better visualize how this geometry could influence the flexible positions of SIgA Fabs, we modeled potential Fab location onto SIgA structures using a computational conformational-search approach, which approximated the position of each Fab by mapping a vector (beginning at N-terminus of CH2 and ending at the center of mass of Fab CDRs) onto a Fibonacci spherical lattice (FSL) (Marques, 2013) (Figure S4). We reasoned that this approach would broadly survey possible Fab positions without the constraints of the diverse Fc-Fab linkers and HC-LC contacts found in SIgA among mammals (Woof and Kerr, 2006).…”

“…The pdbs files used in Fab modeling were generated using the template mode of SWISS-MODEL (Waterhouse et al, 2018) with reference pdb 4EOW chain A and chain B and CH1-VH1 and CL1-VL1 sequences, respectively. In order to evenly sample all the potential positions, each Fab was rotated such that the center of mass (C.O.M) of the CDR was arranged on a Fibonacci spherical lattice (FSL) of one thousand points (Marques, 2013). During the rotation, the N-terminal residue in the CH2 domain (pivot) was set to be in the center of the FSL.…”

LumiPath – Towards Real-Time Physically-Based Rendering on Embedded Devices

“…-An algorithm for real-time physically-based rendering-like results on embedded devices based on uniformly sampled light fields, which, to the best of our knowledge, is the first algorithm to do so. -A new 2D plenoptic function representation using two Spherical Fibonacci point sets [9], which are sampled uniformly and with arbitrary sampling size providing flexibility in tweaking memory to any embedded device. -Fast neighborhood query of our domain using an extended version of the Keinert Inverse Fibonacci Mapping [7].…”

Light Beam Tracing for Multi-Bounce Specular and Glossy Transport Paths

“…One use of such vectors that are important here are for bin directions when accumulating PDFs and doing numerical integrals on the sphere or hemisphere. Marques et al [61] describe the importance of good quality equidistant vectors in rendering in general. They demonstrate a marked improvement in their simulation results when using good vector distributions.…”

“…Other methods to generate equidistant vectors may also be used. Figure 9.3, for example, shows the result of the Fibonacci spiral sphere (also known as the golden section spiral) method used by Marques et al [61]. The polyhedron subdivision method is preferred, however, because the vertices are explicitly connected into faces during their creation.…”