41-Issue 4

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https://diglib.eg.org/handle/10.2312/2633205

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Browsing 41-Issue 4 by Subject "Modeling and simulation"

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    A Bidirectional Formulation for Walk on Spheres
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Qi, Yang; Seyb, Dario; Bitterli, Benedikt; Jarosz, Wojciech; Ghosh, Abhijeet; Wei, Li-Yi
    Numerically solving partial differential equations (PDEs) is central to many applications in computer graphics and scientific modeling. Conventional methods for solving PDEs often need to discretize the space first, making them less efficient for complex geometry. Unlike conventional methods, the walk on spheres (WoS) algorithm recently introduced to graphics is a grid-free Monte Carlo method that can provide numerical solutions of Poisson equations without discretizing space. We draw analogies between WoS and classical rendering algorithms, and find that the WoS algorithm is conceptually equivalent to forward path tracing. Inspired by similar approaches in light transport, we propose a novel WoS reformulation that operates in the reverse direction, starting at source points and estimating the Green's function at ''sensor'' points. Implementations of this algorithm show improvement over classical WoS in solving Poisson equation with sparse sources. Our approach opens exciting avenues for future algorithms for PDE estimation which, analogous to light transport, connect WoS walks starting from sensors and sources and combine different strategies for robust solution algorithms in all cases.
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    Temporally Sliced Photon Primitives for Time-of-flight Rendering
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Liu, Yang; Jiao, Shaojie; Jarosz, Wojciech; Ghosh, Abhijeet; Wei, Li-Yi
    We derive a class of new Monte Carlo estimators for volumetric time-of-flight rendering, generalizing prior work on transient photon points and beams. Conceptually, our method starts with any steady-state photon primitive – like a photon plane, parallelepiped, or parallelotope – and slices it with a temporal wavefront, producing a primitive of one dimension lower. We show how different unbiased temporally sliced primitives arise by analytically integrating any four dimensions within a novel extended spatio-temporal path space formulation. The differences between these estimators reduce to the determinant of a 4×4 Jacobian matrix, with columns dictated by the chosen dimensions. We then show how to combine the relative strengths of different sliced primitives using multiple importance sampling. Finally, we implement several of the new estimators enabled by our theory and compare them to each other as well as previous techniques.