Can You See the Heat? A Null-Scattering Approach for Refractive Volume Rendering

Fraboni, Basile; Chan, Tsz Kin; Vergne, Thibault; Jeziorski, Jakub

doi:10.1145/3587421.3595427

ACM SIGGRAPH 2023 Talks 2023

DOI: 10.1145/3587421.3595427

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Can You See the Heat? A Null-Scattering Approach for Refractive Volume Rendering

Basile Fraboni¹,

Tsz Kin Chan²,

Thibault Vergne³

et al.

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2024

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Specular Polynomials

Fan,

Guo,

Wang

et al. 2024

ACM Trans. Graph.

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Finding valid light paths that involve specular vertices in Monte Carlo rendering requires solving many non-linear, transcendental equations in high-dimensional space. Existing approaches heavily rely on Newton iterations in path space, which are limited to obtaining at most a single solution each time and easily diverge when initialized with improper seeds. We propose specular polynomials , a Newton iteration-free methodology for finding a complete set of admissible specular paths connecting two arbitrary endpoints in a scene. The core is a reformulation of specular constraints into polynomial systems, which makes it possible to reduce the task to a univariate root-finding problem. We first derive bivariate systems utilizing rational coordinate mapping between the coordinates of consecutive vertices. Subsequently, we adopt the hidden variable resultant method for variable elimination, converting the problem into finding zeros of the determinant of univariate matrix polynomials. This can be effectively solved through Laplacian expansion for one bounce and a bisection solver for more bounces. Our solution is generic, completely deterministic, accurate for the case of one bounce, and GPU-friendly. We develop efficient CPU and GPU implementations and apply them to challenging glints and caustic rendering. Experiments on various scenarios demonstrate the superiority of specular polynomial-based solutions compared to Newton iteration-based counterparts. Our implementation is available at https://github.com/mollnn/spoly.

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Specular Polynomials

Fan,

Guo,

Wang

et al. 2024

ACM Trans. Graph.

View full text Add to dashboard Cite

show abstract

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Can You See the Heat? A Null-Scattering Approach for Refractive Volume Rendering

Cited by 1 publication

References 4 publications

Specular Polynomials

Specular Polynomials

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