Analytic Approximations for Real-Time Area Light Shading

Lecocq, Pascal; Dufay, Arthur; Sourimant, Gaël; Marvie, Jean-Eudes

doi:10.1109/tvcg.2017.2656889

Cited by 10 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Switching between numerical and analytic evaluations according to some heuristics [Yuan et al 2012] might be potentially helpful. In addition, applying analytical approximations [Lecocq et al 2017] might make the gradient evaluations more efficient.…”

Section: Limitations and Future Workmentioning

confidence: 99%

Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights

Cai

Zhao

et al. 2020

ACM Trans. Graph.

View full text Add to dashboard Cite

Recent work has developed analytic formulae for spherical harmonic (SH) coefficients from uniform polygonal lights, enabling near-field area lights to be included in Precomputed Radiance Transfer (PRT) systems, and in offline rendering. However, the method is inefficient since coefficients need to be recomputed at each vertex or shading point, for each light, even though the SH coefficients vary smoothly in space. The complexity scales linearly with the number of lights, making many-light rendering difficult. In this paper, we develop a novel analytic formula for the spatial gradients of the spherical harmonic coefficients for uniform polygonal area lights. The result is a significant generalization, involving the Reynolds transport theorem to reduce the problem to a boundary integral for which we derive a new analytic formula, showing how to reduce a key term to an earlier recurrence for SH coefficients. The implementation requires only minor additions to existing code for SH coefficients. The results also hold implications for recent efforts on differentiable rendering. We show that SH gradients enable very sparse spatial sampling, followed by accurate Hermite interpolation. This enables scaling PRT to hundreds of area lights with minimal overhead and real-time frame rates. Moreover, the SH gradient formula is a new mathematical result that potentially enables many other graphics applications.

show abstract

Section: Limitations and Future Workmentioning

confidence: 99%

Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights

Cai

Zhao

et al. 2020

ACM Trans. Graph.

View full text Add to dashboard Cite

show abstract

“…The area light is actually what we refer to as an LPAL. While real‐time rendering for scenes with area lights have been intensely studied [Arv95; Dro14; HDHN16; LDSM17], we employed the approach proposed by Heitz et al [HDHN16] because of its fast calculation and applicability to glossy surfaces. Following their method, we calculate the integration using the following formula:…”

Section: Indirect Illumination With Layered Polygonal Area Lightsmentioning

confidence: 99%

“…Considering a line parameterization along this straight line and assuming that the light contribution from a cutting section is a function of the line parameter, we found that the contribution from the slice of volume can be represented in an analytic form. Given that the cutting section of an emissive participating medium can be considered as an area light, we can compute its light contribution efficiently using modern approaches [HDHN16; LDSM17]. In this paper, we refer to these virtual area lights as layered polygonal area lights (LPALs).…”

Section: Introductionmentioning

confidence: 99%

Real‐time Indirect Illumination of Emissive Inhomogeneous Volumes using Layered Polygonal Area Lights

Kuge

Yatagawa

Morishima

2019

Computer Graphics Forum

View full text Add to dashboard Cite

Indirect illumination involving with visually rich participating media such as turbulent smoke and loud explosions contributes significantly to the appearances of other objects in a rendering scene. However, previous real‐time techniques have focused only on the appearances of the media directly visible from the viewer. Specifically, appearances that can be indirectly seen over reflective surfaces have not attracted much attention. In this paper, we present a real‐time rendering technique for such indirect views that involves the participating media. To achieve real‐time performance for computing indirect views, we leverage layered polygonal area lights (LPALs) that can be obtained by slicing the media into multiple flat layers. Using this representation, radiance entering each surface point from each slice of the volume is analytically evaluated to achieve instant calculation. The analytic solution can be derived for standard bidirectional reflectance distribution functions (BRDFs) based on the microfacet theory. Accordingly, our method is sufficiently robust to work on surfaces with arbitrary shapes and roughness values. In addition, we propose a quadrature method for more accurate rendering of scenes with dense volumes, and a transformation of the domain of volumes to simplify the calculation and implementation of the proposed method. By taking advantage of these computation techniques, the proposed method achieves real‐time rendering of indirect illumination for emissive volumes.

show abstract

“…The use of numerical methods to approximate integrals for accurate real-time rendering of surfaces lit by non-occluded area light sources leads to results with noise, hardly compatible with real-time rendering constraints [62].…”

Section: State Of the Artmentioning

confidence: 99%

Analytic approximations of integral transforms in terms of elementary functions: application to special functions

Herrero¹

View full text Add to dashboard Cite

This thesis focuses on the study of new analytical methods for the approximation of integral transforms and, in particular, of special functions that admit an integral representation. The importance of these functions lies in the fact that they are solutions to a great variety of functional equations that model speciﬁc physical phenomena. Moreover, they play an important role in pure and applied mathematics, as well as in other branches of science such as chemistry, statistics or economics. Usually, the integrals deﬁning these special functions depend on various parameters that have a speciﬁc physical meaning. For this reason, it is important to have analytical techniques that allow their computation in a quick and easy manner. The most commonly used analytical methods are based on series expansions of local validity: Taylor series and asymptotic (divergent) expansions that are, respectively, valid for small or large values of the physically relevant variable. However, neither of them is, in general, simultaneously valid for large and small values of the variable. In this thesis we seek new methods for the computation of analytic expansions of integral transforms satisfying the following three properties: (a) The expansions are uniformly valid in a large region of the complex plane. Ideally, these regions should be unbounded and contain the point 0 in their interior. (b) The expansions are convergent. Therefore, it is not necessary to obtain error bounds or to study the optimal term to truncate the expansion: the more terms considered, the smaller the error committed. (c) The expansions are given in terms of elementary functions. We develop a theory of uniform expansions that shows the necessary and suﬃcient conditions to obtain expansions of integral transforms fulﬁlling the three conditions (a),(b) and (c) above. This theory is applied to obtain new series approximations satisfying (a), (b) and (c) of a large number of special functions. The new expansions are compared with other known representations that we may ﬁnd in the literature to show their ad-vantages and drawbacks. In contrast to the Taylor and asymptotic expansions, the main beneﬁt of the uniform expansions is that they are valid in a large region of the complex plane. For this reason, they may be used to replace the function they approximate (which is often diﬃcult to work with) when it appears in certain calculations, such as a factor of an integral or in a diﬀerential equation. Since these developments are also given in terms of elementary functions, such calculations may be carried out easily. Next, we consider a particularly important case: when the kernel of the integral transform is given by an exponential. We develop a new Laplace’s method for integrals that produces asymptotic and convergent expansions, in contrast to the classical Laplace method which produces divergent developments. The expansions obtained with this new method satisfy (a) and (b) but not (c), since the asymptotic sequence is given in terms of incomplete beta functions. Finally, we develop a new uniform asymptotic method 'saddle point near an end point' which does not satisfy (b) and (c) but, unlike the classical 'saddle point near an end point' method, allows us to calculate the coeﬃcients of the expansion by means of a simple and systematic formula.

show abstract

Analytic Approximations for Real-Time Area Light Shading

Cited by 10 publications

References 21 publications

Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights

Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights

Real‐time Indirect Illumination of Emissive Inhomogeneous Volumes using Layered Polygonal Area Lights

Analytic approximations of integral transforms in terms of elementary functions: application to special functions

Contact Info

Product

Resources

About