Edge asymptotics for the radiosity equation over polyhedral boundaries

Rathsfeld, Andreas

doi:10.1002/(sici)1099-1476(199902)22:3<217::aid-mma33>3.0.co;2-h

Cited by 12 publications

(8 citation statements)

References 9 publications

(14 reference statements)

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“…The behavior of diffuse surfaces in close proximity to other surfaces (such as corners) has been explored in [Rathsfeld 1999] and [Atkinson 2000]. Their results confirm the existence of highfrequency change, or light reflexes, around corners.…”

Section: Related Workmentioning

confidence: 92%

Fast and detailed approximate global illumination by irradiance decomposition

Arıkan¹,

Forsyth²,

O’Brien³

2005

ACM SIGGRAPH 2005 Papers

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In this paper we present an approximate method for accelerated computation of the final gathering step in a global illumination algorithm. Our method operates by decomposing the radiance field close to surfaces into separate far-and near-field components that can be approximated individually. By computing surface shading using these approximations, instead of directly querying the global illumination solution, we have been able to obtain rendering time speed ups on the order of 10× compared to previous acceleration methods. Our approximation schemes rely mainly on the assumptions that radiance due to distant objects will exhibit low spatial and angular variation, and that the visibility between a surface and nearby surfaces can be reasonably predicted by simple locationand orientation-based heuristics. Motivated by these assumptions, our far-field scheme uses scattered-data interpolation with spherical harmonics to represent spatial and angular variation, and our near-field scheme employs an aggressively simple visibility heuristic. For our test scenes, the errors introduced when our assumptions fail do not result in visually objectionable artifacts or easily noticeable deviation from a ground-truth solution. We also discuss how our near-field approximation can be used with standard local illumination algorithms to produce significantly improved images at only negligible additional cost.

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Section: Related Workmentioning

confidence: 92%

Fast and detailed approximate global illumination by irradiance decomposition

Arıkan¹,

Forsyth²,

O’Brien³

2005

ACM SIGGRAPH 2005 Papers

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“…But the solution is differentiable in the interior of every segment l [i] . The Hölder exponent α can be calculated explicitely, if the angle between adjacent segments and the quotient of their reflectivity coefficients are given, see [11,16].…”

Section: Description Of the Modified Collocation Methodsmentioning

confidence: 99%

“…A smaller exponent will reduce the work for one iteration, but it will also destroy the optimal rate of convergence. The calculation of the Hölder exponent α can be done in advance, see [11,16].…”

Section: The Integration Error and The Complexity Of The Algorithmmentioning

confidence: 99%

A fast collocation method for the radiosity equation, based on the hierarchical algorithm of Hanrahan and Salzman: the 1d case

Hansen

2005

Adv Comput Math

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In this paper we study a collocation method with piecewise constant trial functions for the solution of the planar radiosity equation. The matrix of the collocation method is approximated by a method which was developed by Hanrahan et al. [9,10]. We prove that the modified collocation method results in a reduction of work while the order of convergence stays the same. Numerical examples demonstrate the theoretical results.

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“…It is known that, for polyhedral domains, K is related to the Mellin convolution (see [18]), which is a noncompact operator on all L p spaces [7]. For conical surfaces Σ, K is known to be noncompact on L 2 (Σ) from the spectral analysis in [10].…”

Section: Noncompactness Of K For Polyhedral Domainsmentioning

confidence: 99%

Noncompactness of Integral Operators Modeling Diffuse-Gray Radiation in Polyhedral and Transient Settings

Druet

Philip

2010

Integr. Equ. Oper. Theory

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While it is well-known that the standard integral operator K of (stationary) diffuse-gray radiation, as it occurs in the radiosity equation, is compact if the domain of radiative interaction is sufficiently regular, we show noncompactness of the operator if the domain is polyhedral. We also show that a stationary operator is never compact when reinterpreted in a transient setting. Moreover, we provide new proofs, which do not use the compactness of K, for 1 being a simple eigenvalue of K for connected enclosures, and for I − (1 − )K being invertible, provided the emissivity does not vanish identically.Mathematics Subject Classification (2010). Primary 45P05; Secondary 45C05.

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Edge asymptotics for the radiosity equation over polyhedral boundaries

Cited by 12 publications

References 9 publications

Fast and detailed approximate global illumination by irradiance decomposition

Fast and detailed approximate global illumination by irradiance decomposition

A fast collocation method for the radiosity equation, based on the hierarchical algorithm of Hanrahan and Salzman: the 1d case

Noncompactness of Integral Operators Modeling Diffuse-Gray Radiation in Polyhedral and Transient Settings

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