Stratified Sampling of Projected Spherical Caps

Ureña, Cristóbal Pasadas; Georgiev, Iliyan

doi:10.1111/cgf.13471

Cited by 13 publications

(23 citation statements)

References 17 publications

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“…5c. While exact procedures exist for projected spherical caps [Peters and Dachsbacher 2019;Ureña and Georgiev 2018] there is no known analytic solution that achieves stratified sampling for projected spherical triangles. Ureña et al [2000] proposed an approximate importance sampling procedure based on adaptive subdivisions of the sampling domain, while Arvo [2001] relies on the numerical inversion of a cumulative distribution function.…”

Section: Sampling Slopes Within Trianglesmentioning

confidence: 99%

Slope-space integrals for specular next event estimation

et al. 2020

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Sampling Slopes Within Trianglesmentioning

confidence: 99%

Slope-space integrals for specular next event estimation

et al. 2020

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“…The relative flux observed as a function of viewing angle is proportional to the area of the cap projected on to a plane perpendicular to the viewing angle. We use the result of Ureña & Georgiev (2018) to perform the projection. The maximum flux is set to the analytic result of Kasen (2010).…”

Section: Type Ia Companion Shock Coolingmentioning

confidence: 99%

Observing the earliest moments of supernovae using strong gravitational lenses

Foxley-Marrable

Collett

Frohmaier

et al. 2020

Monthly Notices of the Royal Astronomical Society

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We determine the viability of exploiting lensing time delays to observe strongly gravitationally lensed supernovae (gLSNe) from first light. Assuming a plausible discovery strategy, the Legacy Survey of Space and Time (LSST) and the Zwicky Transient Facility (ZTF) will discover ∼110 and ∼1 systems per year before the supernova (SN) explosion in the final image, respectively. Systems will be identified $11.7^{+29.8}_{-9.3}$ d before the final explosion. We then explore the possibility of performing early-time observations for Type IIP and Type Ia SNe in LSST-discovered systems. Using a simulated Type IIP explosion, we predict that the shock breakout in one trailing image per year will peak at ≲24.1 mag (≲23.3) in the B-band (F218W), however evolving over a time-scale of ∼30 min. Using an analytic model of Type Ia companion interaction, we find that in the B-band we should observe at least one shock cooling emission event per year that peaks at ≲26.3 mag (≲29.6) assuming all Type Ia gLSNe have a 1 M⊙ red giant (main sequence) companion. We perform Bayesian analysis to investigate how well deep observations with 1 h exposures on the European Extremely Large Telescope would discriminate between Type Ia progenitor populations. We find that if all Type Ia SNe evolved from the double-degenerate channel, then observations of the lack of early blue flux in 10 (50) trailing images would rule out more than 27 per cent (19 per cent) of the population having 1 M⊙ main sequence companions at 95 per cent confidence.

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“…There have been active research projects focusing on sampling [Arvo 1995b[Arvo , 2001Gamito 2016;Guillén et al 2017;Peters and Dachsbacher 2019;Ureña et al 2013;Ureña and Georgiev 2018] to reduce variance and improve convergence rate. On the other hand, solutions based on closed-form integration leveraging spherical distribution approximation have been proposed [Dupuy et al 2017;Heitz et al 2016] recently.…”

Section: Introductionmentioning

confidence: 99%

Spherical Light Integration over Spherical Caps via Spherical Harmonics

Zhou

Wei

2020

SIGGRAPH Asia 2020 Technical Communications

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Monte Carlo(5.47s) Ours(5.20s) Reference Monte Carlo(6.57s)/Ours(7.01s)/Reference Figure 1: Equal time comparison of Monte Carlo rendering and our method. This breakfast scene is lit by 2 sphere lights (left) and 1 quad light (right). Our method uses order 16 SH expansions for the rough gold BRDF (highlighted on the left) and order 8 for diffuse BRDF. We compare relative MSE numbers for full image (top) and several insets (bottom). Our method can outperform Monte Carlo sampling (MIS) method for direct lighting with good approximation of low frequency BRDF.

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Stratified Sampling of Projected Spherical Caps

Cited by 13 publications

References 17 publications

Slope-space integrals for specular next event estimation

Slope-space integrals for specular next event estimation

Observing the earliest moments of supernovae using strong gravitational lenses

Spherical Light Integration over Spherical Caps via Spherical Harmonics

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