Graphics Reference
In-Depth Information
2.2 Previous Work
There were a lot of methods for rendering scattering in the Earth's atmosphere,
starting with the work by Klassen [Klassen 87]. Early real-time approaches used
very simple models due to hardware limitations of the time. Assuming flat
Earth, constant density atmosphere and constant light intensity, Hoffman and
Preetham derived a fully analytical solution for the airlight integral [Hoffman
and Preetham 02]. The resulting model produces reasonable results, but only for
ground views. Still, the sky looks unnatural, especially near the horizon. A more
accurate model was proposed by Riley et al. [Riley et al. 04]. They also assumed
Earth was flat, but the density of the atmosphere in their model decreased ex-
ponentially. To obtain a closed form solution for airlight integral, they ignored
scattering on aerosols. Some attempts were made to approximate complex ef-
fects in the atmosphere with analytic functions [Preetham et al. 99]. Mitchell
simulated light shafts using screen-space radial blur [Mitchell 08].
More physically accurate approaches perform numerical integration of the
scattering integral with either slicing [Dobashi et al. 02] or ray marching [O'Neil 04,
Schuler 12]. To accelerate numerical integration, different techniques were pro-
posed related basically to the way optical depth is computed inside the inte-
gral. Nishita et al. [Nishita et al. 93], Dobashi et al. [Dobashi et al. 02] and
O'Neil [O'Neil 04] used different pre-computed lookup tables. In his later work,
O'Neil replaced the lookup table with a combination of ad hoc analytic func-
tions [O'Neil 05]. Schuler presented suciently accurate analytical expression
based on the approximation to the Chapman function [Schuler 12].
Some researchers tried to pre-compute the scattering integral as much as pos-
sible. While generally it depends on four variables, Schafhitzel et al. dropped
one parameter and stored the integral using 3D texture [Schafhitzel et al. 07].
Bruneton and Neyret elaborated on this idea and used complete 4D parameter-
ization [Bruneton and Neyret 08]. Their algorithm also approximates multiple
scattering, and accounts for Earth surface reflection. It uses an array of 3D tex-
tures to store the resulting data; manual interpolation for the fourth coordinate
is also required. To render light shafts, they used shadow volumes to compute
the total length of the illuminated portion of the ray. Then they computed in-
scattering, assuming that the illuminated part of the ray is continuous and starts
directly from the camera.
Engelhardt and Dachsbacher developed an elegant and ecient algorithm for
rendering scattering effects in a homogeneous participating medium [Engelhardt
and Dachsbacher 10]. They noticed in-scattered light intensity varies smoothly
along the epipolar lines emanating from the position of the light source on the
screen. To account for this, they proposed a technique that distributes ray march-
ing samples sparsely along these lines and interpolates between samples where
adequate. It preserves high-frequency details by placing additional samples at
depth discontinuities.
