MASARYK UNIVERSITY
FACULTY OF INFORMATICS
Atmospheric effects for
real-time global illumination
BACHELOR'S THESIS
Aron Samuel Kovacs
Brno, Spring 2018
MASARYK UNIVERSITY
FACULTY OF INFORMATICS
Atmospheric effects for
real-time global illumination
BACHELOR'S THESIS
Aron Samuel Kovacs
Brno, Spring 2018
This is where a copy of the official signed thesis assignment and a copy of the
Statement of an Author is located in the printed version of the document.
Declaration
Hereby I declare that this paper is m y original authorial work, which
I have worked out o n m y o w n . A l l sources, references, a n d literature
used or excerpted during elaboration of this work are properly cited
and listed i n complete reference to the due source.
Áron Samuel Kovács
Advisor: M g r . Jan Čejka
i
Acknowledgements
I thank m y advisor M g r . Jan Čejka for his great help w i t h m y thesis.
I w o u l d also like to thank m y family a n d friends for their support.
111
Abstract
Fast simulation of atmospheric effects is an important area of research
for outdoor real-time visualisations. This thesis describes the principles
of real-time rendering of atmospheric effects for the purpose
of their simulation and describes a method for real-time rendering
of volumetric clouds shaded w i t h light provided by the atmosphere.
The described techniques are implemented as example projects using
render library mallumo.
iv
Keywords
global illumination, O p e n G L , real-time computer graphics, Rust, volumetric
clouds
v
Contents
Introduction 1
1 Mallumo 3
2 Theoretical background 5
2.1 Radiant flux 5
2.2 Irradiance 5
2.3 Radiance 5
2.4 Transmittance 5
2.5 Scattering 6
2.5.1 Forward scattering and backscattering 6
2.5.2 Elastic scattering 6
2.5.3 Dominant scattering processes i n Earth's atmosphere
7
2.5.4 Phase functions for Rayleigh and M i e scatterings 7
2.5.5 Single and multiple scattering 8
2.6 Shapes and density of clouds 9
2.7 Turbidity 10
2.8 Lighting of clouds 10
3 Related work 13
3.1 Atmosphere 13
3.1.1 Nishita93 model 13
3.1.2 Nishita96 model 14
3.1.3 Preetham model 15
3.1.4 Haber model 16
3.1.5 Bruneton model 17
3.2 Clouds 18
3.2.1 Skybox a n d skydome 18
3.2.2 Implicit volumes 18
3.2.3 Polygon clouds 19
3.2.4 Particle clouds 19
3.2.5 Procedural clouds 19
4 Implementation 21
4.1 Bruneton model 21
vii
4.1.1 Physical model 21
4.1.2 Rendering equations 22
4.1.3 M e t h o d 23
4.1.4 Precomputation 24
4.1.5 Parametrization 26
4.1.6 Rendering 26
4.1.7 Computational complexity 27
4.1.8 Limitations 27
4.1.9 Implementation details 28
4.2 Clouds 29
4.2.1 Modelling 29
4.2.2 Texture generation 30
4.2.3 Rendering 31
4.2.4 Optimizations 33
5 Results 35
5.1 Sky 35
5.2 Clouds 37
6 Conclusion 45
Bibliography 47
A List of electronic attachments 51
viii
List of Tables
5.1 C l o u d rendering speed at F u l l H D resolution.
List of Figures
1.1 Sponza scene without albedo texture, illuminated directly
and indirectly by the Sun using anisotropic V X G I . 3
2.1 Light entering a scattering m e d i u m , producing forward
scattering and backscaterring. 6
2.2 Single and multiple scattering, courtesy of [4]. 9
2.3 Different types of clouds occurring at w i d e range of
altitudes, courtesy of [1]. 9
3.1 Fisheye skydome rendering of the spectral radiance of the
Nishita93 model, for sun zenith angles 87°, 41°, 31°, 21°,
courtesy of [6]. 13
3.2 Fisheye skydome rendering of the spectral radiance of the
Nishita96 model, for sun zenith angles 87°, 41°, 31°, 21°,
courtesy of [6]. 14
3.3 Fisheye skydome rendering of the spectral radiance of
Preetham, for sun zenith angles 87°, 41°, 31°, 21°. Note
how bright the sky is compared to the previous models,
courtesy of [6]. 15
3.4 Fisheye skydome rendering of the spectral radiance of the
Haber model, for sun zenith angles 87°, 41°, 31°, 21°. Note
how the sky is less orange near the horizon compared to
the Nishita93 and the Nishita96 models, courtesy of
[6]. 16
3.5 Fisheye skydome rendering of the spectral radiance of the
Bruneton model, for sun zenith angles 87°, 41°, 31°, 21°.
Courtesy of [6]. 17
3.6 Implicit volume on the left and perturbed result o n the
right, courtesy of [13]. 18
3.7 A n example of a polygon cloud, courtesy of [14]. 19
4.1 Simplex-Worley noise and Worley noise at increasing
frequencies. 30
4.2 Worley noise at increasing frequencies. 31
4.3 C u r l noise. 31
5.1 Rendering of the sky w i t h the Sun at the zenith angle of
0°, w i t h the camera looking straight up. 35
xi
5.2 Rendering of the sky w i t h the Sun at the zenith angle of
60°. 36
5.3 Rendering of the sky w i t h the Sun at the zenith angle of
93°, meaning the Sun is below the horizon. 36
5.4 Rendering of the clouds w i t h R = 32 and rapidly moving
camera. Figure 5.5 is enclosed i n the red square. 38
5.5 Detail of Figure 5.4. 38
5.6 Rendering of the clouds w i t h D equal to 1, N equal to 512,
and w i t h the Sun at the zenith angle of 50°. 41
5.7 Rendering of the clouds w i t h D equal to 1, N equal to 512,
and w i t h the Sun at the zenith angle of 66°. 41
5.8 Rendering of the clouds w i t h the field of view of 16°, D
equal to 1, and N equal to 512. Note the artefacts caused
by discretisation of the noise functions and insufficient
step length. 42
5.9 Rendering of the clouds w i t h the field of view of 16°, D
equal to 4, and N equal to 512. 42
5.10 Rendering of the clouds w i t h D equal to 1, and N equal to
512. 43
5.11 Rendering of the clouds w i t h D equal to 1, and N equal to
128. 43
xii
Introduction
Atmosphere and clouds are an important part of a landscape. To provide
their realistic simulation i n real-time interactive applications,
more often than not, a great effort is spent to make them look convincing.
However, i n many cases, this effort falls short, and the results
may not be of desired quality.
Lately, advances i n hardware have made it possible to render volumetric
clouds i n real-time. The method described i n this thesis is
based on the work of researchers i n Guerrilla Games company, w h o
presented their work i n 'The Real-time Volumetric Cloudscapes of
Horizon: Zero Dawn' on the S I G G R A P H 2015 Advances i n Real-Time
rendering i n Games course [1].
The purpose of this thesis is to extend the render library mallumo
with real-time precomputed atmospheric effects such as the colour of
the sky dependent on the position of the Sun, and transmittance of
light of objects inside the atmosphere and beyond the atmospheric
boundary. Implementation of these effects is based on the w o r k of
Bruneton et al. [2]. Provided are also raymarched volumetric clouds
illuminated by the before mentioned atmospheric model.
1
1 Mallumo
M a l l u m o 1
is a global-illumination render library written i n the Rust
p r o g r a m m i n g language. This library uses O p e n G L 4.5 internally to
access G P U features. Mallumo provides safe abstraction over OpenGL,
preventing most errors caused by incorrect usage of the A P I . Most of
the errors are caught i n compile time, which is achieved by repurposing
Rust type system and ownership m o d e l for O p e n G L constructs.
The errors that can not be caught i n compile time, e.g. running out of
G P U memory, are detected during runtime and reported to the user
of this rendering library, i n a w a y that makes it possible to react to
them.
M a l l u m o uses, as is typical, for the basic scene rendering polygon
rasterisation. To provide global illumination effects, such as diffuse
or specular interreflections, dynamic shadows, ambient occlusion,
the user of this library may voxelize the scene and then fed it to the
mallumo rendering pipeline. This is illustrated i n Figure 1.1.
M a l l u m o supports rendering of camera aligned quad, which may
be used either for postprocessing or ray-based rendering methods.
Basic postprocessing, w h i c h is directly supported, includes blurring,
gamma correction, several tone mapping functions, and many others.
Figure 1.1: Sponza scene without albedo texture, illuminated directly
and indirectly by the Sun using anisotropic V X G I .
1. Available on https: //gitlab. com/mallumo/mallumo.
3
2 Theoretical background
This chapter covers theoretical background necessary for the understanding
of atmospheric visual effects. Firstly, it defines basic terms
from radiometry: radiant flux, irradiance, radiance, and transmittance;
then it defines scattering and its subterms. Afterwards, this chapter
provides a brief classification of clouds, their density, and their
lighting.
2.1 Radiant flux
Radiant flux <!>, is the total amount of radiant energy emitted, reflected,
transmitted or received per unit time. Its unit is Watt.
2.2 Irradiance
Irradiance £ is defined as radiant flux received by a surface per unit
area. Its unit is Watt/m2
.
2.3 Radiance
Radiance L is defined as radiant flux emitted, reflected, transmitted
or received by a surface, per unit area per unit solid angle. Its unit is
Watt/m2
sr.
2.4 Transmittance
The transmittance of the material is its effectiveness i n transferring
radiant energy. M o r e specifically, it is the ratio of incoming and outgoing
light, and it refers to the energy loss caused by absorption or
scattering. A s absorption and scattering are affected by the wavelength
of light, transmittance too is non-uniform and depends on the light's
frequency.
5
2. T H E O R E T I C A L B A C K G R O U N D
2.5 Scattering
Scattering is a physical phenomenon where radiation i n the f o r m of
sound, m o v i n g particles or, as relevant to the atmosphere, light deviates
f r o m a straight trajectory due to local non-uniformities. These
may vary, but i n the context of atmospheric scattering, they are mostly
molecules or small particles such as aerosols. The implication of scattering
is that i n the direction f r o m w h i c h light is coming may not be
a source of light, w h i c h is the reason w e perceive the sky as having
colour.
2.5.1 Forward scattering and backscattering
Change of trajectory caused b y scattering is not limited to an arbitrary
range. It is, therefore, useful to provide distinction based o n the
change of direction, and thus to define terms forward scattering and
backscattering. The distinction is simple: forward scattering occurs
w h e n radiation is deflected w i t h i n 90°of the direction of propagation,
and backscattering w h e n the deflection is more than 90°, this is
illustrated i n Figure 2.1.
Figure 2.1: Light entering a scattering m e d i u m , p r o d u c i n g forward
scattering and backscaterring.
2.5.2 Elastic scattering
A scattering process is called elastic if during the scattering process
the energy of the light is conserved, meaning while the trajectory may
change, the energy is constant. Elastic scattering is an idealisation
6
2. T H E O R E T I C A L B A C K G R O U N D
as the energy i n fact changes, but, if the loss of energy is sufficiently
small, it can usually be neglected.
2.5.3 Dominant scattering processes in Earth's atmosphere
There are two dominant scattering processes i n Earth's atmosphere,
namely Rayleigh scattering a n d M i e scattering (both described i n
detail further), with Rayleigh scattering being described as elastic. The
domain of particles, o n w h i c h each scattering has the most influence,
is given by dimensionless parameter a, defined as
DC = 71-*- (2.1)
A
where Dp is the diameter of the particle, and A is the wavelength of
incident radiation. If a is significantly less than 1 then most prevalent
is Rayleigh scattering, if alpha is approximately equal to 1 then
M i e scattering. In case alpha is significantly greater than 1, a class of
geometric scattering models is required, however, i n the case of the
atmosphere, most particles fall within the range of either Rayleigh or
Mie scattering, and thus they are sufficient for accurate representation
of scattering events.
2.5.4 Phase functions for Rayleigh and Mie scatterings
Phase function
Phase function is a type of one-dimensional functions describing angular
distribution of scattered light based on the direction of incoming
light. G i v e n scattering angle ]i, phase function returns the relative
amount of light under ]i.
Rayleigh scattering
Rayleigh scattering is an elastic scattering of light caused by particles
much smaller than the wavelength of the light. Typical particles whose
scattering behaviour can be approximated w i t h Rayleigh scattering
are air molecules, whose size is roughly i n the range of a. Rayleigh
scattering is symmetrical around the axis of incoming light, and the
7
2. T H E O R E T I C A L B A C K G R O U N D
Rayleigh phase function P R for air molecules is given by Rayleigh
theory [3] as:
pR(e) = ^ - ( i + cos2
(e)) (2.2)
ion
M i e scattering
M i e scattering is scattering of light b y particles similar to the wavelength
of the light, e.g. aerosols. M i e phase function is complex and
consists of multiple lobes, which prevalence is given by the size of the
scattering particle. A s the size of the particle exceeds the wavelength,
the front lobe exceeds the other side or backward lobes w h i c h can
be exploited, and M i e phase function PM can be approximated w i t h
Henyey-Greenstein function, which was further improved by Cornette
and Shanks (also k n o w n as Cornette-Shanks phase function) [3]:
PM(0) « _ L ( l - g ^ O W W ) ( 2 . 3 )
87r(2 + £ 2 ) ( 1 + £ 2 _ 2 £ a > s 2
( 9 ) ) i
where g G ( — 1,1) is an asymmetry factor denoting the w i d t h of the
forward lobe.
2.5.5 Single and multiple scattering
Single scattering occurs w h e n radiation is scattered once by localised
scattering centre. However, i n case there are many scattering centres
grouped together, they cause radiation to scatter multiple times which
is called multiple scattering. Single scattering may usually be treated
as a r a n d o m phenomenon, while multiple scattering is more deterministic,
due to many scattering events that tend to average out. W h e n
taking into account elastic scattering processes, such as mentioned
Rayleigh scattering, simulation of multiple scattering is needed, because
radiation may undergo multiple scattering events due to not
losing m u c h energy. Still, the number of scatterings to compute may
not be necessarily high, as Rayleigh scattering is not ideally elastic,
and contribution of higher order scatterings is therefore not as strong.
Eventually, photons w i l l either escape atmosphere into space due to
change of their trajectory or lose energy because of scattering pro-
8
2. T H E O R E T I C A L B A C K G R O U N D
cesses or be absorbed by objects inside the atmosphere including the
planet itself. Single and multiple scattering is illustrated i n Figure 2.2.
Figure 2.2: Single and multiple scattering, courtesy of [4].
2.6 Shapes and density of clouds
Clouds are classified into many different types. The most basic classification
is based on the height on w h i c h they occur, w h i c h is then
further subdivided based on the cloud shapes, as can be seen i n Figure
2.3.
Figure 2.3: Different types of clouds occurring at w i d e range of altitudes,
courtesy of [1].
Roger Clausse and Leopold Facy i n 'The clouds' [5] note that density
of the clouds increases at lower temperatures and that the tem-
9
2. T H E O R E T I C A L B A C K G R O U N D
perature decreases w i t h altitude. This implies that density of clouds
proportionally increases w i t h altitude.
C l o u d shapes and altitude-based density provide a framework for
specifying density at given point, knowing just what type of cloud the
point belongs to, and at w h i c h altitude it is positioned.
Turbidity is the reduction i n the transparency of an object due to
particles suspended w i t h i n w h i c h cause absorption or scattering of
the light. The examples of turbidity i n the atmosphere may include
clouds or smog.
2.8 Lighting of clouds
When a ray of light enters a cloud, it is partially absorbed or scattered.
Scattering of light by aerosols is described by M i e scattering, w h i c h
provides only single scattering. To fully compute ray's path, it is necessary
to trace it through the cloud volume at small steps, w h i c h is
computationally very expensive and not suitable for real-time performance.
Schneider [1] proposes that the cloud volume behaves as a
collector for light, meaning the more a point is surrounded by clouds,
the higher the chance that light is refracted f r o m the cloud towards
the point. The implication of this is that edges are darker than dense
regions and v i e w rays sample more light w h e n going through them.
This so-called Powder term is given by
where d is density of a cloud at given point.
To account for absorption Schneider [1] proposes to use BeerLambert
law, also known as Beer's law, which relates transmittance of
material to its optical depth.
2.7 Turbidity
Powder(d) — 1.0 — e-2d
(2.4)
= e
— T
(2.5)
10
2. T H E O R E T I C A L B A C K G R O U N D
where T is transmittance of the material sample, <$>e is the transmitted
radiant flux, Og is the received radiant flux by that material sample
and T is its optical depth.
Together the attenuation A is given by the following formula
A = PM x Powder x Beer (2.6)
where PM accounts for single scattering and Powder and Beer terms
account for multiple scattering.
11
3 Related work
3.1 Atmosphere
Since atmospheric simulations are an important part of many outdoor
and indoor visualisations, there are many models describing it. They
are mostly based on the same physical basis, however, each makes
different simplifying assumptions which affect both the visual results
and the performance. In this section, few select models w i l l be briefly
described and compared.
3.1.1 Nishita93 model
Figure 3.1: Fisheye skydome rendering of the spectral radiance of the
Nishita93 model, for sun zenith angles 87°, 41°, 31°, 21°, courtesy of
[6].
The Nishita93 model [7], illustrated i n Figure 3.1, is one of the first
physically based atmospheric models. Nishita93 computes only single
scattering and is based on numerical integration along the v i e w ray.
Two transmittance samples are computed, one from the viewer to the
sample, and one from the sample to the Sun. The first transmittance
value is computed dynamically, and the second is precomputed and
stored i n a 2D texture. Precomputation is done w i t h discretising the
atmosphere into n$ spherical concentric layers of constant optical
depths, and w i t h nc concentric cylinders oriented towards the Sun,
whose intersections w i t h the spherical layers are used as sampling
points for the precomputed 2D transmittance texture.
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3- R E L A T E D WORK
Complexity and limitations
The precomputation stage evaluates a single integral w i t h ns samples
for a l l elements of the ns x nc texture, a n d thus has 0(ns
2
nc) time
complexity a n d 0(nsnc) m e m o r y complexity. D u r i n g rendering, a
single integral is evaluated for each pixel w i t h 0(ns) samples using
the precomputed transmittance texture with additional 0(1) memory
complexity necessary for numerical integration.
This model completely ignores multiple scattering, w h i c h makes
it almost always underestimate radiance values by roughly one third
compared to the ground truth.
3.1.2 Nishita96 model
Figure 3.2: Fisheye skydome rendering of the spectral radiance of the
Nishita96 model, for sun zenith angles 87°, 41°, 31°, 21°, courtesy of
[6].
The Nishita96 model [8], illustrated i n Figure 3.2, is a n extension
of Nishita93 w i t h a n approximation of multiple scattering. Multiple
scattering may be of any order, however, the authors compute only
double scattering due to the increasing computational complexity. For
double scattering, it is required to compute integral over all directions
at each sampling point along the v i e w ray. The authors recommend
to compute the integral only for eight directions and to precompute
single scattering for each nx x ny x n z point i n the grid along those
directions, and store it i n a 3 D texture for better performance.
14
3- R E L A T E D WORK
Complexity and limitations
During the precomputation stage, eight 3D tables are computed, each
for one direction. For each vertex, a single scattering is computed
incrementally from one vertex to the next along the axis determined
by the currently computed table which yields 0 ( n 3
) time and memory
complexity. During rendering, similarly to Nishita93, a single integral
is evaluated for each pixel w i t h additional eight lookups into the
precomputed textures, w h i c h leads to 0(ns) time complexity and
0(1) memory complexity.
Using this model the viewer is limited to the positions within the
atmosphere and underestimates radiance, although not as m u c h as
Nishita93, which is caused by only accounting up to second scattering
(per the authors' implementation).
3.1.3 Preetham model
Figure 3.3: Fisheye skydome rendering of the spectral radiance of
Preetham, for sun zenith angles 87°, 41°, 31°, 21°. Note how bright the
sky is compared to the previous models, courtesy of [6].
The Preetham m o d e l [9], illustrated i n Figure 3.3, is still one of
the more used models i n computer graphics due to its simplicity and
performance. This model is directly based on Nishita96 by computing
radiance for many view directions, sun directions and turbidity values
and then fitting them w i t h an analytical function from Perez et al.[10]
using non-linear least square fitting. Preetham m o d e l is limited to
only g r o u n d v i e w and is also limited to the Sun being above the
horizon. W h i l e by itself the Preetham m o d e l does not have aerial
perspective, it is usually paired with an independent equation derived
using the flat Earth hypothesis, which simplifies it. Since the Preetham
15
3- R E L A T E D WORK
model and the aerial perspective equation are separate, it can lead to
inconsistencies, especially near the horizon.
Complexity and limitations
This model has no precomputation phase, and for each pixel, the time
and memory complexity are 0(1).
Because it is based on the Nishita96 model, it accounts only up to
second scattering. It is also limited to the Sun being above the horizon.
The viewer is limited to the ground because the analytical functions
were fitted for the viewer at the ground level, and the complementary
aerial perspective assumes flat Earth. Somewhat surprisingly, the
Preetham m o d e l overestimates the radiance values, probably due
to the analytical functions used, not being an exact fit to the data
extrapolated from the base Nishita96 model.
3.1.4 Haber model
Figure 3.4: Fisheye skydome rendering of the spectral radiance of the
Haber model, for sun zenith angles 87°, 41°, 31°, 21°. Note h o w the
sky is less orange near the horizon compared to the Nishita93 and the
Nishita96 models, courtesy of [6].
The Haber m o d e l [11], illustrated i n Figure 3.4, is based on the
Nishita96 model with storing atmospheric data in ns layers of constant
optical depths, but stores precomputed scattering data in nr x UQ X n§
grid based on spherical coordinates centred on the viewer. Multiple
scattering computations are also more precise as integration occurs
over all directions at each grid cell. The m a i n approximations of the
Haber model consist of replacing Rayleigh and M i e phase functions
16
3- R E L A T E D WORK
w i t h their o w n for all scattering order, w h i c h causes at least for M i e
scattering to lose some energy. Similarly to Nishita93 and Nishita96,
rendering is done w i t h sampling along the view ray.
Complexity and limitations
A s s u m i n g fixed number of scattering orders, computing values for
nr x tiQ x ritp grid takes Oin^-n^-n^ time due to the fact that all
directions are taken into account and 0{nrnQn^) memory for the 3D
texture. Due to the transmittance not being precomputed, each pixel
takes 0(nrns) time w h i c h could, however, be reduced to 0(nr) w i t h
O ( l ) memory.
This model limits the viewer to the ground, because it is computed
for a specific sun zenith angle and a specific viewer altitude. Evaluating
a pixel also takes a comparably long amount of time due to having
quadratic time complexity.
3.1.5 Bruneton model
Figure 3.5: Fisheye skydome rendering of the spectral radiance of the
Bruneton model, for sun zenith angles 87°, 41°, 31°, 21°. Courtesy of
[6].
The Bruneton m o d e l [2], illustrated i n Figure 3.5, precomputes
multiple scattering orders, including sun zenith angles below the
horizon. This model supports all view angles and does not constrain
the viewer i n any way, meaning that all positions are supported. This
m o d e l was implemented as a part of this thesis, and therefore, it is
described i n detail i n the following chapter.
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3- R E L A T E D WORK
3.2 Clouds
Clouds are very difficult to recreate i n computer graphics, especially
when constrained to real-time performance. Over the years there have
been many different techniques and methods, some of them are briefly
described i n this section.
3.2.1 Skybox and skydome
Skybox and skydome provide one of the simplest ways to create clouds.
Either an artist creates 2 D texture or a photo of cloudy sky is taken,
w h i c h is then projected onto box or dome. This box or dome is then
fed into the used graphical pipeline and then rendered. This method is
very performant, since it requires rendering only a couple of polygons,
but is very limited i n its capabilities, and by itself, it is only capable of
providing static clouds.
3.2.2 Implicit volumes
Kniss et al. [12] propose using implicit volumes and a perturbation
texture. The base cloud shape is defined by an analytic function, whose
input is distorted w i t h an offset generated by querying the 3 D noise
texture, as can be seen i n Figure 3.6.
Figure 3.6: Implicit volume on the left and perturbed result on the
right, courtesy of [13].
1 8
3- R E L A T E D WORK
3.2.3 Polygon clouds
Similar to the implicit volumes method, but instead of using an analytic
function to describe the base shape, the bounding volume is defined
by polygon model, an example can be seen i n Figure 3.7.
Figure 3.7: A n example of a polygon cloud, courtesy of [14].
3.2.4 Particle clouds
The idea is to build clouds from small uniform particles. Each particle
is semi-transparent, and after computation of their colour, they are
blended together.
3.2.5 Procedural clouds
Instead of defining the base volume which is then randomly perturbed,
the shape of clouds is created by using noise w i t h certain properties.
Perlin noise or Simplex noise are usually used, w h i c h are layered at
increasing frequencies. This noise is then combined w i t h a height
gradient to better simulate cloud density, that changes w i t h height.
1 9
4 Implementation
This chapter describes the Bruneton m o d e l and its implementation,
and cloud rendering method based on the work presented by Schneider
[1] for the render library mallumo.
4.1 Bruneton model
4.1.1 Physical model
The Bruneton model is a clear sky atmospheric model, which assumes
atmosphere made out of only molecules and small particles such as
aerosols. The atmosphere itself is a spherical layer of these particles
around a globe contrasting the approach made b y some previously
mentioned atmospheric models w h i c h assume flat Earth. The distribution
of particles i n the atmosphere is not uniform, however, the
density at each point is parametrised only by height, not by altitude
or longitude.
A t each point, light that is scattered and absorbed is given by
where fie
R and fie
M are extinction coefficients for Rayleigh and M i e
scatterings.
For small particles, w h i c h are subject to Rayleigh scattering, f5e
R
is equal to scattering coefficient f5s
R due to Rayleigh scattering being
elastic. fis
R is given by the Rayleigh theory[3]:
where h is the altitude, A is the wavelength, n is the index of refraction
of air, N is the molecular density at sea level, and HR is the thickness
of the part of the atmosphere that is affected by Rayleigh scattering.
For aerosols, scattering is given by M i e scattering. While Rayleigh
scattering's behaviour can be accurately described as elastic, ignoring
the loss of energy i n M i e scattering can lead to significant inaccuracies,
as aerosols absorb a sizeable fraction of the incoming light. Therefore, it
(4.1)
(4.2)
21
4. I M P L E M E N T A T I O N
is needed to include absorption coefficient Sa
into extinction coefficient
Be
, w h i c h for M i e scattering becomes
P M = P M + P M (4-3)
Density of aerosols decreases exponentially w i t h height, and as such
BS
M is given by:
^ / a ) = j S s
M ( 0 , A ) e i (4.4)
where HM is the thickness of the part of the atmosphere that is affected
by M i e scattering.
4.1.2 Rendering equations
We define the following:
• L(x, v, s) is the radiance of light reaching x from direction v with
the Sun being i n direction s,
• XQ (X, V) is the extremity of ray originating i n x w i t h direction v
located either at the top of the atmospheric boundary or o n the
ground,
• Earth is a Lambertian surface w i t h a height field of reflectance
a(x,A) and normal n(x).
W i t h these we define the following equations:
ry
ie{R,M}
T ( x , y ) = e x p ( - £ £ 6\{h)dh) (4.5)
T T J I ( \ _ J J2 7r ^(X
0/ s)to.n(xo)dto if inside atmosphere,
1[L\{XQ,S) — <
IU otherwise.
(4.6)
J[L]{y,v,s)= f £ j 6f(y)Pi (o;.z;)L(y,a;,s)da; (4.7)
• / 4 7 r
i e { R , M }
where T is transmittance between x and y, X is radiance of light reflected
at XQ, J is radiance of light at height y i n direction —v.
22
4. I M P L E M E N T A T I O N
LQ(X,V,S)
W i t h these we define following rendering equations:
L(x,v,s) = LQ(X,V,S) + lZ[L](x,v,s) + S[L](x,v,s) (4.8)
T(x, Xo)LSUN v = s and the Sun is not occluded,
0 otherwise.
(4.9)
K[L] (x, v, s) = T(x, x0)X[L] (x0, s) (4.10)
S[L](x,v,s)= T(x,y)J[L](y,v,s)dy (4.11)
Jx
£[L](x,s) = / L(x,co,s)co.n(x)dco (4.12)
Jin
where LQ is the direct sunlight LSUN attenuated b y T, 1Z is the light
reflected at XQ attenuated by T before reaching x, S is the light scattered
towards x between XQ and x, £ is the irradiance of x.
These equations are used directly i n the precomputation and rendering
part of this method.
4.1.3 Method
The method is based on precomputing L as much as possible w i t h only
m i n i m a l approximations and idealisations. To compute L, zero a n d
single scatterings are computed exactly, while computation of multiple
scattering is approximated w i t h the assumption that the Earth is a
perfect sphere of constant reflectance.
W i t h perfect sphere, position and direction can be reduced to only
two parameters: altitude r and v i e w zenith angle u. S u n direction is
given by spherical coordinates 9 and (p, where 9 and (p can be thought
of as intermediate variables for us a n d v. Thus to express functions
dependent o n x, v, s only 4 parameters are needed, 2 for x and v a n d
2 for s.
r = \x\ (4.13)
u = ^ (4.14)
= ^y- (4.15)
v = v • s (4.16)
23
4. IMPLEMENTATION
To take these approximations into account, w e define P ' R , P ' M , L ' ,
L'Q, L'SUN, a', X'Q, T', £', S', J ' , w h i c h are approximations of PR, PM, L,
Lo, Lsun, a, XQ, T, S, S, J, for the case of spherical Earth and w h i c h
are parametrized w i t h r, u, us, and v, as needed. The only exception
is T' w h i c h is parametrized w i t h r a n d u, a n d thus corresponds to
T(x, XQ(X, V)). TO compute transmittance between arbitrary points x
and y, we use the following identity as i n 'Accurate atmospheric scat-
tering'[15]
= TO ( 4
' 1 7 )
where rx a n d ux are given for x b y Equations (4.13) a n d (4.14), a n d
where
where
rd=^d2
+ 2duxrx + rx (4.18)
to = ^ (4-19)
\x-y\ (4.20)
4.1.4 Precomputation
In the precomputation phase three tables are computed: transmittance
table T , irradiance table E , and scattering table S.
T stores transmittance T'(r, u), E stores irradiance E'(r, us) and S
stores scattering S'(r, u, uS/ v).
For T , transmittance T' is computed for all r and u. To precompute
E and S, Algorithm 4.1 is used to compute each scattering order one
after the other. To this end, it uses three intermediate tables A E , A S
and A J of w h i c h two are s u m m e d w i t h their respective tables after
the end of each iteration.
To save space, Bruneton et al. [2] propose storing the red component
of M i e scattering i n the a channel of S. The following equation is
used to approximate the blue and green channels w i t h the red channel
S M ~ S R — - ^ - ^ (4.21)
?>R,r PM,r PR
24
4. I M P L E M E N T A T I O N
The idea behind A l g o r i t h m 4.1 is that we can define L as
1 = 10 + ^ + 12 +... (4.22)
where L, denotes the contribution of light reflected and scattered i
times. The reflection and scattering terms are given by ft and S. Thus
for any i greater than 0, L, is given by
Li = (K + S)[Li-1] (4.23)
w i t h this, L can be rewritten as
L = L 0 + I 4 + L 2 + . . . (4.24)
= L 0 + (ft + S) [L0 ] + (ft + S) [L2 ] + . . .
= L 0 + (ft + S) [L0 ] + (ft + 5) [(ft + S) [L0 ]] + . . .
A l g o r i t h m 4.1 Precompute n scattering orders
T ( r , f 0 <- T ' ( r ^ )
A E ( r , p s ) ^ £ ' [ L [ , ] ( r / F s )
AS(r,u,us,v) 4- S'[L'Q}{r,u,us,v)
E(r,jiB) 4- 0
S(r,n,n8,v) i- lsS(r,u,us,v)
for z ^— 1 to n do
AJ(r, p S / v ) <- J " ' [ T ^ A E + AS] (r, u, us,v)
AM(r,ji8) 4- 8'[tsS]ir,\i3)
lsS(r,u,us,v) 4- $*Q
T(x,y)hJ(\y\,u,us,v)dy
E(r,}is) 4- E(r,}is) + AE(r,}is)
S(r, u, uSl v) 4- S(r, u, us,v) + AS(r, u, us,v)
end for
25
4. I M P L E M E N T A T I O N
4.1.5 Parametrization
In the precomputation phase, several tables are filled with their corresponding
values. While it is useful to think of these tables as simple N
dimensional textures, whose values can be retrieved by keying w i t h
[0,1]N
coordinates, at the hardware level their storage is discretised.
To effectively utilise the [0,1] range, a special m a p p i n g between the
coordinates and their physical counterparts must be devised.
T and E are tables for transmittance and irradiance functions dependent
on r and u. For these naive m a p p i n g w o u l d be sufficient.
However, S is a 4 dimensional table, therefore, it grows rapidly w i t h
more precision and a special care must be taken to conserve memory.
Naive mapping to [0, l ] 4
without large resolution would produce visible
artefacts especially near the horizon, so to better exploit the range
of possible values, Bruneton et al.[2] propose the following mapping
ur (4-25)
1 + ^ i f ^ < 0 a n d A > 0 ,
otherwise.2 2p+2H
I _ g-3^s-0.6
M
* = I _ g -3 .6 (4
-2 7
)
1 + V
where
(4.28)
p = J r 2
- R 2
b (4.29)
H=y/B*-Rl (4.30)
A = r2
u2
- p2
(4.31)
where Rjy is the distance from Earth's centre to the bottom atmospheric
boundary, and Rf is the distance to the top atmospheric boundary.
4.1.6 Rendering
D u r i n g rendering, several terms must be evaluated: SkyColor,
Radiance, Irradiance. SkyColor determines the colour of the unob-
26
4. I M P L E M E N T A T I O N
scured sky, Radiance must be taken into account w h e n observing an
object at point y from point x, and Irradiance is light received by point
x.
Irradiance is stored i n a precomputed f o r m i n E . SkyColor a n d
Radiance are defined as follows
SkyColor\r,]i,]is,v) = L'sun{}i, }is, v)T'(r, }is) + L'sky(r, ji, jiS/v)
(4.32)
Radiance{x,y,}is,v) = L'(rX/jiX/jiS/v) - T(x,y)L'(rd/jid/jiSid/v)
(4.33)
where rx, \ix, r&, ]id are the same as i n Equation (4.17), a n d
L
'sky(r
'V'Vs,v) = £ R[{v)S[{r,}i,}is,v)
ie{RRM}
rx}is + v\x -y\
Usd=
r s
' rd
4.1.7 Computational complexity
Precomputation is the most costly part of this model. It involves computing
integral over all ng x n^ directions for all cells of a 4 D table
yielding for fixed number of scattering orders 0{nr^n^nvnQn^) time
complexity and 0(nrn^n^snv) m e m o r y complexity. Rendering itself
has 0 ( 1 ) time and memory complexity.
4.1.8 Limitations
Limitations for this atmospheric model stem from the approximations,
which make it possible to precompute. Firstly, it assumes ideally spherical
Earth w i t h homogeneous particle distribution dependent solely o n
the distance from the Earth's centre. Thus are discarded any possible
irregularities occurring due to local differences w h i c h surely exist for
any planet, be it changes i n terrain or differences i n the atmosphere.
Furthermore, as a consequence of atmospheric homogeneity, a clear
sky is assumed meaning clouds are not compatible with this model i n
the sense of affecting the scattering of light.
(4.34)
(4.35)
2 7
4. I M P L E M E N T A T I O N
4.1.9 Implementation details
Tables parametrized b y r, ]i, ]is a n d v are 4 dimensional. M a l l u m o ,
w h i c h is based o n O p e n G L , does not support 4 D textures. D u e to
this, the implementation of these tables is done i n the following way,
similarly to the original implementation: internally they are regular
3D textures, but each 2 D layer stores 3 D information as sublayers
positioned next to each other. Interpolation for the three coordinates
that are stored regularly is done b y built-in linear interpolation, as
provided b y O p e n G L . M a n u a l linear interpolation is used for the
fourth coordinate.
This implementation uses the same size of the textures as were
used by the authors:
• T is 256 x 64, has 3 channels, each of them is 4 byte float, taking
192 K B ,
• E , A E are 64 x 16, have 3 channels, each of them is 4 byte float,
taking 12 K B ,
• S, A S , A J are 32 x 128 x 32 x 8, where the w i d t h is 32 x 8, the
height is 128 and the depth is 32, have 4 channels, each of them
is 4 byte float, taking 16 M B .
This method produces H D R images, meaning they are not bound
to (0,1) range i n each R G B component, but instead the upper b o u n d
is positive infinity. To convert this image into (0,1) range this implementation
uses filmic tone mapping.
The precomputation part should be faster than the original implementation,
due to better exploitation of O p e n G L capabilities. To name
a few, the original implementation embeds parameters into the shader
source code, which is repeatedly done for each triplet of wavelengths.
This way of changing values requires recompiling shaders, for fifteen
precomputed wavelengths it w o u l d compile thirty shaders when only
six are needed. O n the other hand, i n this implementation the values
are changed w i t h uniforms. Furthermore, the original implementation
uses geometry shaders to write to the individual layers of 3 D
textures, instead of this, glNamedFramebufferTextureLayer is used
to attach layers of 3 D textures directly to a framebuffer, skipping the
unnecessary geometry shader stage.
28
4. I M P L E M E N T A T I O N
The m a i n functional difference between this implementation and
the original w o r k by Bruneton et al. is not computing light shafts.
The rationale behind this is computing light shafts requires shadow
volumes, w h i c h mallumo does not provide.
4.2 Clouds
This section describes the implementation of clouds based on the work
presented by Schneider [1].
The method has small precomputation phase i n w h i c h noise textures
are generated. The rendering part consists of raymarching along
the view ray and accumulating light provided by the atmosphere.
4.2.1 Modelling
Modelling approach of clouds is based on raymarching, as described
i n [1]. V i e w direction is determined for each pixel and samples are
accumulated along the view ray. Density is computed at each sample
point, and the sample is illuminated by the atmosphere, the Bruneton
atmospheric model is used i n this implementation, as described i n the
previous chapter.
The density is given by a set of parameters whose product gives
the final density. The first parameter is coverage, w h i c h determines
whether there is a cloud. While technically the coverage parameter is
either 0 or 1, it is better to define it as a gradient, to provide smoother
scale and to prevent hard edges. The second parameter is given by altitude:
the higher the sample, the denser the cloud. The third parameter
is given by the cloud's type. In this implementation, only three types
of clouds are provided: stratus, cumulus and cumulonimbus. Again,
these are implemented as gradients over altitude, and the cloud type
parameter is a gradient over the types of clouds. W i t h this method it
is possible to define numerous types, however, this is not sufficient
for the cloud types, for w h i c h is characteristic that individual clouds
overlay each other, e.g. cirrocumulus.
2 9
4. I M P L E M E N T A T I O N
4.2.2 Texture generation
This method of rendering clouds uses three noise textures a n d one
control texture. A t each point, the three noise textures are queried
and combined, and the control texture provides information about
coverage, cloud type and turbidity The textures are generated from
the following noises:
• Worley noise was introduced by Steven Worley [16] and is regularly
used for caustics and water effects. It has r o u n d features,
w h i c h make it suitable for modelling billow like shapes similar
to clouds.
• Simplex noise was introduced and later improved by K e n Perlin
[17]. Layering 2D Simplex noise at increasing frequencies creates
visually interesting and detailed hills and valleys. This extended
to 3 D provides clouds w i t h a more detailed look.
• C u r l noise is used for fluid, fire, a n d smoke effects, and w h e n
used as a lookup table is a relatively inexpensive method to
distort cloud shapes and add turbulence.
Two of the three noise textures are created b y modulating a n d
layering inverted Worley and Simplex noise. Curl noise is used for the
third one:
• The first texture is used for providing base shape for the clouds
and has four channels, i n the first one is combined SimplexWorley
noise and i n the other three is Worley noise at increasing
frequencies. Its resolution is 1283
, has 4 channels, each of them
is 4 byte float, and takes 32MB.
Figure 4.1: Simplex-Worley noise and Worley noise at increasing fre-
quencies.
30
4. I M P L E M E N T A T I O N
The second texture provides detail to the base shape, it has three
channels, each of them is Worley noise at increasing frequencies.
Its resolution is 323
, has 4 channels, each of them is 4 byte float,
and takes 384KB.
Figure 4.2: Worley noise at increasing frequencies.
The third texture has curl noise at all three channels, its resolution
is 1282
, has 3 channels, each of them is 4 byte float, and
takes 192KB.
Figure 4.3: C u r l noise.
• The control texture is a 2D texture and has three channels. The
first one contains coverage of the sky, the second one is turbidity,
and the third one is used for the cloud type.
4.2.3 Rendering
Rendering clouds is done by raymarching. That means that given a
point and a vector, a set of points is sampled along the ray. In the case
of clouds, the data that are collected f r o m samples are densities at
each sample point. The densities that are collected are used i n several
ways. W h e n raymarching a view ray, density is used to occlude what
31
4. I M P L E M E N T A T I O N
is behind the sample, and at each view ray's sample it is also required
to determine its colour, w h i c h is given by the following equation
Colour = Attnospherelrradiance x PM X Beer x Powder (4.36)
Atmosphere irradiance is computed as described i n the previous section.
The Powder term requires density at sample which is computed
by Algorithm 4.2 and the Beer term requires optical depth to the light
source, w h i c h is just another raymarching f r o m the position of the
sample towards the light.
Algorithm 4.2 Sample cloud density
Input:
x sample coordinates
/ base scale
C, C s control texture, scale
S, Ss Simplex-Worley texture, scale
W, Ws Worley texture, scale
U, Us curl texture, scale
Output:
Density sample density
Control «— C(xxz x / x Cs )
Coverage «— ExtractCoverage(C, Control)
CloudType «— ExtractCloudType(C,Control)
Turbidity «— ExtractTurbidity(C, Control)
CloudTypeDensity «— CloudType^ensny
AltitudeDensity «— AltitudeDensity Gradient{CloudType,Xy)
StableDensity «— CloudTypeDensity x AltitudeDensityx
Turbidity
BaseDensity S(x x / x Ss) x StableDensity
CurlOffset«— U(xxz x J xUs)
DetailErosion «— W(x x / x W j + CurlOffset) x StableDensity
Density max(BaseDensity — DetailErosion,0)
32
4- I M P L E M E N T A T I O N
4.2.4 Optimizations
Raymarching is costly w h i c h leads to poor framerate. This can be
partially alleviated with the following techniques, at the loss of visual
quality. Luckily, pixel level details are not necessary for clouds, so the
loss is not that important.
Downsampling
The most basic optimisation technique is to simply render at a lower
resolution and then stretch the image.
Reprojection
Reprojection is based o n exploiting the fact, that the camera does not
move rapidly between frames. Thus the majority of pixels w o u l d have
mostly correct values if they were not redrawn, albeit they may be
slightly moved, which is corrected by taking into account the previous
view matrix. Algorithm 4.3 is parametrised w i t h Z , w h i c h is the side
of a square of which one pixel is computed each frame. Randomizing
the order of the pixels slightly reduces artefacts, that are created by
having old values next to each other.
33
4. I M P L E M E N T A T I O N
Algorithm 4.3 Reproject previous accumulated frame
Input:
Q pixel's texture space coordinates
N size of the square of pixels belonging to the same group
V view matrix
W previous view matrix
P projection matrix
F previous frame
Fs subframe
S frame size
Ss subframe size
Z subframe number
Output:
Colour colour of the pixel
Cn = [Q X SJ
Offset <- Cn mod N
FragmentFrameNumber ^— N x Offsety + Offsetx
if FragmentFrameNumber = Z mod N2
then
Colour <- Fs (( LQ x SS J + 0.5)/Ss)
return
end if
Cw 4- ToWorldSpace(Ct,P,W)
Reprojected <— P x V x Cw
if Inside(ReprojectedXy, Square(Point(l,l),Point(—1, —1)) then
Colour <- F(ToTextureSpace(Reprojectedxy))
else
Colour <- Fs(Ct)
end if
3 4
5 Results
In this chapter are presented results of this thesis implementation.
Benchmarks were compiled w i t h Rust 1.26, and were done o n 3 PCs,
all running W i n d o w s 10, w i t h the following G P U s : N V I D I A GeForce
G T X 860M, N V I D I A GeForce GTX1070 and A M D Radeon R X Vega 64.
These G P U s are listed as G l , G 2 , G 3 respectively i n the tables below.
The results are obtained by averaging 500 runs.
5.1 Sky
In this section are presented results for sky rendering.
Rendering of the frame of F u l l H D resolution(1920 * 1080) takes
1.463 ms, 0.447 ms, 0.421 ms for G l , G2, G 3 respectively. Renderings
of the sky w i t h the Sun being at various zenith angles are s h o w n i n
Figures 5.1, 5.2, a n d 5.3.
Figure 5.1: Rendering of the sky w i t h the Sun at the zenith angle of 0°,
w i t h the camera looking straight up.
35
5. RESULTS
Figure 5.3: Rendering of the sky w i t h the S u n at the zenith angle of
93°, meaning the Sun is below the horizon.
36
5. RESULTS
5.2 Clouds
In this section, different configurations of rendering parameters for
cloud renderings are compared i n terms of rendering speed and artefacts.
The clouds are illuminated by the Bruneton model, while using
the sky as i n the previous section.
A s mentioned previously, raymarching is costly. O n G l at F u l l H D
resolution without any optimisations and w i t h 256 samples per view
ray, the p r o g r a m was killed by the operating system due to the rendering
taking too long, w h i c h is unacceptable for any application.
Because of this, several configurations for optimisation techniques
are compared i n terms of speed and visual quality. To this end, we
define downsampling factor D , w h i c h is the reduction i n size of one
dimension, reprojection factor R, which is the same as Z i n Algorithm
4.3, and N w h i c h is the number of samples per view ray.
We constrain D to 1, 2 and 4. D o w n s a m p l i n g by the factor of 8
would lead to too much loss of details. R does not have an effect w h e n
not m o v i n g the camera, as it is composed f r o m the previous frames,
however, if the camera is m o v i n g , there may be artefacts due to the
pixel values being too old. This means that on sufficiently performant
G P U s this is not a concern, even w i t h larger R. However, on slower
G P U s this may quickly lead to visual errors. This is shown i n Figures
5.4 and 5.5 with overexaggerated R. Due to this, we constrain ourselves
to R being either 2 or 4, meaning that the full frame is composed from 4
or 16 frames respectively. W h e n considering that 30 frames per second
are needed to create the illusion of motion, at worst the oldest values
are half a second old. Tested values for N were 128, 256 and 512. The
m i n i m u m value chosen is 128, due to the fact that lower values would
produce too many obvious visible artefacts.
37
5. RESULTS
Figure 5.4: Rendering of the clouds w i t h R = 32 and rapidly m o v i n g
camera. Figure 5.5 is enclosed i n the red square.
Figure 5.5: Detail of Figure 5.4.
38
5. RESULTS
Table 5.1 shows that:
• Doubling D reduces the rendering time to half, i n some configurations
to one third, this is slightly unexpected as doubling D
reduces the final image to a fourth of its size. One possible explanation
is the overhead of the cloud rendering method, possibly
waiting too long for the texture lookups.
• D o u b l i n g R reduces the rendering time by two thirds o n some
configurations a n d b y third o n others. This can be explained
by the overhead of reprojection, w h i c h is not w o r t h o n smaller
resolutions, w h i c h downsampling imitates.
• D o u b l i n g N increases the rendering time roughly twofold, the
explanation is that each view ray needs twice as many computa-
tions.
D R N Gl(ms) G2(ms) G3(ms)
1 2 512 1258.392 132.948 88.641
1 2 256 733.992 77.371 49.814
1 2 128 464.685 48.893 29.570
1 4 512 484.961 56.288 35.162
1 4 256 285.216 32.842 19.767
1 4 128 182.437 21.083 12.060
2 2 512 598.094 55.686 34.406
2 2 256 287.245 32.250 19.339
2 2 128 182.501 20.671 11.512
2 4 512 216.141 23.176 17.586
2 4 256 126.971 13.378 9.390
2 4 128 80.595 8.484 5.405
4 2 512 235.653 23.323 17.229
4 2 256 136.876 13.254 9.250
4 2 128 87.532 8.256 5.265
4 4 512 80.553 9.456 13.209
4 4 256 46.604 5.229 6.955
4 4 128 29.207 3.193 3.736
Table 5.1: C l o u d rendering speed at F u l l H D resolution.
39
5. RESULTS
Results for cloud rendering are shown i n Figures 5.6 and 5.7 w i t h
the Sun being at various positions.
The loss of details i n clouds for some D and N configurations
is highlighted i n Figures 5.8, 5.9, 5.10 and 5.11. Configurations w i t h
various R values are not compared, because for the chosen values of R,
only some pixel values are old enough to produce some visibly wrong
pixels and only w i t h rapidly moving camera.
The effect of changing D is s h o w n i n Figures 5.8 and 5.9. W h i l e
increasing D leads to higher performance, as s h o w n i n Table 5.1, it
directly causes the loss of details. Note, that the image is only a small
part of the resultant image, and the decrease i n details is not as obvious
w i t h regularly used values for the field of view. Artefacts caused by
discretisation of the noise functions into small resolution tables and
insufficient step length can be seen i n Figure 5.8. Again, this is not
noticeable w i t h the regularly used field of view values.
The effect of changing N is s h o w n i n Figures 5.10 and 5.11. The
number of samples impacts the length of the step w h e n raymarching
through the c l o u d volume. W i t h a lower number of samples, less
density is accumulated, especially w h e n pockets of high density are
missed.
40
5. RESULTS
Figure 5.6: Rendering of the clouds with D equal to 1, N equal to 512,
and w i t h the Sun at the zenith angle of 50°.
Figure 5.7: Rendering of the clouds with D equal to 1, N equal to 512,
and w i t h the Sun at the zenith angle of 66°.
41
5. RESULTS
Figure 5.8: Rendering of the clouds w i t h the field of v i e w of 16°, D
equal to 1, and N equal to 512. Note the artefacts caused by discretisation
of the noise functions and insufficient step length.
Figure 5.9: Rendering of the clouds w i t h the field of v i e w of 16°, D
equal to 4, and N equal to 512.
42
5. RESULTS
Figure 5.10: Rendering of the clouds w i t h D equal to 1, and N equal
to 512.
Figure 5.11: Rendering of the clouds w i t h D equal to 1, and N equal
to 128.
4 3
6 Conclusion
This thesis extended the render library m a l l u m o w i t h an accurate
low-cost atmospheric model, and w i t h a cloud m o d e l p r o v i d i n g a
robust framework for specifying the weather, capable of r u n n i n g i n
real-time.
These extensions were tested w i t h various optimisation configurations.
Results were then compared i n terms of computational speed
and image quality.
Future w o r k for this thesis includes voxelization of the clouds,
which may then be fed into mallumo's render pipeline, and thus provide
voxel-based visual effects, such as dynamic shadows, or ambient
occlusion for diffusing transparent media, whose usage w i l l be therefore
consistent with the already existing solution. Possible future work
may also include implementing voxel shadow volumes based o n the
work of K l e h m et al. [18], and extending the atmospheric model w i t h
light shafts.
4 5
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49
A List of electronic attachments
A l o n g w i t h the thesis, the attachments are included i n attachments.
z i p file consisting of:
• / b i n / folder, w h i c h contains executable files atmosphere .exe
and clouds . exe, along w i t h manual. t x t ,
• /mallumo/ folder, w h i c h contains the entire m a l l u m o library
extended with the atmospheric and cloud modules. Source code
created as a part of this thesis can be found i n
- /src/atmosphere/
- /assets/shaders/atmosphere/,
- /src/clouds/
- /assets/shaders/clouds/,
- / s r c / r e p r o j e c t i o n . r s
- /assets/shaders/reprojection.frag.
51