an analytical approach for simulating aerial...
TRANSCRIPT
AN ANALYTICAL APPROACH FOR SIMULATING AERIAL PERSPECTIVE
EFFECTS ON DISTANT OBJECTS
IRWANDI HIPNI MOHAMAD HIPINY
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Master of Science (Computer Science)
Faculty of Computer Science and Information System
Universiti Teknologi Malaysia
OCTOBER 2006
iii
To
my wife, hamimahujir &
my mom, juliadolhassan
iv
ACKNOWLEDGEMENT
Thanks to ALLAH S.W.T. for giving me His blessings in the form of true
friends who help me throughout this eventful yet wonderful journey. Only God
Himself can ever repay your benevolent act of kindness. Thank you to my
supervisors: Associate Prof. Safie Mat Yatim and Nor Azam Md. Sherrif; my
mentor: Associate Prof. Sarudin Kari; my lecturers: Associate Prof. Daut Daman,
Nik Isrozaidi Nik Ismail and Mohd Shafry Mohd Rahim; my associates in UTM:
Muhamad Najib Zamri, Rio Affendi, Hasbullah Anthony Hasbi, Asyraf Khairuddin,
Mohd. Hafiz Ahmad Tajudin, Asrulakmar Mohd Yusof, Loh Mun San, Lee Kong
Weng, Baldeve Paunoo, Saandilian Devadas, Tan Kim Heok, Adlur Rahman Ali
Omar, Mohd. Amri Bakri; my mom: Julia Dolhassan, and my three sisters. Last but
not least, a big thank you to my wife, Hamimah Ujir, for putting up with me
throughout this wonderful two years of my life; the frequent help with grammatical
error and format revision as well as the occasional financial support! Again, thank
you all from the bottom of my heart.
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ABSTRACT
Aerial perspective effects are an integral part of a virtual application for
outdoor simulation. These effects are modelled using the light transfer equation;
borrowed from the field of physics. Typically, these applications make do with a
watered-down version of the equation since the physically correct version requires
heavy nested loops and complex optical depth estimation. The normal practice is to
assume the atmosphere’s density as constant to allow the usage of distance between
points as optical depth. However, this move causes failure in capturing the
darkening effect of sky area approaching zenith, due to density fluctuations as the
altitude increases. An analytical-based approach is proposed here to solve the above
problem. A look-up table containing five-parameter coefficients of a chosen
parametric luminance function was prepared in advance as a function of altitude,
turbidity and Sun position. During the real-time visualization, a single rendering
equation is used to determine each vertex’s display colour. Adding the initial colour
value of the current vertex to its atmosphere-contributed colour value solves the
equation. The atmosphere-contributed colour is obtained by an exponential
interpolation of five separate colour values. Each value represents the colour of the
intersected sky patch at each reference layer. The intersected sky patch is found by
finding which sky patch coordinate solves the vector equation of a line passing
through the camera’s point and the current vertex’s point. By referring to the look-
up table, these five colour values are computed using the chosen parametric
luminance function. This approach was implemented using the Cg Language as a
vertex shader. Test results have shown that the proposed approach is able to produce
visually correct daylight sky colour distributions at any altitude within the 30km
range.
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ABSTRAK
Kesan perspektif udara merupakan komponen utama bagi sesebuah aplikasi
maya untuk simulasi persekitaran luar. Kesan-kesan ini dimodelkan dengan
persamaan pemindahan cahaya yang dipinjam dari bidang fizik. Kebiasaannya,
aplikasi-aplikasi sebegini hanya mengimplementasikan versi ringkas persamaan
tersebut memandangkan versi asal dibebani oleh gegelung bersarang pelbagai lapisan
serta pengiraan kedalaman optik yang rumit. Lazimnya, ketumpatan udara dianggap
malar supaya parameter kedalaman optik boleh diganti dengan nilai jarak di antara
dua titik. Walau bagaimanapun, langkah ini menyebabkan tiada kesan penggelapan
di kawasan langit yang menghampiri zenit, berpunca dari perubahan aras ketumpatan
udara semasa kenaikan paras altitud. Satu pendekatan berasaskan analitikal
dicadangkan sebagai langkah penyelesaian untuk permasalahan tersebut. Sebuah
jadual rujukan yang mengandungi nilai lima parameter bagi satu persamaan luminans
berparameter terpilih disediakan lebih awal. Ianya dirujuk berdasarkan nilai altitud,
aras kekeruhan langit serta posisi matahari. Semasa visualisasi masa nyata, satu
persamaan tunggal digunakan untuk mengira warna paparan bagi setiap vertek.
Persamaan ini diselesaikan menerusi operasi penambahan nilai warna asal vertek
semasa dengan nilai warna sumbangan atmosfera. Nilai warna sumbangan atmosfera
dikira dengan rumus interpolasi secara eksponen terhadap lima nilai warna berbeza.
Setiap nilai mewakili warna bagi petak langit bersilang di setiap lapisan rujukan.
Petak langit bersilang diperolehi dengan mencari koordinat petak langit yang berjaya
menyelesaikan persamaan vektor untuk garisan yang melalui titik kamera dan titik
vertek semasa. Kelima-lima nilai warna tadi dikira menerusi persamaan luminans
berparameter terpilih dengan merujuk kepada jadual rujukan. Dengan menggunakan
bahasa pengaturcaraan Cg, pendekatan ini diimplementasi sebagai aturcara
pembayang vertek. Hasil-hasil ujian membuktikan keupayaan pendekatan ini dalam
menghasilkan kepelbagaian taburan warna langit di waktu siang yang tepat dari segi
visual, sehingga paras altitud 30km.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
TITLE PAGE i
DECLARATION OF ORIGINALITY AND
EXCLUSIVENESS
ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xi
LIST OF FIGURES xii
LIST OF EQUATIONS xiv
LIST OF ABBREVIATIONS xvi
LIST OF APPENDICES xvii
1 INTRODUCTION
1.1 Introduction 1
1.2 Research Background 2
1.3 Current Issues 4
1.3.1 Speed Versus Physical Accuracy 4
1.3.2 Solving Out-of-Gamut Colour 4
1.3.3 Transferring the Computational Burden to GPU 5
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1.4 Problem Statement 6
1.5 Goal 7
1.6 Research Objectives 7
1.7 Research Scopes 8
1.8 Research Contributions 8
1.9 Organization of Thesis 9
2 LITERATURE REVIEW
2.1 Introduction 11
2.2 Previous Works 11
2.2.1 Simulation-Based Methods 11
2.2.2 Analytical-Based Methods 13
2.2.3 Aerial Perspective-Based Methods 16
3 METHODOLOGY
3.1 Introduction 19
3.2 Summary of Previous Methods 20
3.2.1 LTE-Based Model Versus Analytical
Luminance Model
21
3.2.2
Increasing Altitude Effect Towards the Daylight
Sky Colour
21
3.2.3 Discussion 22
3.3 Requirement Specification 22
3.4 The Methodology of the Proposed Method 24
3.4.1 Synthetic Data Preparation 24
3.4.1.1 Atmospheric Profiling Task 25
3.4.1.2 Reference Altitudes 26
3.4.1.3 All-Sky Colour Distribution Maps 27
3.4.2 APACC Model 27
3.4.2.1 Colour Interpolation Scheme 28
ix
3.4.3 Improvised Single Aerial Perspective Rendering
Algorithm
28
3.4.3.1 Sky Patch Association Test 31
3.4.3.2 Distance-Based Transparency Model 32
3.5 Conclusion 32
4 IMPLEMENTATION
4.1 Introduction 33
4.2 Pre-Processing Module 33
Atmospheric Profiling Task 33 4.2.1
4.2.1.1 Identifying the Reference Altitudes 38
4.2.2 Preparing the All-Sky Colour Distribution Maps
at Each Reference Altitude
38
4.2.2.1 Luminance to XYZ 39
4.2.2.2 XYZ to Yxy 39
4.2.3 Developing the APACC Model 40
4.3 Run-Time Processing Module 40
4.3.1 Developing an Improvised Single Aerial
Perspective Rendering Algorithm
40
4.3.1.1 Developing the Sky Patch’s
Association Test
41
4.3.1.2
Developing the Sky Patch’s Colour
Interpolation Scheme
42
4.3.1.3 Developing the Distance-Based
Transparency Model
42
RESULTS AND ANALYSIS
5.1 Introduction 43
5.2 System Specification 43
5
5.3 Atmospheric Profiling Task Results 44
5.4 APACC Model Results 45
x
5.4.1
Daylight Sky Colour as Observed at Ground-
Level
45
5.4.2 Daylight Sky Colour Observed at Varying
Turbidity
46
5.4.3 Daylight Sky Colour Observed at High Altitude 47
5.5 Improvised Single Aerial Perspective Rendering
Equation Results
48
5.5.1 Due to the Distance 48
5.5.2 Due to the Angular Angle From the Sun 49
5.6 Analysis 49
5.6.1 Visual-Correctness of the Rendered Results 49
6 CONCLUSION
6.1 Introduction 52
6.2 Summary of the Proposed Method 52
6.3 Drawbacks and Future Suggestions 54
BIBLIOGRAPHY 56
APPENDIX A 61
APPENDIX B 64
APPENDIX C 67
APPENDIX D 70
APPENDIX E 73
APPENDIX F 74
APPENDIX G 75
APPENDIX H 78
xi
LIST OF TABLES
TABLE NO. TITLE PAGE
3.1 LTE-based model versus analytical luminance
model
21
5.1 Hardware specifications 43
5.2 Software specifications 44
5.3 Vertical profile and effective path length, at each
reference altitude
44
xii
LIST OF FIGURES
FIGURE NO. TITLE PAGE
1.1 Aerial-perspective effects in action 1
2.1 Klassen’s fog model 12
2.2 Nishita et al’s cylindrical coordinates system. 12
3.1 Sky patch, as a function of zenith and azimuth 20
3.2 Semantic diagram of the proposed method 24
3.3 Sky colour distribution map 27
3.4 Single scattering of sunlight in the Earth’s
atmosphere
29
3.5 Attenuation of distant objects by atmospheric
scattering
30
4.1 Research framework 34
4.2 Vertical profiles and effective path lengths plotted
against altitude, with an increment of 2km
35-36
4.3 Pseudo code for preparing the all-sky colour
distribution maps
38
4.4 Pseudo code for spectra (luminance) to XYZ 39
4.5 Pseudo code for XYZ to Yxy 40
4.6 Pseudo code for the sky patch association test 41
4.7 Pseudo code for the sky patch colour interpolation 42
5.1 Rendered sky images as the Sun’s zenith angle
declines, approaching sunset.
46
5.2 Rendered sky images at similar Sun position but
with different turbidity values
47
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5.3 Rendered versus actual images of the daylight sky
at ascending altitudes
47
5.4 Aerial perspective effects due to the distance 48
5.5 Aerial perspective effects due to the angular angle
from the Sun
48
5.6 Visual comparison between high-altitude sky
images, rendered using Hoffman and Preetham’s
method, Nielsen’s method and the proposed
method
50
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LIST OF EQUATIONS
EQUATIONS NO. TITLE PAGE
2.1 Kittler’s clear sky luminance formula 13
2.2 Moon and Spencer’s overcast sky luminance
distribution model
13
2.3 Perez et al’s five-parameter model 14
2.4 Perez et al’s luminance formula 14
2.5 Preetham et al’s luminance-Y distribution function
coefficients
15
2.6 Preetham et al’s chromaticity-x distribution
function coefficients
15
2.7 Preetham et al’s chromaticity-y distribution
function coefficients
15
2.8 Preetham et al’s chromaticity-x formula 15
2.9 Preetham et al’s chromaticity-y formula 15
2.10 Hoffman and Preetham’s single aerial perspective
rendering equation
16
2.11 Hoffman and Preetham’s extinction coefficient
formula
16
2.12 Hoffman and Preetham’s in scattering component
formula
16
2.13 Rayleigh total scattering constant 17
2.14 Mie total scattering constant 17
2.15 Nielsen’s modified Rayleigh scattering phase
function
18
2.16 Nielsen’s new ( )sFex
formulation 18
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3.1 Integral of the light scattering equation for each
point P along the path: camera to sky patch
29
3.2 Integral of the light scattering equation for each
point P along the path: camera to distant object
30
3.3 The proposed method’s version of equation (3.2) 31
3.4 Vector formed between two points in 3D space 31
3.5 Line equation 31
4.1 Gueymard’s effective ozone temperature
correlation function
36
4.2 Relative humidity formula 37
4.3 Saturation vapour pressure formula 37
4.4 Actual vapour pressure formula 37
4.5 Gueymard’s O2 and CO2 scale heights function 37
4.6 Gueymard’s correction factor, Ct 37
4.7 Gueymard’s incremental precipitable water
formula
38
4.8 The improvised single aerial-perspective rendering
equation, based on the Beer’s Law
41
4.9 The proposed distance-based transparency model 42
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LIST OF ABBREVIATIONS
ABBREVIATION DESCRIPTION
2D - Two-dimensional
3D - Three-dimensional
ABCDE - Perez et al’s (1993) five-parameter coefficients
APACC - Analytical parametric atmosphere-contributed colour
BRDF - Bidirectional reflectance distribution function
CIE - International Commission of Illumination
COESA - Committee on Extension to the Standard Atmosphere
CPU - Central processing unit
CRT - Cathode ray tube
fps - Frames per second
GPU
HDR
-
-
Graphical processing unit
High Dynamic Range
IDMP - International Daylight Measurement Program
LTE - Light transfer equation
RGB - Additive colour (red, green and blue)
SMARTS2 - Simple Model for the Atmospheric Radiative Transfer
of Sunshine
SPCTRL2 - Simple Solar Spectral Model for Direct and Diffuse
Irradiance on Horizontal and Tilted Planes at the
Earth's Surface for Cloudless Atmospheres
SPD - Spectral power distribution
XYZ - A set of tristimulus values (X, Y and Z), derived from
the CIE 1931 colour matching experiment
Yxy - Luminance Y, chromaticity x and chromaticity y
xvii
LIST OF APPENDICES
APPENDIX TITLE PAGE
A The five-parameter coefficients look-up table for
luminance (Y), as a function of Sun angles,
turbidity and altitude.
61
B The five-parameter coefficients look-up table for
chromaticity (x), as a function of Sun angles,
turbidity and altitude.
64
C The five-parameter coefficients look-up table for
chromaticity (y), as a function of Sun angles,
turbidity and altitude.
67
D The zenith’s Yxy coefficients look-up table, as a
function of Sun angles, turbidity and altitude
70
E Geometrical parameters of the solar trajectory 73
F Density plotted against altitude, between the US
Standard Atmosphere (McCartney, 1976) and a
simple exponential model
74
G RGB-colour from spectral distribution 85
H Frame-per-second (fps) result 78
CHAPTER 1
INTRODUCTION 1.1 Introduction
The task of rendering an object seen through the Earth’s atmosphere is of far
greater importance nowadays, due to the surge of interest in using interactive virtual
landscape in areas such as computer gaming, military, tourism et cetera (VTP, 2005).
An object’s rendered colour is what gives it a sense of scale and distance. Flight
simulator is an example of such application; enabling the pilot to traverse the vast
virtual sky without any constraints.
Figure 1.1 Aerial perspective effects in action (Nielsen, 2003). Notice the
darkening of sky area closer to zenith as the altitude increases.
This altitude-flexible navigation requires the parameter ensuing effects
towards the daylight sky colour to be captured correctly; a feature typically missing
from the current batch of aerial perspective rendering methods (Nielsen, 2003). In
2
addition, the increasing contents and details of such virtual landscape in today
applications require the aerial perspective rendering problem to have a lesser priority
in the system resources allotment (Nielsen, 2003). Present methods were based on a
taxing real-time solving of the light transfer equation (LTE), thus forced to employ
an inferior light attenuation model and restricts the light attenuation calculation at
trichromatic wavelengths only. Subsequently, the colour precision of the final
rendered scene will askew slightly.
Johnson and Fairchild reported in their findings (1999) that the usage of a
trichromatic value instead of a full-spectral representation of colour causes large
colour shifts. The light attenuation processes, namely: i) in-scattering, ii) out-
scattering and iii) absorption are important phases as they solely determine the
arriving spectral colour at the end of the viewing path. To lose valuable colour
information here is simply disastrous. Minnaert, in his famous book on the light
physics through the Earth’s atmosphere (1954), noted that ozone absorption is the
key reason why the zenith sky remains blue during low Sun altitudes. Present aerial
perspective rendering methods (Hoffman and Preetham, 2002; Nielsen, 2003)
excluded absorption from their light attenuation model. They justified the exclusion
based on the claim by Haltrin (1996) which states that the absorption of the visible
light is negligible except for the ozone layer. For this reason, layers below the ozone
layer can be treated as a full scattering-only medium. The exclusion is not entirely
surprising since these works are more ontogenetic-based than teleological; the two
polar extremes on modelling approach (Barr, 1991).
1.2 Research Background
In the past, real-time rendering of outdoor scenes has primarily dealt with the
problem of increasing the geometric detail of visible terrain (Nielsen, 2003). The
problem of sky dome visualization and aerial perspective rendering usually took the
backseat. Rudimentary methods such as texture mapping and vertex colour
interpolation scheme were commonly used to provide the impression of the daylight
3
sky. Meanwhile, aerial perspective effects on distant objects were faked using
simple range-based fog.
Scientific improvements were then made, as witnessed in works on analytical
sky luminance model (Moon and Spencer, 1942; Kittler, 1967; Perez et al, 1993;
Preetham et al, 1999). These models were based on fits of actual data except for
Preetham et al’s (1999), which employed simulated data. Examples of such actual
sky luminance measurement are (LBL, 1986; Lam, 1996; Lau, 1999). These
measurements were taken at a unique site for at least a year. The scarcity of such
mature actual data forced researchers to use synthetic data instead. Existing solar
spectral models such as SMARTS2 (Gueymard, 1995) and SPCTRL2 (Bird and
Riordan, 1986) are able to approximate a sky radiance/luminance/colour distribution
map on a given set of inputs. Nevertheless, the existing framework design of a sky
luminance model can only provide the sky dome’s colour (viewing paths with
infinite length); not for a viewing path that is intersected by an object.
Early aerial perspective rendering methods such as Hoffman and Preetham
(2002), and Dobashi et al (2002) overcame the above shortcoming of sky luminance
models. Since the daylight sky colour distribution and aerial perspective effects on
distant objects are both caused by the exact same process: the travelling light
interactions with the Earth’s atmosphere, the two phenomenons can therefore be
simulated using a single equation as a function of the optical depth. The above
methods were based on the numerical solution of the light transfer equation (LTE); a
term discussed thoroughly in Sloup (2002). Since the LTE is evaluated in real-time
for an arbitrary viewing path, any variations on its: i) optical depth and ii) angular
angle from the Sun will be reflected back into its spectral colour result. This feature
is unavailable in a sky luminance model whereas the two attributes are fixed.
Conversion issues of spectra to a displayable value unit are govern by the
International Commission of Illumination, abbreviated from its French title:
Commission Internationale de l’Eclairage, (CIE). See Poynton (1995) for further
reading on this matter.
4
All of the above methods, bar Nielsen’s (2003), hold an incorrect assumption
that the Earth’s atmosphere density is constant. A daylight sky dome colour
distribution is the same regardless of the observer’s current altitude. This assumption
would not provide a realistic result in a flight simulator application, in which the
observer’s altitude has a significant role to play. Nielsen (2003) extended Hoffman
and Preetham’s (2002) model to consider the increasing altitude effect towards the
daylight sky colour distribution, yet his solution is far from physically-correct.
Various crude simplifications were implemented in Nielsen’s (2003) model, in order
to maintain the interactive frame rates.
1.3 Current Issues
1.3.1 Speed vs. Physical Accuracy
Present aerial perspective rendering methods were burdened by the weight of
the real-time solving of the LTE. This trade-off between speed and physical-
accuracy always results to the reduction of the latter. As mentioned before, these
methods were forced: i) to restrict the light attenuation calculation at trichromatic
wavelengths (RGB) and ii) to use an inferior light attenuation model. These
simplifications were made to maintain the interactive frame rates at an acceptable
level. Musgrave (1993) discussed this dilemma in detail in his thesis. He stressed
that the priority must be given to speed due to the application of the developed model
in a real-time domain. Applications such as a flight simulator need only to convince
user of the simulated scene’s visual realism; regardless of the method used in
achieving it.
1.3.2 Solving the Out-of-Gamut Colour Problem
Tone mapping is a computer graphics technique used to approximate the
appearance of high dynamic range images in media with a more limited dynamic
5
range. Essentially, tone mapping addresses the problem of strong contrast reduction
from the scene radiance values to the displayable range while preserving the image
details and color appearance important to appreciate the original scene content. This
problem, termed as an out-of-gamut colour, typically arisen after conversion between
colour spaces. Examples of tone mapping techniques are (Fattal et al, 2002) and
(Mantiuk et al, 2005).
An interesting approach to tone mapping of High Dynamic Range (HDR)
images is inspired by a theory proposed by Gilchrist et al (1999). Their theory
comprehensively explains many characteristics of the human visual system such as
lightness constancy and its spectacular failures, which are important in the perception
of images. The key concept of this tone mapping method (Krawczyk et al, 2005) is a
decomposition of an HDR image into frameworks of consistent illumination and the
local calculation of the lightness values. The net lightness of an image is calculated
by merging of the frameworks proportionally to their strength. Particularly
important is the anchoring: relating the luminance values to a known brightness
value, namely estimating which luminance value is perceived as white in the scene.
This approach to tone mapping does not affect the local contrast and preserves the
natural colors of an HDR image due to the linear handling of luminance.
Researchers are now actively pursuing techniques to transfer High Dynamic Range
(HDR) imagery to real-time applications (Durand and Dorsey, 2000; Goodnight et al,
2003).
1.3.3 Transferring the Computational Burden to GPU
Recent works have begun investigating the use of modern shader technology
for simulating atmospheric scattering effects (Dobashi et al, 2002; Hoffman and
Preetham, 2002). A shader is a computer program used in 3D computer graphics to
determine the final surface properties of an object or image. This often includes
arbitrarily complex descriptions of light absorption, diffusion, texture mapping,
reflection, refraction, shadowing, surface displacement and post-processing effects.
6
By design, shaders are ideal candidates for parallel execution by multiple graphic
processors, which are usually located on a video card, allowing for scalable
multiprocessing and lessening the burden on the CPU for rendering scenes.
There are two different applications of shaders in real-time shading
languages: i) vertex shader and ii) pixel shader. Vertex shaders are applied for each
vertex and run on a programmable vertex processor. Pixel shaders are used to
compute properties which, most of the time, are recognized as pixel colors. Pixel
shaders are applied for each pixel as opposed to each vertex. They are run on a pixel
processor, which usually features much more processing power than its vertex-
oriented counterpart.
1.4 Problem Statement
The first problem faced by the previous works in this area is the missing
darkening effect on sky area closer to zenith as the altitude increases. Analytical sky
luminance models such as (Moon and Spencer, 1942; Kittler, 1967; Perez et al, 1993;
Preetham et al, 1999) were all fitted from the daylight sky luminance distribution
data measured/simulated at ground level. As the result, these models are unable to
simulate the above effect at all. Aerial perspective rendering methods such as
(Hoffman and Preetham, 2002; Dobashi et al, 2002) assumed that the observer is
always positioned on the ground. They do not simulate the changes in colour and
intensity that appear as the altitude increases rapidly. This allows them to use the
distance between two points (observer and object) directly as the optical depth. This
shortcut would not work in a flight simulator application, as the optical depth
depends on both the viewing path’s length and the average density of the penetrated
atmosphere. As expected, this shortcut will also create problem latter when dealing
with terrain that contains significant differences in height. One immediate solution
that springs to mind is to use an analytical sky luminance model. Since the all-sky
luminance distribution maps are prepared offline before being fitted to a single
parametric equation, the process of obtaining them can therefore be as precise as can
be. Retrieving these luminance values will only require minimal computational cost.
7
Sky luminance distribution at any altitude can theoretically be simulated using any of
the existing solar spectral models. This statement holds true if the required
atmospheric parameters at that particular layer of the atmosphere are available.
However, as being mentioned earlier, a sky luminance model can only provide the
sky dome’s colour. There is no built-in mechanism for rendering aerial perspective
effects on distant objects. This conundrum presents the second problem that needs to
be solved here.
1.5 Goal
The main goal of this research is to develop an improvised single aerial
perspective rendering algorithm. Rather than recalculating the LTE of all of the
viewing paths each time the scene is updated, the algorithm uses an analytical model
instead. The algorithm must be able to render both daylight sky and distant objects,
as seen through the Earth’s atmosphere from varying altitudes.
1.6 Research Objectives
(i) To construct a general Earth’s atmospheric profile up to 30km; where
it will be use together with a chosen solar spectral model to generate
the all-sky colour distribution maps at each reference altitudes.
(ii) To develop an analytical parametric atmosphere-colour contribution
(APACC) model based on fits of the earlier simulated maps.
(iii) To integrate the APACC model in a single aerial perspective
rendering equation. This is done by developing necessary algorithms
that will facilitate the improvised algorithm in rendering aerial
perspective effects on distant objects.
8
1.7 Research Scopes
(i) The term “general Earth’s atmosphere” is used here to represent a
generic atmospheric profile that did not represent any specific site on
Earth. The atmospheric constituents’ measurements used during the
profiling task were obtained from various sites that differ
geographically; selected merely on availability basis.
(ii) The proposed method is only concerned on simulating the aerial
perspective effects on both sky dome and distant objects under a clear
(zero cloud presence) daylight (from sunrise to sunset) sky.
(iii) Other atmospheric effects such as rainbows, mirages, halos et cetera
are not simulated.
(iv) The actual Sun will not be rendered onto the scene.
(v) A stripped-down version of a flight-simulator application, without the
unnecessary bells and whistles, was built as the test bed.
(vi) In the prototype application, i) a 2D orthographic sky dome is used
instead of a 3D hemispherical version, ii) no actual terrain will be
rendered as distant objects are represented by two 3D boxes, iii) the
Sun position and turbidity are preset before each demo run, iv) the
camera (observer) can only moves on its y-axis (altitude), and v)
transparency is replicated by positioning the two boxes at different
distances from the camera.
1.8 Research Contributions
This research contributes to the following aspects:
(i) By using an analytical model to replace the traditional real-time
solving of the light transfer equation, the cost of determining the
arriving spectral colour at the end of each arbitrary viewing path in
the rendered scene is reduced significantly.
9
(ii) By treating the Earth’s atmosphere density as an exponential function
of altitude, the sky colour distribution effects exhibited when
observed at high altitudes can be captured correctly.
(iii) By packaging the proposed method in a single rendering equation
form, it can easily be implemented in a modern real-time graphical
rendering pipeline, either as a vertex or pixel shader, thus unloading a
huge amount of workloads from the CPU to the GPU.
This work is considered as an applied research, hence benefiting the
following areas:
(i) Computer games – A computationally-efficient method will enable
low-end computers to render the aerial perspective effects at an
acceptable interactive frame rates. Flight simulator game reaps the
most benefits.
(ii) Military/airline industry – Help familiarize beginner pilot with the
various daylight sky conditions (turbidity level and time setting) as
expected to be observed in the real world. Aerial perspective effects
assist pilot to judge both scale and distance properly.
(iii) Tourism – Virtual tourism via the “fly-through” method.
1.9 Organization of Thesis
This thesis contains six chapters as follows:
Chapter 1 briefly introduces the topic of aerial perspective effects computer
modelling and its related research backgrounds. The problem statements are defined
next. Goal, objectives and scopes of research are then stated clearly and concisely.
Research contributions are also listed and elaborated.
Chapter 2 conducts a literature review on all three given research objectives.
This chapter covers the topic of: i) atmospheric profiling and the preparation of the
10
all-sky colour distribution maps, ii) analytical luminance models, and iii) real-time
aerial perspective rendering methods.
Chapter 3 presents the research methodology. Every algorithm that were
used to accomplish the research objectives are presented and justified here.
Chapter 4 reports on the implementation of the proposed methodology. The
methodology is designed to be implemented modularly by two phases: i) pre-
processing (offline) and ii) run-time processing (real-time). This chapter illustrates
the workflow of these modules using relevant pseudo codes and diagrams.
Chapter 5 shows the research results and their individual analysis. Properties
of the proposed method are then highlighted by comparing them with previous
methods’ results.
Chapter 6 summarizes and concludes this study. It also outlines the topics for
future work.