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ICS Summer School, Roscoff
Introduction to Scientific VisualizationInstructors: Chantal
Oberson Ausoni†, Jérémie Foulon†,Pascal Frey†,?, Julien Tierny‡
† ICS-UPMC, Paris, France‡ LTCI (UMR 5141) Telecom Paris Tech,
France
? Lab. J.L. Lions, UMR 7598, UPMC Univ Paris 06, Paris,
France
Class notes can be downloaded at www.ljll.math.upmc.fr/
frey/visu.html
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Outline of the lectures
PART I - FUNDAMENTALS
1. Introduction to scientific visualization
1.1 Visualization at large
1.2 Definitions and purposes, motivations, concerns
1.3 Technological aspects
2. Computer graphics primer
2.1 Introduction to CG
2.2 The quest for realism
2.3 Illumination models
3. Mathematical primer
3.1 Geometric transformations, motivations
3.2 Affine and projective transformations
3.3 Rotations in 3D
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Outline of the lectures
PART II - ADVANCED CONCEPTS
4. Surface representation and approximation
4.1 Curves and surfaces
4.2 Differential geomery
4.3 Parametrized surfaces
4.4 Discrete surfaces, triangulations
5. Data analysis and visualization
5.1 Data structures
5.2 Scalar fields
5.3 Vector fields
5.4 Tensor fields
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References• Computer graphics
1. Agoston M.K., Computer graphics and geometric modeling,
implementation and algorithms, Springer,(2005).
2. Birn J., Digital lighting & rendering, New Riders,
(2010).
3. Gallardo A., 3D lighting, history, concepts & techniques,
Charles River Media, (2000).
4. Govil-Pai S., Principles of computer graphics, theory and
practice using OpenGL and Maya, Springer,(2004).
5. Hansen C.D., Johnson C.R. (eds), The Visualization Handbook,
Academic Press, (2005).
6. Levkowitz H., Color theory and modeling for computer
graphics, visualization, and multimediaapplications, Springer,
(1997).
7. Mukundan R., Advanced methods in computer graphics with
examples in OpenGL, Springer, (2012).
8. Salomon D., Computer graphics and geometric modeling,
Springer, (1999).
9. Tufte E.R., Graves-Morris P.R., The visual display of
quantitative information, Graphics press Cheshire,(1983).
10. Watt A., Watt M., Advanced animation and rendering
techniques, Addison-Wesley, (1992).
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References (2)• Scientific Visualization
1. Farin G., Hansford D., Mathematical principles for scientific
computing and visualization, AK PetersLtd, (2008).
2. Giaquinto M., Visual thinking in mathematics, an
espistemological study, Oxford University Press,(2007).
3. Hauser H., Hagen H., Thiesel H. (eds.), Topology-based
methods in visualization, Springer, (2007).
4. Javidi B., Okano F., Son J.Y. (eds.), Three-dimensional
imaging, visualization and display, Springer,(2009).
5. Laidlaw D.H., Vilanova A. (eds.), New developments in the
visualization and processing of tensorfields, Springer, (2012).
6. Möller T., Hamann B., Russell R. (eds.), Mathematical
foundations of scientific visualization, com-puter graphics and
massive data exploration, Springer, (2009).
7. Peikert R. et al. (eds.), Topological methods in data
analysis and visualization II, Springer, (2012).
8. Schroeder W., Martin K., Lorensen B., The visualization
toolkit, Prentice-Hall, (1997).
9. Tufte E.R., The visual display of quantitative information,
2nd ed., Graphics Press, (2001).
10. Wright H., Introduction to scientific visualization,
Springer, (2007).
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References (3)• Geometry
1. Anderson J.W., Hyperbolic geometry, Springer, (2005).
2. Audin M., Geometry, Springer UTX, (2003).
3. Berger M., Geometry, UTX, Springer, (1987).
4. Berger M., Senechal L.J., Geometry Revealed: A Jacob’s Ladder
to Modern Higher Geometry,Springer, (2010).
5. Dorst L., Fontijne D., Mann S., Geometric algebra for
computer science, an object-oriented approachto computer graphics,
Morgan-Kaufmann, (2007).
6. Goldman R., Rethinking quaternions, theory and computation,
Morgan & Claypool publishers,(2010).
7. Perwas Ch., Geometric algebra with applications in
engineering, Geometry and Computing, 4,Springer, (2009).
8. Petersen P., Riemannian geometry, GTM 171, Springer,
(2006).
9. Pressley A., Elementary differential geometry, UMS, 2nd ed.,
Springer, (2010).
10. Stillwell J., The four pillars of geometry, Springer,
(2005).
11. Vince J.A., Quaternions for computer graphics, Springer,
(2011).
12. Vince J.A., Geometric algebra for computer graphics,
Springer, (2008).
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References (4)
• OpenGL
1. Angel E., Schreiner D., Interactive computer graphics, a
top-down approach with shader-basedOpenGL, 6th ed., Addison-Wesley,
(2012).
2. Cozzi P., Riccio Ch. (eds.), OpenGL insights, CRC Press,
(2012).
3. Glaeser G., Stachel H., Open geometry: OpenGL + advanced
geometry, Springer, (1999).
4. Kempf R., Frazier C. (eds.), OpenGL reference manual, 2nd
ed., Addison-Wesley, (1997).
5. Whitrow R., OpenGL graphics through applications, Springer,
(2008).
6. Woo et al., OpenGL programming guide, 3rd ed.,
Addison-Wesley, (1999).
• Related topics
1. Dey T.K., Curve and surface reconstruction, algorithms with
mathematical analysis, Cambridge Uni-versity Press, (2007).
2. Hjelle O., Daehlen M., Triangulations and applications,
Springer, (2006).
3. Velho L. et al. (eds.), Mathematical optimization in computer
graphics and vision, Morgan Kauf-mann, (2008).
4. Warren J., Weimer H., Subdivision methods for geometric
design, a constructive approach, Morgan-Kaufmann, (2002).
5. Zudilova-Seinstra E. et al. (eds.), Trends in interactive
visualization, state-of-the-art survey, Springer,(2009).
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Schedule
WEEK I
Mornings: lectures 17 hours Afternoons: hands-on sessions 12
hours
Day Schedule Topic
Mo 28/07 9:00-12:00 Scientific Visualization (definitions and
purposes, motivations)14:00-16:00 Computer graphics primer (quest
for realism, rendering)16:30-17:30 M. Baaden’s seminar
Tu 29/07 9:00-12:00 Maths Primer (analytic and proj.
geometry)14:00-17:00 GLUT demos
We 30/07 9:00-12:00 Introduction to C++14:00-17:00 Programming
in 3D
Th 31/07 9:00-12:00 Data structures (regular grid,
triangulations, etc)14:00-17:00 Paraview I (data converter)
Fr 1/08 9:00-12:00 Scalar fields (isosurfaces, etc.)14:00-17:00
Isosurfaces reconstruction
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Schedule (2)
WEEK II
Mornings: lectures 14 hours Afternoons: hands-on sessions 12
hours
Day Schedule Topic
Mo 4/08 9:00-12:00 Continuous surfaces (representation,
differential geometry, etc)14:00-17:00 Bézier surfaces
(interpolation)
Tu 5/08 9:00-12:00 Discrete surfaces (representation,
subdivision)14:00-17:00 Curvature estimates
We 6/08 9:00-12:00 Vector fields (critical points,
etc)14:00-17:00 Paraview II (scalar, vector, tensors analysis)
Th 7/08 9:00-12:00 Tensor fields14:00-17:00 Case studies
Fr 8/08 9:00-11:00 Conclusions
Total
Lectures : 31 hours Hands-on sessions: 24 hours
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Part IFUNDAMENTALS
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Chapter IINTRODUCTION TO SCIENTIFIC
VISUALIZATION
(C. Brownlee et al., Ray tracing using OpenGL Interception,
University of Utah, USA)
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Introduction
Section 1.1Motivations & Applications
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Introduction
[Scientific] visualizationChart junk (E. Tufte)
Which of these visualizations will you remember later?
(Credit: Images courtesy of Michelle Borkin, Harvard SEAS)
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Introduction
[Scientific] visualization
Pantheon is a project developed by the Macro Connections group
at The MIT Media Lab that’s collecting,
analyzing, and visualizing data on historical cultural
popularity and production.
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Introduction
Visualization
Definitions and aims:
• the classical definition of visualization is as follows: the
formation of mental visualimages, the act or process of
interpreting in visual terms or of putting into visual form.
• a new definition is: a tool or method for interpreting image
data fed into a computerand for generating images from complex
multi-dimensional data sets (1987).
• In general, visualization is essentially a mapping process
from computer representa-tions to perceptual representations,
choosing encoding techniques to maximize humanunderstanding and
communication.
• The goal of a viewer might be a deeper understanding of
physical phenomena or math-ematical concepts, but it also might be
a visual proof of computer representations de-rived from such an
initial stage.
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Introduction
Definitions and aims. . .
Herefater is a selection of distinct attempts to formulate the
contents and goals of visualiza-tion processes:
• R.A. Earnshaw: Scientific Visualization is concerned with
exploring data and informa-tion in such a way as to gain
understanding and insight into the data. The goal ofscientific
visualization is to promote a deeper level of understanding of the
data underinvestigation and to foster new insight into the
underlying processes, relying on the hu-mans’ powerful ability to
visualize. In a number of instances, the tools and techniquesof
visualization have been used to analyze and display large volumes
of, often time-varying, multidimensional data in such a way as to
allow the user to extract significantfeatures and results quickly
and easily.
• J. Foley and B. Ribarsky: A useful definition of visualization
might be the binding (ormapping) of data to representations that
can be perceived. The types of bindings couldbe visual, auditory,
tactile, etc., or a combination of these.
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Introduction
Definitions and aims. . . (2)
• R. Friedhoff and T. Kiley The standard argument to promote
scientific visualization isthat today’s researchers must consume
ever higher volumes of numbers that gush, asif from a fire hose,
out of supercomputer simulations or high-powered scientific
instru-ments. If researchers try to read the data, usually
presented as vast numeric matrices,they will take in the
information at snail’s pace. If the information is rendered
graphi-cally, however, they can assimilate it at a much faster
rate.
• B. McCormick, T. DeFanti, and M. Brown: Visualization is a
method of computing.It transforms the symbolic into the geometric,
enabling researchers to observe theirsimulations and computations.
Visualization offers a method for seeing the unseen.It enriches the
process of scientific discovery and fosters profound and
unexpectedinsights. In many fields it is already revolutionizing
the way scientists do science.
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Introduction
Definitions and aims. . . (3)
• P.K. Robertson: Underlying the concept of visualization is the
idea that an observercan build a mental model, the visual
attributes of which represent data attributes in adefinable manner.
This raises several questions:
� What mental models most effectively carry various kinds of
informations ?� Which definable and recognizable visual attributes
of these models are most useful
for conveying specific information either independently or in
conjunction with otherattributes ?
� How can we most effectively induce chosen mental models in the
mind of an ob-server ?
� How can we provide guidance on choosing appropriate models and
their attributesto a human or automated display designer ?
Choosing the appropriate representation can provide the key to
critical and compre-hensive appreciation of the data, thus
benefiting subsequent analysis, processing, ordecision making.
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Introduction
Definitions and aims. . . (4)
• E. Ignatius and H. Senay: In their understanding, scientific
data visualization supportsscientists and relations, prove or
disprove hypotheses, and discover new phenomenausing graphical
techniques.The primary objective in data visualization is to gain
insight into an information spaceby mapping data onto graphical
primitives.
• R.B. Haber and D.A. McNabb: they defined visualization as the
use of computer imag-ing technology as a tool for comprehending
data obtained by simulation or physicalmeasurement. In their
understanding Visualization technology is based on the integra-tion
of older technologies, including computer graphics, image
processing, computervision, computer-aided design geometric
modeling, approximation theory, perceptualpsychology, and user
interface studies.
• S. Wehrend and C. Lewis Progress in scientific visualization
can be accelerated if work-ers could more readily find
visualization techniques relevant to a given problem.
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Introduction
Definitions and aims. . . (5)
• P. Robertson and L. De Ferrari: The size, dimensionality and
the number of parametersof data sets can be expected to increase
significantly. This is accompanied by a corre-sponding increase in
the complexity of the systems being modeled. Many computergraphics
and image-processing techniques are applicable to the visualization
of thesedata and new ways of representing and interacting with data
are evolving. Our abilityto exploit these techniques are limited by
the lack of systematic strategies which, tak-ing into account both
the characteristics of the data and the interpretation aims of
thescientist, can guide the scientist in their use.Our goal is the
systematic, and therefore potentially automatic, generation of
visualrepresentations, given a description of all the important
data characteristics and thespecification of the user’s
interpretation aims. The interpretation aims define
whatcharacteristics of the data, or relations between data
variables, the user is interested inanalyzing by means of visual
representation.
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Introduction
Scientific visualization
• Scientific visualization is concerned with representing
scientific phenomena graphi-cally, as a means of gaining
understanding and insight into the system that is studied inways
previously impossible.
� This may be part of the research process: graphics are used
for understanding,interpretation, exploration, and may guide the
direction of the research itself, fromtweaking parameters to
raising new questions.
� It may be used in production environments, such as medical
procedures, as onepart of a larger mission.
� It may be used for educational purposes, in the classroom,
etc.
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Introduction
Scientific visualization
What happens when display precedes data analysis !
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Introduction
An emerging science
• Scientific visualization is a field in and of itself.� It
involves research in computer graphics, image processing, high
performance com-
puting, mathematics, and other areas.
� Its strategy is to develop fundamental ideas leading to
general tools for real appli-cations. This pursuit is
multidisciplinary in that it uses the same techniques acrossmany
areas of study.
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Introduction
New science, . . . old concern
The use of visualization to present information is not new, it
has been used in maps, scien-tific drawings, and data plots for
over a thousand years.
A rigid obstacle in flowing water creates wake turbulence,
sketch by Leonardo da Vinci in 1509.
(credit: image The Royal Collection, HRM Queen Elizabeth
II).
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Introduction
Visualization in scientific computing
• In October 1986, the Division of Advanced Scientific Computing
(DASC) of the Na-tional Science Foundation (NSF) sponsored a
meeting of a newly-organized Panel onGraphics, Image Processing and
Workstations to provide input to DASC on establish-ing and ordering
priorities for acquiring graphics and image processing hardware
andsoftware at research institutions doing advanced scientific
computing, with particularattention to NSF-funded supercomputer
centers.
• Supercomputer centers had been requesting funds to provide
graphics hardware andsoftware to scientific users but, in point of
fact, existing tools were not adequate tomeeting their needs.
• Computer Graphics and image processing are within computer
science; the applica-tion of computers to the discipline sciences
is called computational science. Applyinggraphics and imaging
techniques to computational science is a while new area of
en-deavor, which Panel members termed Visualization in Scientific
Computing.
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Introduction
Applications fields
The interplay between application areas and specific
problem-solving visualization tech-niques is emphasized by several
major themes in: Engineering (CFD, FEA), Electronic De-sign
Automation, Simulation, Medical Imaging, Geospatial, RF
Propagation, Meteorology,Hydrology, Data Fusion, Ground Water
Modeling, Oil and Gas Exploration and Production,Finance, Data
Mining, etc.
• Uncertainty Visualization: seeks to provide a visual
representation of errors and uncer-tainty for three-dimensional
visualizations. Challenges include the inherent difficultyin
characterizing comparisons among different data sets and the
corresponding errorand uncertainty in the experimental, simulation,
and/or visualization processes.
"True genius resides in the capacity for evaluation of
uncertain, hazardous, and conflicting information."
(W. Churchill)
• Integrated Multi-field Visualization: The output of
computational science simulationsis typically a combination of
fields involving a number of scalar fields, vector fields,or tensor
fields. Similarly, data collected experimentally is often
multi-field in nature.Multi-scale problems with scale differences
of several orders of magnitude pose chal-lenging problems for data
analysis.
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Introduction
Applications fields
• Environmental Scientific Visualization: refers to a collection
of visualization applica-tions that deal with captured and
simulated data in climate research, atmospheric andenvironmental
sciences, earth science, geophysics and seismic research,
oceanography,and the energy industry. Research in these
applications has a huge impact on mankind,and typically faces
serious challenges of data deluge (e.g., very large volumes of
multi-spectral satellite images, large data collections from
different sensor types, ensemblecomputation of very large
simulation models, scattered, time-varying, multi-modal datain
seismic research).
• Scientific Foundation of Visualization: Many fundamental
questions about the theoret-ical and perceptual aspects of
visualization remain unanswered, such as, why is onevisual design
more effective than another, can visual designs be optimized and
how,what is the role of visualization in a scientific workflow and
how can such a role beformalized, can visualization quality be
measured quantitatively and how, and what isthe most informative
way to conduct perceptual and usability studies involving
domainexperts?
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Introduction
Section 1.2Definitions and purposes
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Introduction
Scientific visualization
Definition and purposes of scientific visualization:
• SciVis is a very important part of visualization, as the
visualization of experiments andphenomena is as old as science
itself.
• SciVis is the transformation, selection, or representation of
data from simulations orexperiments, with an implicit or explicit
geometric structure, to allow the exploration,analysis, and
understanding of the data.
• SciVis focuses and emphasizes the representation of higher
order data using primarilygraphics and animation techniques.
• Traditional areas of scientific visualization include: flow
visualization, medical visual-ization, astrophysical visualization,
and chemical visualization.There are several different techniques
to visualize scientific data, with isosurface recon-struction and
direct volume rendering being the more common.
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Introduction
Motivations
• Through the availability of increasingly powerful computers
with increasing amounts ofinternal and external memory, it is
possible to investigate incredibly complex dynamicsby means of ever
more realistic simulations.However, this brings with it vast
amounts of data.
• To analyze these data it is imperative to have software tools
which can visualize thesemulti-dimensional data sets.
• Comparing this with experiment and theory it becomes clear
that visualization of sci-entific data is useful yet difficult.For
complicated, time-dependent simulations, the running of the
simulation may involve the calculation
of many time steps, which requires a substantial amount of CPU
time , and memory resources are still
limited, one cannot save the results of every time step. Hence,
it will be necessary to visualize and store
the results selectively in ‘real time’ so as to avoid
recomputing the dynamics.
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Introduction
Motivations (2)
• The main reasons for scientific visualization are the
following ones :
� it will compress a lot of data into one picture (data
browsing),
� it can reveal correlations between different quantities both
in space and time,
� it can furnish new space-like structures beside the ones which
are already knownfrom previous calculations,
� it opens up the possibility to view the data selectively and
interactively in ‘realtime’. By following the formation and the
deformation as well as the motions ofthese structures in time, one
will gain insight into the complicated dynamics.
• The aim is to integrate the simulation codes into a
visualization environment in orderto analyze the data ’real time’
and to by-pass the need to store every intermediate resultfor later
analysis: the simulation is distributed over a set of
high-performance computersand the actual visualization is done on a
graphical distributive workstation.It is also very useful to have
the possibility to interactively change the simulation pa-rameters
and immediately see the effect of this change through the new
data.
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Introduction
Questions
• The discussion is focussed on the following questions:
� What is the improvement in the understanding of the data as
compared to the situ-ation without visualization?
� Which visualization techniques are suitable for one’s
data?
� Are direct volume rendering techniques to be preferred over
surface rendering tech-niques?
� Can current techniques, like streamline and particle advection
methods, be used toappropriately outline the known visual phenomena
in the system?
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Introduction
Concerns
• The success of visualization not only depends on the results
which it produces, but alsodepends on the environment in which it
has to be done.
• This environment is determined by the available hardware, like
graphical workstations,disk space, color printers, video editing
hardware, and network bandwidth, and by thevisualization
software.For example, the graphical hardware imposes constraints on
interactive speed of visu-alization and on the size of the data
sets which can be handled.
• Many different problems encountered with visualization
software must be taken intoaccount: the user interface, programming
model, data input, data output, data manip-ulation facilities, and
other related items are all important.The way in which these items
are implemented determines the convenience and effec-tiveness of
the use of the software package as seen by the scientist.
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Introduction
Perception of visuals
• Visual attributes:� a clever choice of visual attributes is
paramount to visualization process� redundancy of visual attributes
enhances interpretability
• Interpretation of visual attributes:� natural to interpret,
simple,� acquired reactions to visual attributes: through education
(color ranking, isosur-
faces, etc)
� illusory visual attributes
• Color:� psychophysical process: relates to wavelengths,
spectral distribution and amount
of light entering eye (physics) and perceived sensation with no
linear relation tophysics (psychology).
� no complete theory, variety of color spaces, perceptual
dimensions of color (hue,saturation, intensity).
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Introduction
Perception of visuals
M.C. Escher optical illusion.
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Introduction
Skills
A student who wants to specialize in visualization needs a
broadly based background.
Ideally, he or she will need:
• a strong mathematical background, with calculus, linear
algebra, ordinary and partialdifferential equations, and numerical
analysis.
• in addition to a regular computer science background, the
student would also need astrong grounding in computer graphics plus
some experience in computer animation.
• he or she should have some art courses such as graphics
design, photography, drawing,or painting to obtain the general
principles of design from an artistic viewpoint. Plus,the student
need some science courses such as biology, chemistry, or physics,
to beable to communicate with the scientists.
While it might be extremely difficult, if not impossible to fit
all of this into an undergraduatecurriculum, a program oriented
towards a Masters Degree in Visualization would be quitefeasible .
. .
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Introduction
Skills
In science, novelty emerges only with difficulty, manifested by
resistance, against a back-ground provided by expectations. Thomas
Kuhn (1922-1996)
The eye sees only what the mind is prepared to comprehend. Henri
Bergson (1859-1941)
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Introduction
Section 1.3Technological aspects
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Introduction
Visualization techniques
• A visualization technique is used to create and manipulate a
graphic representationfrom a set of data.
• Some techniques will be appropriate only for specific
applications while others aremore generic and can be used in many
applications.
• It should always be kept in mind that the goal of
visualization is not to understand thedata but to understand the
underlying phenomenon.
• There are three parts to a visualization technique:1. The
construction of an empirical model from the data. This construction
may in-
volve sampling theory considerations, and general mathematical
interpolation / ap-proximation schemes. If the data contains errors
then this must be taken into ac-count.
2. The selection of some schematic means of depicting the model
as some abstractvisualization object, such as an image of a contour
map.
3. The rendering of the image on a graphics display.
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Introduction
Visualization techniques
• For many areas of science and engineering, visualization has
become more than aconvenient tool: it has become a necessity for
interpreting the enormous amounts ofdata being produced by
large-scale instrumentation, experiments and simulations.
• Fortunately, scientific visualization benefits from
technological outcomes.For example, one of the most creative and
useful ways of presenting scientific data isthe large-scale (tiled)
display.Ranging from tabletop versions to fully immersive 3D stereo
virtual reality environ-ments, these displays enable users to
explore features that may be hard or impossibleto identify with
conventional, personal computers.
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Introduction
Visualization devices
Graphics cards: the primary suppliers of the GPUs (video chips
or chipsets) used in videocards are AMD and Nvidia.
Nvidia GeForce GTX Titan Z AMD Radeon R9 295X2
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Introduction
Visualization devices
Graphics cards: specifications and features
Nvidia GeForce GTX Titan Z AMD Radeon R9 295X2dual chip dual
chip
Stream processors 5,760 5,632Engine clock 705 Mhz 1018
MhzCompute performances 21.7 Tflops 11.5 TflopsTexture fill-rate
338 GT/s 358.3 GT/sMemory configuration 12 GB 8 GB
Retail price 2,999 USD 1,499 USD
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Introduction
Visualization techniques
• Large-screen displays: can be found in any number of
industries and research centers.The ability to display created
environments at "full scale" can be of tremendous valueto
researchers and scientists.These displays can be curved for an even
more immersive experience.
Immersive environment for design review created by a
large-screen curved display.
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Introduction
Visualization techniques
Large display (6.5 ⇥ 2.5 m) in use at the Institute for
Scientific Computing and Simulation (UPMC, Paris).
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Introduction
Visualization techniques
• Immersive environments: this system allows the user to walk in
the space, providing atotally immersive, high-resolution
experience.Built from 4 to 6 walls with rear projection, the user
experiences the environment infull scale and in real time.
Research in immersive environments works to virtually place the
viewer in a space.
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Introduction
Visualization techniques
• Active shutter 3D system: is a technique of displaying
stereoscopic 3D images.It works by only presenting the image
intended for the left eye while blocking theright eye’s view, then
presenting the right-eye image while blocking the left eye,
andrepeating this so rapidly that the interruptions do not
interfere with the perceived fusionof the two images into a single
3D image.
• Real-time tracking: concerns the positional measurement of
bodies (subjects or objects)that move in a defined space. Position
and/or orientation of the body can be measured.3 degrees of freedom
(3DOF or 3D) tracking consists in measuring only x, y, z
posi-tions. If position (3 coordinates) and orientation (3
independent angular coordinates)are measured simultaneously, this
is called 6 degrees of freedom (6DOF or 6D) track-ing.
• Haptic technology: is a tactile feedback technology which
recreates the sense of touchby applying forces, vibrations, or
motions to the user.
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Introduction
Software packages• Non-exhaustive set of tools which cover the
functions needed by most researchers for
their scientific visualization needs.
1. Matlab: is a numerical computing package which has gained
wide popularity in thescience and engineering communities. It
provides a large set of plotting options, awwell as the standard
basic visualization tools.
2. VTK-Paraview: the Visualization Toolkit is an open source set
of graphics libraries,accessible using C++, Tcl, Perl, Python, or
Java. ParaView is an open source, freelyavailable visualization
application built on top of VTK.
3. OpenGL: the Open Graphics Library is a standard specifying an
API for applicationsthat produce 2-d and 3-d computer graphics.
4. Open Scene Graph: is an open source high performance 3-d
graphics toolkit. Ascene graph is a hierarchical representation of
all elements of a visual scene Ð onceyou have constructed this
directed graph, the underlying libraries will traverse it andrender
the objects represented by it.
5. Maya: is an interactive, professional 3-d graphics, modeling,
and animation pro-gram, used in the movie, television, and game
industries, as well as for design andarchitectural rendering.
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Introduction
Software packages (2)
The table below shows where the packages fall in the
visualization pipeline:
1. Produce input data: use a CFD simulation program
2. Analyze, filter, reformat: compute the gradient of
pressure
3. Apply scientific visualization techniques: compute the
pathlines
4. Map to geometry: produce a set of polygons representing the
domain
5. Rendering: create an image from a virtual camera of the
polygonal model
6. Viewing: use a web browser to view the resulting image
Tool input data analysis sci-vis geometry rendering
viewingexperiments xMatlab x x x x x xVTK-Paraview x x x x x
xOpenGL x xOpenScene Graph x xMaya x x
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Introduction
Software packages (3)
Paraview (Sandia Natl. Lab., Los Alamos Natl. Lab., Kitware
Inc.).
Visualization of the result of OpenFOAM combustion calculations
(background color represents the
temperature, the arrows represents the gas velocity and their
colors represent the concentration of oxygen.
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Introduction
Software packages (4)OpenSceneGraph (open source 3D application
programming interface).
TerrainView is the free 3D viewer of ViewTec for interactive
visualization od 3D data.
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Introduction
Software packages (5)
Maya Autodesk (3D computer graphics software).
Autodesk Maya 2013 (Alias Systems Corp., Autodesk Inc.).
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Introduction
Software packages (5)Ensight (FEA and CFD post-processing).
Ensight 10 (CEI-Computational Engineering International,
Inc.).
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Chapter IICOMPUTER GRAPHICS PRIMER
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Computer Graphics
Section 1.1Introduction to CG
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Introduction
Computers have powerful graphics processors to support
sophisticated applications. Butthese involve assertive skills in
computer graphics and "elementary" mathematics, in partic-ular
concerning :
1. the geometric transformations:
• affine geometry,• projections,• homogeneous coordinates,•
quaternion based representation.
2. the quest for realism:the purpose of visualization algorithms
is to convince the user that the graphical repre-sentation of a 3D
model is a slightly altered vision of reality. This involves:
• color coding• rendering equations
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Computer Graphics
Processing demands
• Scientific visualization and (obviously) computer games are
some of the most demand-ing applications at present;
• To make objects appear on the display, these applications send
polygons to a graphicsprocessor. These polygons have various
attributes (like color, texture, and transparency)and are displayed
with various technologies (antialiasing, smooth shading, and
others).
• For a polygon to be displayed, certain pixels must be colored
in certain ways. Thus,polygon rate (the number of polygons
displayed per second) and fill rate (the numberof pixels colored
per second) are both used to measure performance.
• But complex scenes for interactive display can easily contain
1 million polygons, ofwhich maybe 100,000 are visible (the others
being hidden by things in front of themor outside the field of
view), each occupying perhaps 10 pixels on average. In manycases, a
single polygon occupies less than a single pixel.
• This happens in part because complex shapes are modeled with
polygonal meshes.
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The graphics pipelineThe term graphics pipeline is used because
the transformation from mathematical modelto pixels on the screen
involves multiple steps, and in a typical architecture, these are
per-formed in sequence; the results of one stage are pushed on to
the next stage so that the firststage can begin processing the next
polygon immediately.
ptg11539634
1.6 The Graphics Pipeline 15
Application
Texturedata
Polygonmeshes
Geometrictransfor-mations
Rasterizeand light
Imageassembly Display
FragmentsGraphics card
Polygonmesh
vertices
View
Lightingdata
Polygondata
Vertexdata
Figure 1.8: The graphics pipeline, version 1.
of one stage are pushed on to the next stage so that the first
stage can begin pro-cessing the next polygon immediately.
Figure 1.8 shows a simplified view of this pipeline: Data about
the scene beingdisplayed enters at various points to produce output
pixels.
For many purposes, the exact details of the pipeline do not
matter; one canregard the pipeline as a black box that transforms a
geometric model of a sceneand produces a pixel-based perspective
drawing of those polygons. (Parallel-projection drawings are also
possible, but we’ll ignore these for the moment.)On the other hand,
some understanding of the nature of the processing is
valuable,especially in cases where efficiency is important. The
details of the boxes in thepipeline will be revealed throughout the
book.
Even with this simple black box you can write a great many
useful programs,ignoring all physical considerations and treating
the transformation from modelto image as being defined by the black
box rather than by physics (like the non-quadratic light-intensity
falloff mentioned above).
The past decade has, to some degree, made the pipeline shown
aboveobsolete. While graphics application programming interfaces
(APIs) of the pastprovided useful ways to adjust the parameters of
each stage of the pipeline, thisfixed-function pipeline model is
rapidly being superseded in many contexts.Instead, the stages of
the pipeline, and in some cases the entire pipeline, are
beingreplaced by programs called shaders. It’s easy to write a
small shader that mimicswhat the fixed-function pipeline used to
do, but modern shaders have grownincreasingly complex, and they do
many things that were impossible to do on thegraphics card
previously. Nonetheless, the fixed-function pipeline makes a
goodconceptual framework onto which to add variations, which is how
many shadersare in fact created.
1.6.1 Texture Mapping and ApproximationOne standard component of
the black box is the texture map. With texture map-ping, we take a
polygon (or a collection of polygons) and assign a color to
eachpoint via a lookup in a texture image; the technique is a
little like applying a stencil
The graphics pipeline.
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Computer Graphics
Basic graphics systems
• a typical graphics program runs on the CPU, processing input
from the devices andsending instructions to the GPU describing what
should be displayed;
• graphical models are created in some convenient coordinate
system;� for example, a cube that is to be used as one of a pair of
dice might be modeled
as a unit cube, centered at the origin in 3-space. This
coordinate system is calledmodeling space or object space.
� This cube is then placed in a scene: a model of a collection
of objects and lightsources. The resultant coordinates of the cube
are said to be in world space.
� The location and direction of a virtual camera is also given
in world space, as are thepositions and physical characteristics of
virtual lights. Consider a set of coordinateaxes whose origin is at
the center of the virtual camera and whose negative z-axispoints
along the camera view. All objects in world space have coordinates
in thiscoordinate system as well; these coordinates are called
camera-space coordinates.
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Computer Graphics
Building blocks for rendering
• The physics of light: light propagates along straight-line
rays in empty space, stoppingwhen it meets a surface, Light bounces
from any shiny surface that it meets, followingan "angle of
incidence equals angle of reflection" model, or is absorbed by the
surface.
• Materials: assumption about objects is that they are composed
of materials that eitherreflect or absorb light at their surfaces.
Because we assume that light only interactswith the surfaces of
materials, we represent objects by their surfaces, which are in
turngenerally represented by polyhedra with triangular faces.
• The human visual system: our visual system organizes the
patterns of light and darknessthat arrive at the eye and attempts
to make sense of them. The visual system is extremelywell adapted
to bad input !an understanding of the perception process lets us
make informed decisions about whatkinds of approximations we can
make while still retaining visual fidelity.
• Mathematics: in addition to basic knowledge in algebra and
arithmetic, you need tobe familiar witg trigonometry, linear
algebra, integration and differentiation, geometricand topological
notions, etc.
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Computer Graphics
Data structures for graphics
Certain data structures pop up repeatedly in graphics
applications: they address fundamen-tal underlying ideas like
surfaces, space, and scene structure.
• Triangle meshes or triangulations: are generally used to
represent surfaces, so a mesh isnot just a collection of unrelated
triangles, but rather a network of triangles that connectto one
another through shared vertices and edges to form a single
continuous surface.Connectivity: indexed meshes are the most common
in-memory representation of tri-angle meshes, but triangle strips
may be more efficient.
• Scene graphs: a universal problem in graphics applications is
arranging the objectsin the desired positions. This is done using
transformations, but complex scenes cancontain a great many
transformations and organizing them well makes the scene mucheasier
to manipulate.
• Spatial data structures: related to the ability to quickly
locate geometric objects inparticular regions of space.
� structures that group objects together into a hierarchy are
object partitioning schemes;� structures that divide space into
disjoint regions are space partitioning schemes.
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Triangular meshes
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Computer Graphics
Section 1.2The Quest for Realism
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Rendering example
An image created using POV-RAY
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Computer Graphics
Rendering example
Intermixing virtuality and reality
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Computer Graphics
Rendering
• Rendering: process of generating an image from a model by
means of computer algo-rithms.
• A scene file contains objects in a strictly defined language
or data structure; it wouldcontain geometry, viewpoint, texture,
lighting, and shading information as a descriptionof the virtual
scene.
• the general challenges to overcome in producing a 2D image
from a 3D representationstored in a scene file are outlined as the
graphics pipeline along a rendering device,such as a GPU.A GPU is a
purpose-built device able to assist a CPU in performing complex
rendering calculations.
• Many rendering algorithms have been designed, and software
used for rendering mayemploy a number of different techniques to
obtain a final image.
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Computer Graphics
Local vs. global illumination
• Local illumination: is only the light provided directly from a
light source (such as a spotlight). Direct light is emitted from a
light source and travels in a straight path to theilluminated point
(either on a surface or in a volume). With direct illumination
onlyeach light source’s contribution is used to calculate the
overall light contribution to anygiven illuminated point.
• Global illumination: is a general name for a group of
algorithms used in 3D computergraphics that are meant to add more
realistic lighting to 3D scenes. Such algorithmstake into account
not only the light which comes directly from a light source
(directillumination), but also subsequent cases in which light rays
from the same source arereflected by other surfaces in the scene,
whether reflective or not (indirect illumination)
• Images rendered using global illumination algorithms appear
more photorealistic thanimages rendered using only direct
illumination algorithms, but computationally moreexpensive.
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Computer Graphics
Rendering classes
• A few classes of more-efficient light transport modelling
techniques have emerged:� rasterization: geometrically projects
objects in the scene to an image plane, without
advanced optical effects; it is the rendering method used by all
graphics cards;
� ray casting considers the scene as observed from a specific
point of view, calculatingthe observed image based only on geometry
and very basic optical laws of reflectionintensity, and perhaps
using Monte Carlo techniques to reduce artifacts. In raycasting the
geometry which has been modeled is parsed pixel by pixel, line by
line,from the point of view outward, as if casting rays out from
the point of view;
� ray tracing is similar to ray casting, but employs more
advanced optical simulation,and usually uses Monte Carlo techniques
to obtain more realistic results at a speedthat is often orders of
magnitude slower;
� radiosity is a method which attempts to simulate the way in
which directly illu-minated surfaces act as indirect light sources
that illuminate other surfaces. Thisproduces more realistic shading
and seems to better capture the ’ambience’.
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Computer Graphics
Color perception
• To achieve this level of realism (accuracy), the sensation
(perception) of colors corre-sponding to the observation of a
digital image must be very close to the sensation thatthe viewer
would feel in the real world.
• The perception of color by humans depends on the amount of
light that reaches theeye. Strength (i.e. quantity) is determined
by the radiance of visible points. Thus, eachobject in a 3d scene
reflects incident light by changing its color or intensity.
• Reflexion models describe both the color and the evolution of
this color when a pa-rameter of the acquisition is changed.
• Another important parameter of a surface is its roughness (or
its smoothness, according)which determines the specular
reflection.
• To model these complex phenomena, it is essential to know the
structure of mathemat-ical or physical interactions between light
and object, and its action on the eye (theoryof electromagnetic
waves).
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Computer Graphics
Nature and properties of light
• Dual nature: light, as observed, can be manifest as a wave or
a particle.
• Interactions: light travels in both a vacuum as well as most
media, and its interactionwith matter is observable. Its behavior
can be categorized in several ways:
� Reflection: is the throwing or bouncing back of light as it
hits a surface;
� Refraction: is the bending of light as it crosses from one
medium to another;
� Transmission: is the conduction or conveying of light through
a medium;
� Diffraction: is the apparent bending of light around an edge
that results in intensityand directional changes.
� Interference: is the wavelike interaction of light that
results in amplification, cancel-lation, or composite generation of
the resultant light wave;
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Computer Graphics
Nature and properties of light
• Interactions (cont’d):
� Scattering: is the spreading or dispersal of light as it
interacts with matter or media;
� Diffusion: is the even scattering of light by reflection from
a surface.
� Absorption: is the nonconductance or retention of light by a
matter or media thatdoes not result in either reflection or
transmission;
� Polarization: is the selective transmission of light based on
its orientation.
� Dispersion: is the effect of light being separated or broken
into different wavelengthsbecause the light passed through a second
medium that has a different refractionindex from the first.
• A light interaction could have one or more of these
manifestations happening at thesame time.
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Computer Graphics
Light behavior
• Light is radiation: it obeys the rules of radiation. Radiation
has properties and qualitiesthat are quantifiable and well as
predictable.
� Thermal radiation: depends on the temperature of the object
emitting it. Sunlightand light from burning objects are
examples.
� Reflected radiation: is reflected off objects and is
indirectly distributed.
• Light is the emission of energy as it is transferred around
and seeks a lower, more stablestage (electronic spectrum). The
property of fading over a distance (think of heat) iscalled the
inverse square law.Formally stated, irradiance (power per unit
expressed in watts/meter2) is inversely pro-portional to the square
of the distance from the source in the absence of media scatter-ing
and absorption.
• Wein’s law: states that the wavelength of the peak radiance
decreases linearly as thetemperature increases. It could also be
defined as "The hotter the object gets, the bluerthe radiation it
emits."
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Light behavior
Wein’s law:
The wavelength at which most radiation is emitted is inversely
proportional to the absolute temperature.
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Computer Graphics
Color as a tri-stimulus medium
• Color is a sensation produced in the brain in response to the
incidence of light on theretina of the eye.
• The sensation of color is caused by differing qualities of the
light emitted by lightsources or reflected by objects. It may be
defined in terms of :
� the observer: the definition is referred to as perceptual and
subjective (i.e., it de-pends on the observer’s judgment).
� the characteristics of light by which the individual is made
aware of objects or lightsources.
• However, the light received by the retina is composed of a
spectrum of different ener-gies in different wavelengths. Only at
the eye, the particular spectrum is translated tothe experience of
a particular color. Moreover, many different spectra are perceived
asthe same color (metamerism, Newton ca. 1704).
• both specifications can be accurately defined in a
three-dimensional space.
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Perceived colors: observer
• The three components that specify color in terms of the
observer are:
1. Hue: specifies the actual "color" that we see (red, yellow,
etc.)
2. Intensity/lightness/brightness: specifies the achromatic
(luminance) component, whichis the amount of light emitted or
reflected by the color. It can be thought of as "howmuch black is
mixed in the color".The term intensity refers to achromatic colors.
The term lightness refers to objects,and is associated with
reflected light. The term brightness is used for light sources,and
is associated with emitted light.
3. Saturation: specifies purity in terms of mixture with white,
or vividness of hue. It isthe degree of difference from a gray of
the same lightness or brightness.Increased lightness causes a
perceived decreased saturation, and vice versa.
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Computer Graphics
Perceived colors: light
• The three components that specify color in terms of light
are:
1. Dominant wavelength: specifies the actual "color" that we
see, and corresponds tothe subjective notion of hue.
2. Luminance: specifies the amount of light or reflection. For
an achromatic light it isthe light’s intensity. For a chromatic
color it corresponds to the subjective notion oflightness or
brightness.
3. Purity: specifies the spectral distribution that produces a
certain color of light. It isthe proportion of pure light of the
dominant wavelength and white light needed todefine the color.
Purity corresponds to the perceptual notion of saturation.
• A particular color can be described uniquely by three
components even though it is aresponse to light, which is an
infinite-dimensional vector of energy levels at
differentwavelengths. This means that the mapping between the
spectral distribution of lightand the perceived color is a
many-to-one mapping. Thus, many spectra are perceivedas the same
color.
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Human visual system
The front-end interface of our visual system is the eye, which
consists of several components:
• The pupil controls the amount of light admittedto the eye (a
camera’s aperture is modeled afterthe pupil).
• Two lenses, the cornea, which is fixed, and avariable-focus
lens, provide distance adaptation.
• The retina, located at the back of the eye, pro-vides the
first layer of "image processing" of ourvisual system.
The retina contains five layers of cells, in charge of several
early image processing tasks.The first layer contains four types of
photoreceptors. These are light sensitive cells, groupedto filter
different light phenomena.
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Computer Graphics
The retina
• Approximately 120 million rods, which are achromatic light
sensitive cells (i.e., theyonly see B/W), are responsible for night
and other low light level vision.
• Day time color vision is provided by approximately 8 million
cones of three types,which operate like filters for different
ranges of wavelength:
1. S-type cones: short wavelength, with peak sensitivity at 440
nm (violet),
2. M-type cones: medium wavelength, with peak sensitivity at 550
nm (green),
3. L-type cones : long wavelength, with peak sensitivity at 570
nm (yellow)
• Cones are mainly concentrated in the central vision center of
the retina, in particular inthe fovea; rods are mainly concentrated
in the periphery of the retina.
• There are no photoreceptors in the optic disk, where the
optical nerve connects pho-toreceptors in the retina to ganglion
cells in the brain, transferring image signals to thebrain for
further processing.
• Four other classes of cells in the retina handle image
compression and lateral inhibition.
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Computer Graphics
Color vision: trichromacy
• It is accepted among color scientists as well as
psychologists, that human color percep-tion is a three-dimensional
space.
• Trichromacy starts at the retina, where the cones provide
three broadband filters, tunedto three overlapping ranges of
wavelength (blue, green, red filters).
• each cone filter mechanism by itself is "colorblind" (the
signal out of a particular cone filterwould be indentical whether
it is the result ofthe component on the left of the peak of
thefilter, or the one on the right),
• the perceived hue depends on the three-dimensional vector of
signals detected by thethree cone mechanisms in combination.
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Color models
• A color model (color space): is a three-dimensional body used
to represent some colororganization according to a particular
choice of three coordinates that describe color(date back to L. Da
Vinci ca. 1500).
• The RGB space: color display monitors createdifferent colors c
2 R3 by additive mixtures ofthe three primaries Red, Green and
Blue. Thevalue c
i
of these 3 components is the sum of therespective sensitivity
functions and the incominglight:
c
i
=
Z�
max
�
min
s
i
(�) ⇠(�) d� 8i = 1,2,3
where ⇠(�) is the light spectrum and si
repre-sent the sensitivity functions for the R,G,B sen-sors. RGB
model
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Computer Graphics
Materials• The understanding of light and color is important;
however, what happens to that light
after it leaves the light source and affects the objects in the
scene is also important.
• Real-world material properties can be broken down into two
parts: the specular com-ponents and the diffuse components.
• Different types of reflection are characterized by different
models describing materials:1. conductive materials (metals):
rapidly attenuate the incident wave, so the reflection
is essentially a surface phenomenon;
2. poorly conductive materials (dielectric, e.g. glass): they
let the light penetratedeeply, so the description of the modeling
requires modelling the optical phenom-ena in the material;
3. optically homogeneous materials: characterized by a constant
refractive index in-side;
4. optically inhomogeneous materials: including compounds of
many colorant parti-cles whose optical properties are different
from those of the support material (e.g.paper, textile, paint,
plastics, ...).
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Section 1.3Illumination models
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Rendering equation• The rendering equation is an integral
equation in which the equilibrium radiance leav-
ing a point is given as the sum of emitted plus reflected
radiance under a geometricoptics approximation.
• The physical basis for the rendering equation is the law of
conservation of energy. As-suming that L denotes radiance, we have
that at each particular position and direction,the outgoing light
L
o
is the sum of the emitted light Le
and the reflected light which isthe sum of the incoming light
L
i
from all directions, multiplied by the surface reflectionand
cosine of the incident angle.
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Reflection
• A reflection model describes the interaction between the light
and a surface based onthe properties of the material thereof and
the nature of the light and its incidence.
• The incident light on the surface of a material can undergo
various interaction there-with. In the case of an opaque surface,
three phenomena occur which give the materialthe appearance that we
know: the absorption, specular reflection and diffuse
reflection.
Reflection: part of the luminous flux is absorbed by the
material.
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Reflection model
1. Specular reflection (speculum, mirror): produced by polished
surfaces, metal contacts.Descartes’ law applies to the reflected
beam. Light can only be seen in this reflectiondirection.
The specular reflection Rs
is given by theformula:
R
s
=
1
4⇡
F.D.G
hN,LihN,V iwhere hN,Li denotes the cosine of theangle between
the outer normal N andthe light direction L, and hN, V i is
thecosine of the angle between N and thedirection of the
observer.
F characterizes the reflectance of the material (the ratio of
the reflected flux to the incidentflux, depending on the wavelength
and angle of incidence).
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Reflection model
2. The diffuse reflection: produced by rough and matt surfaces
which reflect the lightuniformly in all directions (it is necessary
to consider all of these directions). Lambertmodel characterizes
this type of reflection:
R
d
=
F
0
⇡
,
where F0
is the coefficient of reflection under normal incidence.
This approximation is valid only for metallic objects, since the
reflectance spectrum ofthe object varies very little with the angle
of incidence.
The diffusion takes place at depth and the light emitted is so
tinged with the colorpigments.
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Computer Graphics
Illumination models
• The Lambertian model: the oldest known model (ca. 1760) and
still the most used todescribe the phenomena of reflection within
the dielectric which emit a constant lightin all
directions.Lambert’s law connects the intensity with the angle
between the normal and the direc-tion of the incident beam:
I
d
= k
d
I
p
cos ✓
where kd
is a coefficient of diffuse reflection, Ip
denotes the intensity of the pointsource and cos ✓ = hN,Li.
• Bowknight’s model (1970) includes an ambient term to
illuminate the invisible parts ofthe source, but visible to the
observer:
I
r
= I
a
k
r
+ k
d
I
p
cos ✓ , (1)
where kr
is a reflection coefficient for the ambient light modeled by the
term Ia
.
• We can introduce an attenuation factor of the light fa
= 1/d
2 which decreases pro-portionally to the inverse of the distance
between the source and the surface.
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-
Computer Graphics
Illumination models
• The Phong reflection model: the intensity of specular
reflection depends on the angleof incidence, the wavelength of the
incident light and the properties of the material.The state
equation of state is Fresnel equation.
• Only an observer located in the angle of incidence can see the
specular reflectionlight. In this model, the intensity of specular
reflection is proportional to the cosine ofthe angle of
reflection:
I
s
= I
p
k
s
cos
n
� (2)
where ks
denotes the coefficient of re-flectivity of the surface n is an
exponentwhich approach the spatial distributionof the reflected
specular light.
Spatial distribution of the reflected specular light.
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Computer Graphics
Phong model
• By adding the terms of equations (1)) and (2), we obtain the
Phong reflection model:
I = I
a
k
a
+ f
a
I
p
(k
d
cos ✓ + k
s
cos
n
�) . (3)
Phong specular reflection model.
� as in Lambert’s model, this equation is written for each of
the primary colors;� if multiple light sources are used, their
effects are combined:
I = I
a
k
a
+
mX
j=1
f
a
I
p,j
⇣k
d
cos ✓
j
+ k
s
cos
n
�
j
⌘.
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