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SCIENTIFIC VISUALIZATION DOWN TO BASICS

                                           Emiliano Martínez Rivera
                            Multimedia Creation, Design and Engineering Master 2011
                            BES La Salle, Universitat Ramon Llull - Barcelona, Spain



                        ABSTRACT
                                                                       "A useful definition of visualization might be the
Computers help us handle and process tons of information          binding (or mapping) of data to a representation that can be
data. Most of the time all this data is so dense, it’s almost     perceived. The types of binding could be visual, auditory,
impossible to understand from just looking at a bunch of          tactile, etc. or a combination of these." [5]
numbers. Some of the data could be analyzed by computers,
but most of the time there must be somebody, a real thinking           "Visualization is more than a method of computing.
person, who shall interpret the data and take conclusions         Visualization is the process of transforming information into
from it to make decisions, analyze. Scientific Visualization      a visual form, enabling users to observe the information.
is about converting numbers into a representation of reality,     The resulting visual display enables the scientist or engineer
something more graphic so that a human being can                  to perceive visually features which are hidden in the data but
understand and/or communicate.                                    nevertheless are needed for data exploration and analysis."
                                                                  [6]
    Index Terms— Computer Science, Computer Graphics,
Infographics, Visualization, Scientific Modeling, Shape,          1.2. Synthesis of Definitions
Art, Animation, Engineering drawings, Virtual Reality,
Image Processing [1]                                              “Mapping from computer representations to perceptual
                                                                  (visual) representations, choosing encoding techniques to
                   1. INTRODUCTION                                maximize human understanding and communication” [2]

The present paper aims to describe the Scientific                 1.3. Scientific Visualization Goals
Visualization in clear terms so that any reader, no matter the
knowledge level, can understand.                                     exploration/exploitation of data and information
                                                                     enhancing understanding of concepts and processes
1.1. Example Definitions [2]                                         gaining new (unexpected, profound) insights
                                                                     making invisible visible
     "Visualization is a method of computing. It transforms          effective presentation of significant features
the symbolic into the geometric, enabling researchers to             quality control of simulations, measurements
observe their simulations and computations. Visualization
                                                                     increasing scientific productivity
offers a method for seeing the unseen. It enriches the
                                                                     medium of communication/collaboration
process of scientific discovery and fosters profound and
unexpected insights. In many fields it is already
                                                                  1.4. Adjacent Disciplines
revolutionizing the way scientists do science." [3]
                                                                  Following is a general comparison of Visualization (V) with
    "Scientific visualization is a new, exciting field of
                                                                  some adjacent disciplines to better understand the
computational science spurred on in large measure by the
                                                                  differences:
rapid growth in computer technology, particular in graphics
workstation hardware and computer graphics software.
                                                                     Computer Graphics (CG)
[Visualization tools] are beginning to impact our daily lives
through usage in the arts, particularly film animation, and           Efficiency of algorithms versus effectiveness of use.
they hold great promise for scientific research and
education. When computer graphics is applied to scientific           Computer Vision (CV)
data for purposes of gaining insight, testing hypothesis, and         Mapping from pictures to abstract description versus
general elucidation, we speak of scientific visualization." [4]       mapping from abstract description to pictures.
   Image Processing (IP)                                      => NSF Committee to solve problems
    Mapping from data domain to data domain versus
    mapping from data domain to picture domain                 Committee on "Graphics, Image Processing, and
                                                               Workstations" (1986)
   (Visual) Perception (VP)                                    sponsored by NSF / Division of Advanced Scientific
    General and scientific explanation of human abilities         Computing
    and limitations versus goal oriented use of visual
    perception in complex information presentation.            Goal of committee
                                                                recommendations to HW/SW builders to improve
   Art and Design (AD)                                           scientific productivity
    Aesthetics and style      versus   expressiveness   and
    effectiveness                                              Result of committee
                                                                recommendations to research communities to develop
1.5. History                                                      new concepts/techniques for "Visualization in Scientific
                                                                  Computing (ViSC)"
One of the earliest examples of three-dimensional scientific
visualization was Maxwell's thermodynamic surface,             Solidifying goals
sculpted in clay in 1874 by James Clerk Maxwell.[7]             workshop on "Visualization in Scientific Computing"
                                                                sponsors: e.g. NSF and NASA

                                                               Key Publication: [3]


                                                                    2. COMMON QUESTIONS AND CONCERNS

                                                               The discussion is focused on the following questions:

                                                               1.   What is the improvement in the understanding of the
                                                                    data as compared to the situation without visualization?

                                                               2.   Which visualization techniques are suitable for one's
                                                                    data? Are direct volume rendering techniques to be
                                                                    preferred over surface rendering techniques?

                                                               3.   Can current techniques, like streamline and particle
                                                                    advection methods, be used to appropriately outline the
                                                                    known visual phenomena in the system?
    This prefigured modern scientific          visualization
techniques which use computer graphics.[8]                          The success of visualization not only depends on the
                                                               results which it produces, but also depends on the
    Notable early two-dimensional examples include the         environment in which it has to be done. This environment is
flow map of Napoleon’s March on Moscow produced by             determined by the available hardware, like graphical
Charles Joseph Minard in 1869;[9] the “coxcombs” used by       workstations, disk space, color printers, video editing
Florence Nightingale in 1857 as part of a campaign to          hardware, and network bandwidth, and by the visualization
improve sanitary conditions in the British army;[9] and the    software. For example, the graphical hardware imposes
dot map used by John Snow in 1855 to visualize the Broad       constraints on interactive speed of visualization and on the
Street cholera outbreak.[9]                                    size of the data sets which can be handled. Many different
                                                               problems encountered with visualization software must be
Need and opportunity                                           taken into account. The user interface, programming model,
 increased data rates from                                    data input, data output, data manipulation facilities, and
       o measuring devices: e.g. space missions,               other related items are all important. The way in which these
            medical instruments ("fire hose")                  items are implemented determines the convenience and
       o scientific        computing:     e.g.     national    effectiveness of the use of the software package as seen by
            supercomputer centers                              the scientist. Furthermore, whether software supports
 mature and cheap technology: powerful graphical              distributive processing and computational steering must be
   workstations, color, sufficient memory and storage          taken into account. [10]
3. CLASSIFICATION OF TECHNIQUES                           5.1.2. Isosurfaces

Classification of visualization techniques is often based on     This technique produces surfaces in the domain of the scalar
the dimension of the domain of the quantity that is              quantity on which the scalar quantity has the same value, the
visualized, i.e. the number of independent variables of the      so-called isosurface value. The surfaces can be colored
domain on which the quantity acts, and on the type of the        according to the isosurface value or they can be colored
quantity, i.e. scalar, vector, or tensor.                        according to another scalar field using the texture technique.
                                                                 The latter case allows for the search for correlation between
     Visualization techniques can also be divided into           different scalar quantities.
surface rendering techniques, and (direct) volume rendering
techniques. Surface rendering is an indirect geometry based      5.1.3. Cutting planes
technique which is used to visualize structures in 3D scalar
or vector fields by converting these structures into surface     This technique makes it possible to view scalar data on a
representations first and then using conventional computer       cross-section of the data volume with a cutting plane. One
graphics techniques to render these surfaces. Direct volume      defines a regular, Cartesian grid on the plane and the data
rendering is a technique for the visualization of 3D scalar      values on this grid are found by interpolation of the original
data sets without a conversion to surface representations.       data.

                                                                 5.1.4. Orthogonal slicers
                   4. COLOR CODING
                                                                 It often occurs that one wants to focus on the influence of
Colors and light are essential to visualization. Most            only two independent variables (i.e. coordinates). Thus, the
visualization techniques contain a step in which data values     other independent variables are kept constant. This is what
are mapped to colors to make the range of the data visible.      the orthogonal slicer method does. For example, if the data
The interpretation of results produced by these visualization    is defined in spherical coordinates and one wants to focus on
techniques depends crucially on the mapping of data to           the angular dependences for a specific radius, the orthogonal
colors because the human eye is more sensitive to some           slicer method constructs the corresponding sphere. No
parts of the visible spectrum of light than to other parts and   interpolation is used since the original grid with the
the brain may interpret different color patterns differently.    corresponding data is inherited.
There exist quite a few color coding systems like the known
RGB, CMY, and HSV systems.                                       5.1.5. Vector glyphs

                                                                 This technique uses needle or arrow glyphs to represent
5. VISUALIZATION TECHNIQUES AND METHODS                          vectors at each data point. The direction of the glyph
                                                                 corresponds to the direction of the vector and its magnitude
This chapter introduces the visualization techniques and         corresponds to the magnitude of the vector. The glyphs can
methods. The focus is on 3D scalar and vector techniques,        be colored according to a scalar field.
because often data consists of 3D scalar and vector fields.
                                                                 5.1.6. Streamlines, streaklines, and particle advection
5.1. Surface rendering techniques
                                                                 This is a set of methods for outlining the topology, i.e. the
This section briefly describes a general set of 3D scalar and    field lines, of a vector field. Generally, one takes a set of
vector surface rendering techniques. The first four              starting points, finds the vectors at these points by
descriptions deal with scalar field techniques and the other     interpolation, if necessary, and integrates the points along
two with vector field techniques.                                the direction of the vector. At the new positions the vector
                                                                 values are found by interpolation and one integrates again.
5.1.1. Scalar glyphs
                                                                 The difference between streamlines and streaklines is that
Scalar glyphs is a technique which puts a sphere or a            the streamlines technique considers the vector field to be
diamond on every data point. The scale of the sphere or          static whereas the streaklines technique considers the vector
diamond is determined by the data value. The scalar glyphs       field to be time dependent. Hence, the streakline technique
may be colored according to the same scalar field or             interpolates not only in the spatial direction, but also in the
according to another scalar field. In this way correlations      time direction.
can be found.
5.1.7. Textures                                                 5.3.1. Flipbook animation

This is a technique to color arbitrary surfaces, e.g. those     This is a well known technique. The generated images are
generated by the isosurface techniques, according to a 3D       displayed one after the other. Its name is attached to the
scalar field. An interpolation scheme is used to determine      thumbing or flipping through a series of images.
the values of the scalar field on the surface. A colormap is
used to assign the color.                                       5.3.2. Keyframe animation

5.2. Volume rendering techniques                                For this technique one only has to generate so-called
                                                                keyframes. Keyframes mark changes in the characteristics
Volume rendering techniques have been developed to              of the motion. Interpolation techniques are used to generate
overcome problems of the accurate representation of             a set of images between two keyframes.
surfaces in the isosurface techniques. In short, these
problems are related to making a decision for every volume                              6. CONCLUSIONS
element whether or not the surface passes through it and this
can produce false positives (spurious surfaces) or false        In such a rapidly evolving field, it is important to be aware
negatives (erroneous holes in surfaces), particularly in the    of the latest developments, as well as those areas of ongoing
presence of small or poorly defined features. Volume            research. Two important recent developments are of special
rendering does not use intermediate geometrical                 importance. The first has been the explosion of the internet.
representations, in contrast to surface rendering techniques.   The growth of the web has created a new medium by which
It offers the possibility for displaying weak or fuzzy          visualization can be presented with a high level of
surfaces. This frees one from the requirement to make a         interaction.
decision whether a surface is present or not.
                                                                The second recent (and continuing) development is the
Two implementations of volume rendering are Ray casting         increase in speed of PCs, as well as the reduction in cost of
and Splatting. The two methods differ in the way the RGBA       high end workstations. This is bringing the world of
volume is projected onto the 2D viewing plane.                  Scientific Visualization to every possible user.

5.2.1. Ray casting                                                                       7. REFERENCES

For every pixel in the output image a ray is shot into the      [1]  The Institute Of Electrical And Electronics Engineers (IEEE), “2009
                                                                     IEEE Taxonomy” Version 1.01 Supplied as additional material
data volume. At a predetermined number of evenly spaced              2009Taxonomy_v101.pdf.
locations along the ray the color and opacity values are        [2] Gitta Domik [domik@siggraph.org] “Tutorial on Visualization”
obtained by interpolation. The interpolated colors and               University of Paderborn - Germany
opacities are merged with each other and with the               [3] McCormick, B.H., T.A. DeFanti, M.D. Brown (ed), “Visualization in
                                                                     Scientific Computing”, Computer Graphics Vol. 21, No. 6,
background by compositing in back-to-front order to yield            November 1987
the color of the pixel.                                         [4] H. Aref, R. D. Charles and T. T. Elvins, “Scientific Visualization of
                                                                     Fluid Flow”, in C.A. Pickover and S.K. Tewksbury (eds), Frontiers of
5.2.2. Splatting                                                     Scientific Visualization, 1994,Wiley Interscience.
                                                                [5] J. Foley and B. Ribarsky, “Next-generation Data Visualization
                                                                     Tools”, in Scientific Visualization, 1994, Advances and Challenges,
This technique was developed to improve the speed of                 Ed: L. Rosenblum, R.A. Earnshaw, J. Encarnacao, H. Hagen, A.
calculation of volume rendering techniques like ray casting,         Kaufman, S. Klimenko, G. Nielson, F. Post, D. Thalmann , Academic
at the price of less accurate rendering. A projection is made        Press.
                                                                [6] N. Gershon, “From Perception to Visualization”, in Scientific
for every voxel and the resulting splats are composited on           Visualization, 1994, Advances and Challenges, Ed: L. Rosenblum,
top of each other in back-to-front order to produce the final        R.A. Earnshaw, J. Encarnacao, H. Hagen, A. Kaufman, S. Klimenko,
image.                                                               G. Nielson, F. Post, D. Thalmann , Academic Press.
                                                                [7] James Clerk Maxwell and P. M. Harman (2002), “The Scientific
                                                                     Letters and Papers of James Clerk Maxwell”, Volume 3; 1874-1879,
5.3. Animation techniques                                            Cambridge University Press, ISBN 0521256275, p. 148 [link]
                                                                [8] Thomas G.West (February 1999). "James Clerk Maxwell, Working in
These techniques simulate continuous motion by rapidly               Wet Clay". SIGGRAPH Computer Graphics Newsletter 33 (1): 15–
displaying images. The viewer is given the impression that           17. [link]
                                                                [9] Michael Friendly (2008). "Milestones in the history of thematic
he is watching a continuous motion. To achieve this                  cartography, statistical graphics, and data visualization" Supplied as
impression the graphical hardware needs image display rates          additional material milestone.pdf.
of at least 25 images per second, since otherwise motion        [10] Scientific Visualization Laboratory, Georgia Tech “Scientific
will look shaky.                                                     Visualization Tutorial” [link]

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Scientific visualization

  • 1. SCIENTIFIC VISUALIZATION DOWN TO BASICS Emiliano Martínez Rivera Multimedia Creation, Design and Engineering Master 2011 BES La Salle, Universitat Ramon Llull - Barcelona, Spain ABSTRACT "A useful definition of visualization might be the Computers help us handle and process tons of information binding (or mapping) of data to a representation that can be data. Most of the time all this data is so dense, it’s almost perceived. The types of binding could be visual, auditory, impossible to understand from just looking at a bunch of tactile, etc. or a combination of these." [5] numbers. Some of the data could be analyzed by computers, but most of the time there must be somebody, a real thinking "Visualization is more than a method of computing. person, who shall interpret the data and take conclusions Visualization is the process of transforming information into from it to make decisions, analyze. Scientific Visualization a visual form, enabling users to observe the information. is about converting numbers into a representation of reality, The resulting visual display enables the scientist or engineer something more graphic so that a human being can to perceive visually features which are hidden in the data but understand and/or communicate. nevertheless are needed for data exploration and analysis." [6] Index Terms— Computer Science, Computer Graphics, Infographics, Visualization, Scientific Modeling, Shape, 1.2. Synthesis of Definitions Art, Animation, Engineering drawings, Virtual Reality, Image Processing [1] “Mapping from computer representations to perceptual (visual) representations, choosing encoding techniques to 1. INTRODUCTION maximize human understanding and communication” [2] The present paper aims to describe the Scientific 1.3. Scientific Visualization Goals Visualization in clear terms so that any reader, no matter the knowledge level, can understand.  exploration/exploitation of data and information  enhancing understanding of concepts and processes 1.1. Example Definitions [2]  gaining new (unexpected, profound) insights  making invisible visible "Visualization is a method of computing. It transforms  effective presentation of significant features the symbolic into the geometric, enabling researchers to  quality control of simulations, measurements observe their simulations and computations. Visualization  increasing scientific productivity offers a method for seeing the unseen. It enriches the  medium of communication/collaboration process of scientific discovery and fosters profound and unexpected insights. In many fields it is already 1.4. Adjacent Disciplines revolutionizing the way scientists do science." [3] Following is a general comparison of Visualization (V) with "Scientific visualization is a new, exciting field of some adjacent disciplines to better understand the computational science spurred on in large measure by the differences: rapid growth in computer technology, particular in graphics workstation hardware and computer graphics software.  Computer Graphics (CG) [Visualization tools] are beginning to impact our daily lives through usage in the arts, particularly film animation, and Efficiency of algorithms versus effectiveness of use. they hold great promise for scientific research and education. When computer graphics is applied to scientific  Computer Vision (CV) data for purposes of gaining insight, testing hypothesis, and Mapping from pictures to abstract description versus general elucidation, we speak of scientific visualization." [4] mapping from abstract description to pictures.
  • 2. Image Processing (IP) => NSF Committee to solve problems Mapping from data domain to data domain versus mapping from data domain to picture domain Committee on "Graphics, Image Processing, and Workstations" (1986)  (Visual) Perception (VP)  sponsored by NSF / Division of Advanced Scientific General and scientific explanation of human abilities Computing and limitations versus goal oriented use of visual perception in complex information presentation. Goal of committee  recommendations to HW/SW builders to improve  Art and Design (AD) scientific productivity Aesthetics and style versus expressiveness and effectiveness Result of committee  recommendations to research communities to develop 1.5. History new concepts/techniques for "Visualization in Scientific Computing (ViSC)" One of the earliest examples of three-dimensional scientific visualization was Maxwell's thermodynamic surface, Solidifying goals sculpted in clay in 1874 by James Clerk Maxwell.[7]  workshop on "Visualization in Scientific Computing"  sponsors: e.g. NSF and NASA Key Publication: [3] 2. COMMON QUESTIONS AND CONCERNS The discussion is focused on the following questions: 1. What is the improvement in the understanding of the data as compared to the situation without visualization? 2. Which visualization techniques are suitable for one's data? Are direct volume rendering techniques to be preferred over surface rendering techniques? 3. Can current techniques, like streamline and particle advection methods, be used to appropriately outline the known visual phenomena in the system? This prefigured modern scientific visualization techniques which use computer graphics.[8] The success of visualization not only depends on the results which it produces, but also depends on the Notable early two-dimensional examples include the environment in which it has to be done. This environment is flow map of Napoleon’s March on Moscow produced by determined by the available hardware, like graphical Charles Joseph Minard in 1869;[9] the “coxcombs” used by workstations, disk space, color printers, video editing Florence Nightingale in 1857 as part of a campaign to hardware, and network bandwidth, and by the visualization improve sanitary conditions in the British army;[9] and the software. For example, the graphical hardware imposes dot map used by John Snow in 1855 to visualize the Broad constraints on interactive speed of visualization and on the Street cholera outbreak.[9] size of the data sets which can be handled. Many different problems encountered with visualization software must be Need and opportunity taken into account. The user interface, programming model,  increased data rates from data input, data output, data manipulation facilities, and o measuring devices: e.g. space missions, other related items are all important. The way in which these medical instruments ("fire hose") items are implemented determines the convenience and o scientific computing: e.g. national effectiveness of the use of the software package as seen by supercomputer centers the scientist. Furthermore, whether software supports  mature and cheap technology: powerful graphical distributive processing and computational steering must be workstations, color, sufficient memory and storage taken into account. [10]
  • 3. 3. CLASSIFICATION OF TECHNIQUES 5.1.2. Isosurfaces Classification of visualization techniques is often based on This technique produces surfaces in the domain of the scalar the dimension of the domain of the quantity that is quantity on which the scalar quantity has the same value, the visualized, i.e. the number of independent variables of the so-called isosurface value. The surfaces can be colored domain on which the quantity acts, and on the type of the according to the isosurface value or they can be colored quantity, i.e. scalar, vector, or tensor. according to another scalar field using the texture technique. The latter case allows for the search for correlation between Visualization techniques can also be divided into different scalar quantities. surface rendering techniques, and (direct) volume rendering techniques. Surface rendering is an indirect geometry based 5.1.3. Cutting planes technique which is used to visualize structures in 3D scalar or vector fields by converting these structures into surface This technique makes it possible to view scalar data on a representations first and then using conventional computer cross-section of the data volume with a cutting plane. One graphics techniques to render these surfaces. Direct volume defines a regular, Cartesian grid on the plane and the data rendering is a technique for the visualization of 3D scalar values on this grid are found by interpolation of the original data sets without a conversion to surface representations. data. 5.1.4. Orthogonal slicers 4. COLOR CODING It often occurs that one wants to focus on the influence of Colors and light are essential to visualization. Most only two independent variables (i.e. coordinates). Thus, the visualization techniques contain a step in which data values other independent variables are kept constant. This is what are mapped to colors to make the range of the data visible. the orthogonal slicer method does. For example, if the data The interpretation of results produced by these visualization is defined in spherical coordinates and one wants to focus on techniques depends crucially on the mapping of data to the angular dependences for a specific radius, the orthogonal colors because the human eye is more sensitive to some slicer method constructs the corresponding sphere. No parts of the visible spectrum of light than to other parts and interpolation is used since the original grid with the the brain may interpret different color patterns differently. corresponding data is inherited. There exist quite a few color coding systems like the known RGB, CMY, and HSV systems. 5.1.5. Vector glyphs This technique uses needle or arrow glyphs to represent 5. VISUALIZATION TECHNIQUES AND METHODS vectors at each data point. The direction of the glyph corresponds to the direction of the vector and its magnitude This chapter introduces the visualization techniques and corresponds to the magnitude of the vector. The glyphs can methods. The focus is on 3D scalar and vector techniques, be colored according to a scalar field. because often data consists of 3D scalar and vector fields. 5.1.6. Streamlines, streaklines, and particle advection 5.1. Surface rendering techniques This is a set of methods for outlining the topology, i.e. the This section briefly describes a general set of 3D scalar and field lines, of a vector field. Generally, one takes a set of vector surface rendering techniques. The first four starting points, finds the vectors at these points by descriptions deal with scalar field techniques and the other interpolation, if necessary, and integrates the points along two with vector field techniques. the direction of the vector. At the new positions the vector values are found by interpolation and one integrates again. 5.1.1. Scalar glyphs The difference between streamlines and streaklines is that Scalar glyphs is a technique which puts a sphere or a the streamlines technique considers the vector field to be diamond on every data point. The scale of the sphere or static whereas the streaklines technique considers the vector diamond is determined by the data value. The scalar glyphs field to be time dependent. Hence, the streakline technique may be colored according to the same scalar field or interpolates not only in the spatial direction, but also in the according to another scalar field. In this way correlations time direction. can be found.
  • 4. 5.1.7. Textures 5.3.1. Flipbook animation This is a technique to color arbitrary surfaces, e.g. those This is a well known technique. The generated images are generated by the isosurface techniques, according to a 3D displayed one after the other. Its name is attached to the scalar field. An interpolation scheme is used to determine thumbing or flipping through a series of images. the values of the scalar field on the surface. A colormap is used to assign the color. 5.3.2. Keyframe animation 5.2. Volume rendering techniques For this technique one only has to generate so-called keyframes. Keyframes mark changes in the characteristics Volume rendering techniques have been developed to of the motion. Interpolation techniques are used to generate overcome problems of the accurate representation of a set of images between two keyframes. surfaces in the isosurface techniques. In short, these problems are related to making a decision for every volume 6. CONCLUSIONS element whether or not the surface passes through it and this can produce false positives (spurious surfaces) or false In such a rapidly evolving field, it is important to be aware negatives (erroneous holes in surfaces), particularly in the of the latest developments, as well as those areas of ongoing presence of small or poorly defined features. Volume research. Two important recent developments are of special rendering does not use intermediate geometrical importance. The first has been the explosion of the internet. representations, in contrast to surface rendering techniques. The growth of the web has created a new medium by which It offers the possibility for displaying weak or fuzzy visualization can be presented with a high level of surfaces. This frees one from the requirement to make a interaction. decision whether a surface is present or not. The second recent (and continuing) development is the Two implementations of volume rendering are Ray casting increase in speed of PCs, as well as the reduction in cost of and Splatting. The two methods differ in the way the RGBA high end workstations. This is bringing the world of volume is projected onto the 2D viewing plane. Scientific Visualization to every possible user. 5.2.1. Ray casting 7. REFERENCES For every pixel in the output image a ray is shot into the [1] The Institute Of Electrical And Electronics Engineers (IEEE), “2009 IEEE Taxonomy” Version 1.01 Supplied as additional material data volume. At a predetermined number of evenly spaced 2009Taxonomy_v101.pdf. locations along the ray the color and opacity values are [2] Gitta Domik [domik@siggraph.org] “Tutorial on Visualization” obtained by interpolation. The interpolated colors and University of Paderborn - Germany opacities are merged with each other and with the [3] McCormick, B.H., T.A. DeFanti, M.D. Brown (ed), “Visualization in Scientific Computing”, Computer Graphics Vol. 21, No. 6, background by compositing in back-to-front order to yield November 1987 the color of the pixel. [4] H. Aref, R. D. Charles and T. T. Elvins, “Scientific Visualization of Fluid Flow”, in C.A. Pickover and S.K. Tewksbury (eds), Frontiers of 5.2.2. Splatting Scientific Visualization, 1994,Wiley Interscience. [5] J. Foley and B. Ribarsky, “Next-generation Data Visualization Tools”, in Scientific Visualization, 1994, Advances and Challenges, This technique was developed to improve the speed of Ed: L. Rosenblum, R.A. Earnshaw, J. Encarnacao, H. Hagen, A. calculation of volume rendering techniques like ray casting, Kaufman, S. Klimenko, G. Nielson, F. Post, D. Thalmann , Academic at the price of less accurate rendering. A projection is made Press. [6] N. Gershon, “From Perception to Visualization”, in Scientific for every voxel and the resulting splats are composited on Visualization, 1994, Advances and Challenges, Ed: L. Rosenblum, top of each other in back-to-front order to produce the final R.A. Earnshaw, J. Encarnacao, H. Hagen, A. Kaufman, S. Klimenko, image. G. Nielson, F. Post, D. Thalmann , Academic Press. [7] James Clerk Maxwell and P. M. Harman (2002), “The Scientific Letters and Papers of James Clerk Maxwell”, Volume 3; 1874-1879, 5.3. Animation techniques Cambridge University Press, ISBN 0521256275, p. 148 [link] [8] Thomas G.West (February 1999). "James Clerk Maxwell, Working in These techniques simulate continuous motion by rapidly Wet Clay". SIGGRAPH Computer Graphics Newsletter 33 (1): 15– displaying images. The viewer is given the impression that 17. [link] [9] Michael Friendly (2008). "Milestones in the history of thematic he is watching a continuous motion. To achieve this cartography, statistical graphics, and data visualization" Supplied as impression the graphical hardware needs image display rates additional material milestone.pdf. of at least 25 images per second, since otherwise motion [10] Scientific Visualization Laboratory, Georgia Tech “Scientific will look shaky. Visualization Tutorial” [link]