Graph Design Doc

7/30/2019 Graph Design Doc

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GRAPH DESIGN

AVIK MUKHERJEE 619-MP- 09 JANAK ANAND 629MP-09 SHASHANK SINGH 656 -MP-09


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What is a graph ?

In the most common sense of the term, a graph is an ordered pair G

= (V, E) comprising a set V of vertices or nodes together with a set E

of edges or lines, which are 2-element subsets of V (i.e., an edge is

related with two vertices, and the relation is represented as

unordered pair of the vertices with respect to the particular edge).

To avoid ambiguity, this type of graph may be described precisely as

undirected and simple.

Computer graphics are graphics created using computers and, moregenerally, the representation and manipulation of image data by a

computer with help from specialized software and hardware. The development of computer graphics has made computers easier

to interact with, and better for understanding and interpreting

many types of data. Developments in computer graphics have had a

profound impact on many types of media and have revolutionized

animation, movies and the video game industry.

Developments in computer graphics have also revolutionized theway we plot graphs.

Accurate visual 2d and 3d graphs can now be produced throughminimum effort on a computer.

A large amount of data can now be plotted.


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SCIENTIFIC VISUALISATION

Scientific visualisation is an interdisciplinary branch of science

primarily concerned with the visualization of three-dimensional

phenomena (architectural, meteorological, medical, biological,

etc.), where the emphasis is on realistic renderings of volumes,

surfaces, illumination sources, and so forth, perhaps with a dynamic

(time) component".It is also considered a branch of computer

science that is a subset of computer graphics. The purpose of

scientific visualization is to graphically illustrate scientific data to

enable scientists to understand, illustrate, and glean insight from

their data.

One of the earliest examples of three-dimensional scientificvisualisation was Maxwell's thermodynamic surface, sculpted in

clay in 1874 by James Clerk Maxwell. This prefigured modern

scientific visualization techniques that use computer graphics.

Notable early two-dimensional examples include the flow map ofNapoleons March on Moscow produced by Charles Joseph Minard

in 1869, the coxcombs used by Florence Nightingale in 1857 as

part of a campaign to improve sanitary conditions in the Britisharmy, and the dot map used by John Snow in 1855 to visualise the

Broad Street cholera outbreak.

Scientific visualization using computer graphics gained in popularityas graphics matured. Primary applications were scalar fields and

vector fields from computer simulations and measured data. The

primary methods for visualizing 2D scalar fields are color mapping

and drawing contours (isosurfaces). For 3D scalar fields the primary

methods are volume rendering and isosurfaces. Methods forvisualizing vector fields include glyphs (graphical icons) such as

arrows, streamlines and streaklines, particle tracing, line integral

convolution (LIC) and topological methods. Later, visualization


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techniques such as hyperstreamlines were developed to visualize

2D and 3D tensor fields.

TYPES OF VISUALISATION

Computer animation

Computer animation is the art, technique, and science of creatingmoving images via the use of computers. It is becoming more

common to be created by means of3D computer graphics,

though 2D computer graphics are still widely used for stylistic, low

bandwidth, and faster real-time rendering needs. Sometimes the

target of the animation is the computer itself, but sometimes the

target is another medium, such as film. It is also referred to as CGI(Computer-generated imagery or computer-generated imaging),

especially when used in films.

Computer simulation

Computer simulation is a computer program, or network ofcomputers, that attempts to simulate an abstract model of a

particular system. Computer simulations have become a useful part

of mathematical modelling of many natural systems in physics, and

computational physics, chemistry and biology; human systems ineconomics, psychology, and social science; and in the process of

engineering and new technology, to gain insight into the operation

of those systems, or to observe their behavior.The simultaneous

visualization and simulation of a system is called visulation.

Computer simulations vary from computer programs that run a fewminutes, to network-based groups of computers running for hours,

to ongoing simulations that run for months. The scale of events

being simulated by computer simulations has far exceeded anything

possible (or perhaps even imaginable) using the traditional paper-

and-pencil mathematical modeling: over 10 years ago, a desert-

battle simulation, of one force invading another, involved the

modeling of 66,239 tanks, trucks and other vehicles on simulated


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terrain around Kuwait, using multiple supercomputers in

the DoD High Performance Computer Modernization Program.

Information visualization

Information visualization is the study of"the visual representation of large-scale collections of non-

numerical information, such as files and lines of code in software

systems, library and bibliographic databases, networks of relations

on the internet, and so forth".

Information visualization focused on the creation of approaches forconveying abstract information in intuitive ways. Visualrepresentations and interaction techniques take advantage of the

human eyes broad bandwidth pathway into the mind to allow

users to see, explore, and understand large amounts of information

at once.The key difference between scientific visualization and

information visualization is that information visualization is often

applied to data that is not generated by scientific inquiry. Some

examples are graphical representations of data for business,

government, news and social media.Interface technology and perception

Interface technology and perception shows how new interfaces anda better understanding of underlying perceptual issues create new

opportunities for the scientific visualization community.


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Surface rendering

Surface rendering is the process of generating an image froma model, by means of computer programs. The model is a

description of three dimensional objects in a strictly defined

language or data structure. It would contain geometry,

viewpoint, texture, lighting, and shading information. The image is

a digital image or raster graphicsimage. The term may be by

analogy with an "artist's rendering" of a scene. 'Rendering' is also

used to describe the process of calculating effects in a video editing

file to produce final video output. Important rendering techniques

are:

Scanline rendering and rasterisation A high-level representation of an image necessarily contains

elements in a different domain from pixels. These elements are

referred to as primitives. In a schematic drawing, for instance, line

segments and curves might be primitives. In a graphical user

interface, windows and buttons might be the primitives. In 3D

rendering, triangles and polygons in space might be primitives.

Ray casting

Ray casting is primarily used for realtime simulations, such as thoseused in 3D computer games and cartoon animations, where detail

is not important, or where it is more efficient to manually fake the

details in order to obtain better performance in the computational

stage. This is usually the case when a large number of frames need

to be animated. The resulting surfaces have a characteristic 'flat'

appearance when no additional tricks are used, as if objects in thescene were all painted with matte finish

Radiosity

Radiosity, also known as Global Illumination, is a method thatattempts to simulate the way in which directly illuminated surfaces


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act as indirect light sources that illuminate other surfaces. This

produces more realistic shading and seems to better capture the

'ambience' of an indoor scene. A classic example is the way that

shadows 'hug' the corners of rooms

Ray tracing

Ray tracing is an extension of the same technique developed inscanline rendering and ray casting. Like those, it handles

complicated objects well, and the objects may be described

mathematically. Unlike scanline and casting, ray tracing is almost

always a Monte Carlo technique, that is one based on averaging a

number of randomly generated samples from a model.

Volume rendering

Volume rendering is a technique used to display a 2D projection ofa 3D discretely sampled data set. A typical 3D data set is a group of

2D slice images acquired by a CT or MRI scanner. Usually these are

acquired in a regular pattern (e.g., one slice every millimeter) and

usually have a regular number of image pixels in a regular pattern.

This is an example of a regular volumetric grid, with each volume

element, or voxel represented by a single value that is obtained by

sampling the immediate area surrounding the voxel.

Volume visualization

According to Rosenblum (1994) "volume visualization examines aset of techniques that allows viewing an object without

mathematical representing the other surface. Initially used

in medical imaging, volume visualization has become an essential

technique for many sciences, portraying phenomena become anessential technique such as clouds, water flows, and molecular and

biological structure. Many volume visualization algorithms are

computationally expensive and demand large data storage.

Advances in hardware and software are generalizing volume

visualization as well as real time performances"


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SEISMOGRAPH

Seismometers are instruments that measure motions of theground, including those of seismic waves generatedby earthquakes, volcanic eruptions, and other seismic sources.

Records of seismic waves allow seismologists to map the interior of

the Earth, and locate and measure the size of these different

sources.

The word derives from the Greek , seisms, a shaking orquake, from the verb ,se, to shake; and , mtron,

measure and was coined by David Milne-Home in 1841.

Seismograph is another Greek term from seisms and,grph, to draw. It is often used to mean seismometer,

though it is more applicable to the older instruments in which the

measuring and recording of ground motion were combined than to

modern systems, in which these functions are separated. Both

types provide a continuous record of ground motion; this

distinguishes them from seismoscopes, which merely indicate thatmotion has occurred, perhaps with some simple measure of how

large it was

The modern broadband seismograph can record a very broad rangeof frequencies. It consists of a small "proof mass", confined by

electrical forces, driven by sophisticated electronics. As the earth

moves, the electronics attempt to hold the mass steady through

a feedback circuit. The amount of force necessary to achieve this is

then recorded.

seismic imaging

Reflection seismology (or seismic reflection) is a methodof exploration geophysics that uses the principles of seismology to


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estimate the properties of the Earth's subsurface

from reflected seismic waves. The method requires a

controlled seismic source of energy, such asdynamite/Tovex, a

specialized air gun or a seismic vibrator, commonly known by the

trademark name Vibroseis. Reflection seismology is similar

tosonar and echolocation.

Synthetic seismogram

A synthetic seismogram is the result of forward modelling

the seismic response of an input earth model, which is defined in

terms of 1D, 2D or 3D variations in physical properties.

In hydrocarbon explorationthis is used to provide a 'tie' between

changes in rock properties in a borehole and seismic reflection data

at the same location. It can also be used either to test possible

interpretation models for 2D and 3D seismic data or to model the

response of the predicted geology as an aid to planning a seismic

reflection survey. In the processing of wide-angle reflection and

refraction (WARR) data, synthetic seismograms are used to further

constrain the results of seismic tomography.

In earthquake seismology, synthetic seismograms are used either tomatch the predicted effects of a particular earthquake source fault

modelwith observed seismometer records or to help constrain the

Earth's velocity structure. Synthetic seismograms are generated

using specialist geophysical software.

1D synthetics

Seismic reflection data is initially only available in the time domain.

In order that the geology encountered in a borehole can be tied tothe seismic data, a 1D synthetic seismogram is generated. This is

important in identifying the origin of seismic reflections seen on the

seismic data. Density and velocity data are routinely measured

down the borehole using wireline logging tools. These logs provide

data with a sampling interval much smaller than the vertical


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resolution of the seismic data. The logs are therefore often

averaged over intervals to produce what is known as a 'blocked-

log'.[3] This information is then used to calculate the variation

in acoustic impedance down the well bore using the Zoeppritz

equations.[4] This acoustic impedance log is combined with the

velocity data to generate a reflection coefficient series in time. This

series is convolved with a seismic wavelet to produce the synthetic

seismogram. The input seismic wavelet is chosen to match as

closely as possible to that produced during the original seismic

acquisition, paying particular attention to phase and frequency

content.

1.5D seismic modelling

The convolutional 1D modelling produces seismograms containing

approximations of primary reflections only. For more accurate

modelling involving multiple reflections, head waves, guided waves

and surface waves, as well as transmission effects and geometrical

spreading, full waveform modelling is required. For 1D elastic

models the most accurate approach to full waveform modelling is

known as the reflectivity method.[5] This method is based on theintegral transform approach, whereby the wave field (cylinidrical or

spherical wave) is represented by a sum (integral) of time-harmonic

plane waves.[6] The reflection and transmission coefficients for

individual plane waves propagating in a stack of layers can be

computed analytically using a variety of methods, such as matrix

propagator,[7][8][9][10][11] global matrix[12] or invariant

embedding.[13] This group of methods is called 1.5D because the

earth is represented by a 1D model (flat layers), while wavepropagation is considered either in 2D (cylindrical waves) or 3D

(spherical waves).


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2D synthetic seismic modeling

A similar approach can be used to examine the seismic response ofa 2D geological cross-section. This can be used to look at such

things as the resolution of thin beds or the different responses ofvarious fluids, e.g. oil, gas or brine in a potential reservoir sand. It

may also be used to test out different geometries of structures such

as salt diapirs, to see which gives the best match to the original

seismic data. A cross-section is built with density and seismic

velocities assigned to each of the individual layers. These can be

either constant within a layer or varying in a systematic fashion

across the model both horizontally and vertically. The software

program then runs a synthetic acquisition across the model to

produce a set of 'shot gathers' that can be processed as if they were

real seismic data to produce a synthetic 2D seismic section. The

synthetic record is generated using either a ray-tracing algorithm or

some form of full waveform modelling, depending on the purpose

of the modelling. Ray-tracing is quick and sufficient for testing the

illumination of the structure, but full waveform modelling will be

necessary to accurately model the amplitude response.

3D synthetic seismic modelling

The approach can be further expanded to model the response of a3D geological model. This is used to reduce the uncertainty in

interpretation by modelling the response of the 3D model to a

synthetic seismic acquisition that matches as closely as possible to

that actually used in acquiring the data that has been

interpreted. The synthetic seismic data is then processed using the

same sequence as that used for the original data. This method can

be used to model both 2D and 3D seismic data that has been

acquired over the area of the geological model. During the planning

of a seismic survey, 3D modelling can be used to test the effect of


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variation in seismic acquisition parameters, such as the shooting

direction or the maximum offset between source and receiver, on

the imaging of a particular geological structure.

WARR data modelling

Initial processing of such data is normally carried out using atomographic approach in which the time of observed first arrivals is

matched by varying the velocity structure. The model is further

refined using forward modelling to generate synthetic seismograms

for individual shot gathers.

Geologic modelling

Geologic modelling or Geomodelling is the applied science ofcreating computerized representations of portions of the

Earth's crust based on geophysical and geological observations

made on and below the Earth surface. A Geomodel is the numerical

equivalent of a three-dimensional geological map complemented

by a description of physical quantities in the domain of

interest.Geomodelling is related to the concept of Shared Earth

Model which is a pluridisciplinary, interoperable and updatableknowledge base about the subsurface.

In 2 dimensions a geologic formation or unit is represented by a

polygon, which can be bounded by faults, unconformities or by its

lateral extent, or crop. In geological models a geological unit is

bounded by 3-dimensional triangulated or gridded surfaces. The

equivalent to the mapped polygon is the fully enclosed geological

unit, using a triangulated mesh. For the purpose of property or fluidmodelling these volumes can be separated further into an array of

cells, often referred to as voxels (volumetric elements). These 3D

grids are the equivalent to 2D grids used to express properties of

single surfaces.


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Geomodelling generally involves the following steps:

Preliminary analysis of geological context of the domain of study. Interpretation of available data and observations as point sets orpolygonal lines (e.g. "fault sticks" corresponding to faults on a

vertical seismic section).

Construction of a structural model describing the main rockboundaries (horizons, unconformities, intrusions, faults)[3]

Definition of a three-dimensional mesh honoring the structuralmodel to support volumetric representation of heterogeneity

(see Geostatistics) and solving thePartial Differential

Equations which govern physical processes in the subsurface

(e.g. seismic wave propagation, fluid transport in porous media).

Geomodelling and CAD share a lot of common technologies.Software is usually implemented using object-oriented

programming technologies in C++, Java or C# on one or multiple

computer platforms. The graphical user interface generally consistsof one or several 3D and 2D graphics windows to visualize spatial

data, interpretations and modelling output. Such visualization is

generally achieved by exploitinggraphics hardware. User interaction

is mostly performed through mouse and keyboard, although 3D

pointing devices and immersive environments may be used in some

specific cases.

Geometric objects are represented with parameteric curves andsurfaces or discrete models such as polygonal meshes.


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Modflow

MODFLOW is the U.S. Geological Survey modular finite-

difference flow model, which is a

computer code that solves the groundwater flow equation. The

program is used by hydrogeologists to simulate the flow

of groundwater through aquifers. The code is free software, written

primarily in Fortran, and can compile and run

onDOS, Windows or Unix-like operating systems.

Since its original development in the early 1980s, the USGS have

released four major releases, and is now considered to be the de

facto standard code for aquifer simulation. Currently, there are at

least five actively developed commercial and non-

commercial graphical user interfaces for MODFLOW.

Limitations

The water must have a constant density, dynamic viscosity (andconsequently temperature) throughout the modelling domain

(SEAWAT is a modified version of MODFLOW which is designed for

density-dependent groundwater flow and transport)

The principal components of anisotropy of the hydraulicconductivity used in MODFLOW is displayed on the right.

This tensor does not allow non-orthogonal anisotropies, as could be

expected from flow in fractures. Horizontal anisotropy for an entire

layer can be represented by the coefficient "TRPY"

Spectrogram

A spectrogram is a time-varying spectral representation (forming animage) that shows how the spectral density of a signal varies withtime. Also known as spectral waterfalls, sonograms, voiceprints,

or voicegrams, spectrograms are used to identify phonetic sounds,

to analyse the cries of animals; they were also used in many other

fields including music, sonar/radar, speech processing, seismology,


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etc. The instrument that generates a spectrogram is called

a spectrograph.

The most common format is a graph with two geometricdimensions: the horizontal axis represents time, the vertical axisis frequency; a third dimension indicating theamplitude of a

particular frequency at a particular time is represented by

the intensity or colour of each point in the image.

There are many variations of format: sometimes the vertical andhorizontal axes are switched, so time runs up and down; sometimes

the amplitude is represented as the height of a 3D surface instead

of color or intensity. The frequency and amplitude axes can beeither linear or logarithmic, depending on what the graph is being

used for. Audio would usually be represented with a logarithmic

amplitude axis (probably in decibels, or dB), and frequency would

be linear to emphasize harmonic relationships, or logarithmic to

emphasize musical, tonal relationships.

Spectrograms are usually created in one of two ways: approximatedas a filterbank that results from a series of bandpass filters (this wasthe only way before the advent of modern digital signal processing),

or calculated from the time signal using the short-time Fourier

transform (STFT). These two methods actually form two different

quadratic Time-Frequency Distributions, but are equivalent under

some conditions.

The bandpass filters method usually uses analog processing todivide the input signal into frequency bands; the magnitude of eachfilter's output controls a transducer that records the spectrogram as

an image on paper.


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Creating a spectrogram using the STFT is usually a digital process.Digitally sampled data, in the time domain, is broken up into

chunks, which usually overlap, and Fourier transformed to calculate

the magnitude of the frequency spectrum for each chunk. Eachchunk then corresponds to a vertical line in the image; a

measurement of magnitude versus frequency for a specific moment

in time. The spectrums or time plots are then "laid side by side" to

form the image or a three-dimensional surface.[4]

Molecular graphics

Molecular graphics (MG) is the discipline and philosophy ofstudying molecules and their properties through graphicalrepresentation. IUPAClimits the definition to representations on a

"graphical display device".Ever since Daltons's atoms

and Kekul's benzene, there has been a rich history of hand-drawn

atoms and molecules, and these representations have had an

important influence on modern molecular graphics. Algorithms

Reference frames

Drawing molecules requires a transformation between molecularcoordinates (usually, but not always, in Angstrom units) and the

screen. Because many molecules are chiral it is essential that the

handedness of the system (almost always right-handed) is

preserved. In molecular graphics the origin (0, 0) is usually at the

lower left, while in many computer systems the origin is at top left.

If the z-coordinate is out of the screen (towards the viewer) themolecule will be referred to right-handed axes, while the screen

display will be left-handed.

Molecular transformations normally require:

scaling of the display (but not the molecule).


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translations of the molecule and objects on the screen. rotations about points and lines. Conformational changes (e.g. rotations about bonds) requirerotation of one part of the molecule relative to another. The

programmer must decide whether a transformation on the screen

reflects a change of view or a change in the molecule or its

reference frame.

In early displays only vectors could be drawn e.g. (Fig. 7) which areeasy to draw because no rendering or hidden surface removal isrequired.

On vector machines the lines would be smooth but on rasterdevices Bresenham's algorithm is used (note the "jaggies" on some

of the bonds, which can be largely removed

with antialiasing software.)

Atoms can be drawn as circles, but these should be sorted so thatthose with the largest z-coordinates (nearest the screen) are drawn

last. Although imperfect, this often gives a reasonably attractive

display. Other simple tricks which do not include hidden surface

algorithms are:

coloring each end of a bond with the same color as the atom towhich it is attached

drawing less than the whole length of the bond (e.g. 10%-90%) tosimulate the bond sticking out of a circle.

adding a small offset white circle within the circle for an atom tosimulate reflection.

Data visualization


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Data visualization is the study of the visual representation of data,meaning "information that has been abstracted in some schematic

form, including attributes or variables for the units of information"

According to Friedman (2008) the "main goal of data visualization isto communicate information clearly and effectively through

graphical means. It doesnt mean that data visualization needs to

look boring to be functional or extremely sophisticated to look

beautiful. To convey ideas effectively, both aesthetic form and

functionality need to go hand in hand, providing insights into a

rather sparse and complex data set by communicating its key-

aspects in a more intuitive way. Yet designers often fail to achieve a

balance between form and function, creating gorgeous data

visualizations which fail to serve their main purpose to

communicate information".Indeed, Fernanda Viegas and Martin M.

Wattenberg have suggested that an ideal visualization should not

merely communicate clearly, but stimulate viewer engagement and

attention

Data visualization is closely related to informationgraphics, information visualization, scientificvisualization,

and statistical graphics. In the new millennium, data visualization

has become an active area of research, teaching, and development.

According to Post et al. (2002), it has united the field of scientific

and information visualization. As demonstrated by Brian Willison,

data visualization has also been linked to enhancing agile softwaredevelopment and customer engagement.

KPI Library has developed the Periodic Table of VisualizationMethods, an interactive chart displaying various data visualization


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methods . It details 6 types of data visualization methods: data,

information, concept, strategy, metaphor and compound

Graph drawing is an area of mathematics and computerscience combining methods from geometric graph theory

and information visualization to derive two-dimensional depictions

of graphs arising from applications such as social

network analysis, cartography, and bioinformatics.]

A drawing of a graph or network diagram is a pictorialrepresentation of the vertices and edges of a graph. This drawing

should not be confused with the graph itself: very different layouts

can correspond to the same graph. In the abstract, all that mattersis which pairs vertices are connected by edges. In the concrete,

however, the arrangement of these vertices and edges within a

drawing affects its understandability, usability, fabrication cost,

and aesthetics. The problem gets worse, if the graph changes over

time by adding and deleting edges (dynamic graph drawing) and

the goal is to preserve the user's mental map

Software

Software, systems, and providers of systems for drawing graphs

include:

Cytoscape, open-source software for visualizing molecularinteraction networks

Gephi, an open-source network analysis and visualization software Graphviz, an open-source graph drawing system from AT&T

Corporation

Mathematica, a general purpose computation tool that includes 2Dand 3D graph visualization and graph analysis tools.

Microsoft Automatic Graph Layout, a .NET library (formerly calledGLEE) for laying out graphs


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Tom Sawyer Software Tom Sawyer Perspectives is a graphics-basedsoftware for building enterprise-class data visualization and social

network analysis applications. It is a Software Development Kit

(SDK) with a graphics-based design and preview environment.

Tulip (software) yEd, a widely used graph editor with graph layout functionality.

CYTOSCAPE

Cytoscape is an open source bioinformatics software platformfor visualizing molecular interaction networks and integratingwith gene expression profiles and other state data. Additional

features are available as plugins. Plugins are available for network

and molecular profiling analyses, new layouts, additional file format

support and connection with databases and searching in large

networks

Usage While Cytoscape is most commonly used for biological research

applications, it is agnostic in terms of usage. Cytoscape can be usedto visualize and analyze network graphs of any kind involving nodes

and edges (e.g., social networks). A key aspect of the software

architecture of Cytoscape is the use of plugins for specialized

features. Plugins are developed by core developers and the greater

user community.

Mathematica

Mathematica is a computational software program used inscientific, engineering, and mathematical fields and other areas of

technical computing. It was conceived by Stephen Wolfram and is

developed by Wolfram Research.


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Computable data

Mathematica includes collections of curated data provided for usein computations.

Mathematica is also integrated with Wolfram Alpha, an onlineservice which provides additional data, some of which is kept

updated in real time. Some of the data sets include astronomical,

chemical, geopolitical, language, biomedical and weather data, in

addition to mathematical data (such as knots and polyhedra).

Features

Elementary mathematical function library Specialmathematical function library Matrix and data manipulation tools including support for sparse

arrays

Support for complex number, arbitrary precision, interval arithmeticand symbolic computation

2D and 3D data and function visualization and animation tools Solvers for systems of equations, diophantine

equations, ODEs, PDEs, DAEs, DDEs and recurrence relations

Numeric and symbolic tools for discrete and continuous calculus Multivariate statistics libraries including fitting, hypothesis testing,

and probability and expectation calculations on over 100

distributions.

Constrained and unconstrained local and global optimization Programming language

supporting procedural, functional and object oriented constructs

Toolkit for adding user interfaces to calculations and applications


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Tools for image processing[5] and morphological imageprocessing including image recognition

Tools for visualizing and analysing graphs Tools for combinatoric problems Tools for text mining including regular expressions and semantic

analysis

Data mining tools such as cluster analysis, sequencealignment and pattern matching

Number theory function library Tools for financial calculations including bonds, annuities,

derivatives, options etc.

Group theory functions Libraries for wavelet analysis on sounds, images and data Control systems libraries Continuous and discrete integral transforms Import and export filters for data, images, video,

sound, CAD, GIS,[6] document and biomedical formats

Database collection for mathematical, scientific, and socio-economic information and access to WolframAlpha data andcomputations

Technical word processing including formula editing and automatedreport generating


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Tools for connecting toDLLs. SQL, Java, .NET, C++, FORTRAN, CUDA, OpenCL and http based

systems

Tools for parallel programing Using both "free-form linguistic input" (a natural language user

interface) [7] and Mathematica language in notebook when

connected to the Internet

References

www.wikipedia.com www.google.com\images Schaums outline computer graphics

Documents

Graph Design Doc