Visualization of Data Sets

7/23/2019 Visualization of Data Sets

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Visualization of Data Sets



Data Sets

• Data sets are classied: – Spatial distribution

– Data type

• 2D data sets – distributed over asurface

• 3D data sets – distributed over theinterior of a cube, a sphere, or someother region of space

• Data types include: scalars, vectors,

tensors and multivariate data



Scalar vs Vector

•

scalar !uantity is a one dimensionalmeasurement of a !uantity, li"etemperature, or #eight$

• vector has more than one number

associated #ith it$

• simple e&ample is velocity$ 't has amagnitude, called speed, as #ell as a

direction, li"e (orth or South#est or )*degrees #est of (orth$

• scalar is +ust a number, and a vector is anumber #ith a direction involved$



Visual epresentation forScalar

• Scalar !uantity – single value

• SDS – contain values that may bedistributed in time, as #ell as overspatial positions

• -g of physical scalar !uantities .energy, density, mass, temperature,pressure, charge, resistance,re/ectivity, fre!uency, etc

• 0ommon visualizing method – graphs

or charts



• Pseudo-color methods – distinguishdi1erent values in a scalar data sets

• Color-coding techniques – combined#ith graph and chart methods

• Contour plots – to display isolines

lines of constant scalar value for adata set distributed over a surface$

• 't display the 3.dimensional

relationship in t#o dimensions, #ith &.and y.factors predictors plotted onthe &. and y.scales and responsevalues represented by contours$







4he dar"er regions indicate higher !uality$ 4he contour levels reveal a pea" centered inthe vicinity of 35 minutes 4ime and

625o

4emp$ 7uality scores in this pea"region are greater than 8$





• Volume rendering – some#hat li"e

an 9.ray picture, a method forvisualizing a three.dimensional dataset$



Visual epresentation forVector

• vector !uantity V in three.dimensional space has three scalarvalues (Vx,Vy,Vz), one for each

coordinate direction, and a t#o.dimensional vector has t#ocomponents (Vx,Vy).

•

Vector representation – magnitude |V| and its direction u$

• Vector !uantities may be functions ofposition, time and other parameters$



• ne #ay – plot each data point as asmall arrow that sho#s the

magnitude and direction of the vector

• epresent vector values by plottingfeld lines or streamlines

• ;ield lines are commonly used forelectric, magnetic, and gravitationalelds

• Streamlines can be displayed as #idearro#s, particularly #hen a #hirlpool,or vorte&, e1ect is present$





Visual epresentation for 4ensor

• tensor !uantity in three.dimensionalspace has nine components and canbe represented #ith a 3 by 3 matri&$

• <sually second.order tensor, higher.order tensors do occur$

• Second.order tensors are stress and

strain in a material sub+ected toe&ternal forces, conductivity orresistivity of an electrical conductor$



• 4he stress tensor in 0artesian

coordinates, for e&ample, can berepresented as:

• =hysical tensor !uantities aresymmetric, so that the tensor hasonly si& distinct values

• 'nstead of trying to visualize all si&components of a tensor, #e canreduce the tensor to a vector or a

scalar









Visual epresentation for

>ultivariate Data ;ields

• >ultiple data values – a mi&ture ofscalar, vector, and even tensors

• ;or a /uid./o# problem, #e mayhave /uid velocity, temperature, anddensity values at each three.dimensional position

• 0onstruct graphical ob+ects,sometimes referred to as glyphs,#ith multiple parts$

• -ach part of a glyph represents a



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Visualization of Data Sets