Advanced visualization with VisNow platform Data calculations · 9 v = momentum/density vn =...

UNIVERSITY OF WARSAW

Interdisciplinary Centre for Mathematical

and Computational Modellingwww.icm.edu.pl

Advanced visualization with VisNow platform Data calculations

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

http://creativecommons.org/licenses/by-nc-nd/4.0/




• Data values = component

• Data values – scalar or vector numerical values in each gridnode

• Independently on field structure each component in a givenfield has the same number of entries (= number of nodes in the field)

• Therefore, in each grid node the same mathematicalcalculation can be performer on the existing values

• Simliarly to array operations e.g. in MATLAB

VisNow – data calculations




• Module – component calculator• Performs mathematical operations on data components

• Base on evaluation of single-line mathematical expressions for the whole components (data arrays)

• Functionality:• Mathematical operators: + - * / ^

• Functions: sqrt, log, log10, exp, abs, sin, cos, tan, asin, acos, atan, signum

• Statistics: avg, stddev

• Vectors (concatenation): ,

• Parentheses: ( )

• Syntax: result_variable = expression

3VisNow – data calculations




• Module – component calculator• Variables and constants:

• Variables = component names or aliases

• Field grid indices (structure)

• i, j, k or index.i, index.j, index.k for regular fields (respectively 1D, 2D and 3D)

• i or index.i for irregular fields

• Grid coordinates (geometry) – x, y, z or coords.x, coords.y, coords.z (for 1, 2 and 3-dimensional space)

• Subindices of vector components:

• name.x, name.y, name.z (respectively for vlen = 1, 2 and 3)

• Constants: E, PI





• Module – component calculator

• Example #1:• Input field has components:

• density (scalar)

• momentum (vector, vlen=3)

• Velocity vector calculation:

v = momentum / density

• X component of velocity vector calculation:

xv = momentum.x / density

• Velocity vector norm calculation:

v = momentum / density

vnorm = sqrt(v.x^2 + v.y^2 + v.z^2)





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1. Read the bluntfin.vnf file with ‘VisNow field reader’ module.




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2. Connect ‘component calculator’ module to the output field.




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v = momentum/density



3. Calculate the velocity vector by dividing momentum vector by density.




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v = momentum/densityvn = sqrt(v.x^2 + v.y^2 + v.z^2)




4. Calculate velocity value (norm of velocity vector).




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v = momentum/densityvn = sqrt(v.x^2 + v.y^2 + v.z^2)vnn = (vn-avg(vn)) / stddev(vn)





5. Normalize the velocity value with average and standard deviation.








5. Normalize the velocity value with average and standard deviation.

6. Run calculations with ’Evaluate’ buton.

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7. Connect ‘glyphs‘ module to the output from ‘component calculator ‘ module and choosecomponent v as glyph size component




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8. In ‘glyphs‘ module set glyph scale and line thickness up to your choice





8. In ‘glyphs‘ module set glyph scale and line thickness up to your choice

9. Colour the glyphs with the calculated vnn component and using blue-white-red, colour map, with selected symmetrical option and upper range equal 3.0

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• Module – component calculator

• Example #2:• Input image of 256x256 size with a single component :

• grayscaleData (scalar)

• Insert a spotlight at the selected point:

p = (i-128)^2+(j-128)^2

r = 100

spot = exp(-p/r)

result = spot * grayscaleData





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1. Read the cameraman.png image with ‘image reader’ module.




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2. Disconnect data from viewer and connect ’component calculator’ module to the first output.




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p = (i-140)^2+(j-180)^2r = 2000spot = exp(-p/r)result = spot * gra



3. Run the calculations of spotlight insertion for the point i=140 j=180






3. Run the calculations of spotlight insertion for the point i=140 j=180

4. Connect ‘field mapper’ module to the resulting field and change colour mapping settings up to your preference (e.g. with use of RGB mapping)

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• Module – multicomponent histogram

• Enables to create 1D, 2D and 3D histograms

• Binning based on data or geometry

• Provides calculations inside each bin for each data component:• Sum

• Minimum

• Maximum

• Mean

• Standard deviation

• Vector variance





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2. Connect ’modify components’ module to the first output port and disconnect both modules from the viewer.






3. Calculate momentum component norm.

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4. Connect ‘multicomponent histogram’ module to the resulting field







4. Connect ‘multicomponent histogram’ module to the resulting field

5. Generate a 1D histogram for density component (without logarithmic scale)

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6. Connect the resulting field to ’field viewer 1D’ module




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7. Generate 1D histogram for the momentum_norm component




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8. Delete ’field viewer 1D’ module and generate 2D histogram for density and momentum_normcomponents






8. Delete ’field viewer 1D’ module and generate 2D histogram for density and momentum_normcomponents

9. Set colour mapping range to 0-40 and connect also ’axes 3D’ module to the viewer

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10. Generate 3D histogram for density, stagnation and momentum_norm components




10. Generate 3D histogram for density, stagnation and momentum_norm components

11. Watch the 3D histogram using ’volume renderer’ module (set colour map and transparencyranges to 0-50)

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visnow.icm.edu.pl

Contact:

[email protected]

Interdisciplinary Centre for Mathematical and Computational Modelling

University of Warsaw

Bartosz Borucki, Krzysztof Nowiński

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

http://creativecommons.org/licenses/by-nc-nd/4.0/

Advanced visualization with VisNow platform Data calculations · 9 v = momentum/density vn =...

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