Kinematics

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Computational Geometry Performance Problems with
respect to GPGPU

2D 3D 4D 6D 10D
Kinematics Computational Geometry Ariel
University Center
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Agenda

• Who are we KCG lab AUC
• Radio Frequency Motivation
• 2D Radio Map Compression
• 3D Ray Tracing
• Volumetric Compression MRI, FMRI
• Robot Configuration Space (6D-10D)
• Open issue Gaussian physical simulations serial
  Fortran simulation challenge.

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Who are we - (KCG)

• KCG lab - Ariel University Center
• Founded 2008 Boaz Ben-Moshe Nir Shvalb
• 10 undergraduate students, 7 graduate, Postdoc
• 6 founded projects Magnet, Mafat
• Simulation, Computational Geometry, Topology,
  Robotis, Optimization
• http//www.ariel.ac.il/projects/kcg/

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RF planning Motivation

• Radio elements
• Client
• Base Station
• Network
• Microwave - LOS
• Satellite
• Cable

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• Goal design an optimal network
• Problems of interest
• Locating Base Stations
• Frequency Assignment
• Connectivity

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• Problems of interest
• Locating Base Stations
• Guarding like.
• Complex objective function.
• Frequency Assignment
• Connectivity

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• Problems of interest
• Locating Base Stations
• Frequency Assignment
• Conflict free frequency
• Connectivity

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• Problems of interest
• Locating Base Stations
• Frequency Assignment
• Connectivity
• Smallest set of Relay Stations.
• Back to the BS-locator.

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Main Obstacles

• Huge inputs ? simplify approximation
• Formalizing ? objective function
• NP hardness ? efficient Heuristics

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Approximating Visibility BCK

• Given a terrain T and a view point p compute the
  set of points on the surface of T that are
  visible from p.
• Alternatively Paint T with two colors (red
  blue) s.t. any blue (red) point is visible
  (invisible) from p.

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left right cross-sections ? pizza slice.
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Lets look at a specific pizza slice
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Radar-like generic algorithm

• Given Terrain (T), view point (vp), and fixed
  angle (aA)
• while(int i0ilt360)
• S1cross-section(i)
• S2cross-section(ia)
• if(close enough(S1, S2))
• extrapolate(S1, S2)
• a A i min(360, i a)
• else a a/2

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Radar-like Threshold
Radar-like 10 deg, low threshold
Radar-like 10 deg, hi threshold
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Error Measure
exact radar approx xor
Error value xor-area / circle-area
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Radar vs Naïve sampling
Naïve sampling Radar visibility
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• Sure, but
• Cross section distribute computation ? memory
  management issues
• Interpolation algorithm ? 2 over head

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JPEG
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• Terrain Simplification ICTS, BSS-07
• Radio Maps
• Any natural 2D matrix
• dip tools, ROI,
• hardware, robustness
• fits GPUs perfectly!

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ICTS experimental results
ICTS
Original
diff
diff
Qslim
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Moving into 3D

• Z-cam ? 2.5D
• 3D Radio Path ray tracing
• MRI Volumetric compression
• FMRI 3.5D

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3D Ray-Tracing

• RF wireless communication in mind!
• ISRC The Israeli Short Range Consortium
• Motivated by

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Problem of interests
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• Given a geometric properties of a building B. and
  the position of both a transmitter T and a
  receiver R.
• Find all 3D geometric paths between T and R with
  bounded length.

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A building benchmark (complex)
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Two floors, 1600 m2 400 walls, several
types Complex doors, windows
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Radio Paths Example?
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• Radio Paths
• 2P, 0R
• 3P, 1R
• 0P, 1R
• 2P, 4R cut off
• penetration point
• reflection point

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Now, all we got to do is to find the best path
between all the pathes we found
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3D Ray-Tracing

• Can it be implemented in using GPGPU?
• Classic problem for distributed machines
• Current tools are extremely slow!
• Current research looking into larger urban
  regions.

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Volumetric Compression

• MRI in mind
• MRI high resolution say 10003 voxels
• JP3D? http//www.jp3d.co.uk/main.html
• Functional MRI for research (no FDA issues)
  3.5D
• Current tools are very slow and limited SPM05

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Robot Configuration Space

• Motion planning (minimal energy)
• Very Simple Robot ? 6 deg of freedom (6 motors)
• Each Motor 20 possible positions ? 6107
  configurations.
• Step Planning shortest energy-path
• Discussion!

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Robot Configuration Space

• Motion planning (minimal energy)
• MRI high resolution say 10003 voxels
• JP3D? http//www.jp3d.co.uk/main.html
• Functional MRI for research (no FDA issues)
  3.5D
• Current tools are very slow and limited SPM05

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physical simulations - serial FORTRAN Gaussian
challenge

• I know practically Nothing about this issue
• Fortran large portion of the code is older then
  us!
• Linda A distributed version of Gaussian
• SGI, Cray machines strange speed-up behavior
• Bar-Ilan has the sources and seems to be
  intrested (yet scaptic).

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Open Discussion

• 2D Radio Maps terrains,
• 3D Z-cam, ray-tracing, MRI, FMRI
• 6D-10D Robot Configuration (ants in mind)
• Other

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