GPU ACCELERATED CONE BASED SHOOTING BOUNCING RAY … · ACKNOWLEDGEMENTS/ REFERENCES • This work...
Transcript of GPU ACCELERATED CONE BASED SHOOTING BOUNCING RAY … · ACKNOWLEDGEMENTS/ REFERENCES • This work...
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GPU ACCELERATED CONE BASED SHOOTING BOUNCING
RAY TRACING
Masters Thesis Defense
Blake Troksa
Advisor: Dr. Branislav Notaros
Committee: Dr. Sudeep Pasricha
Dr. Hamid Chitsaz
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OVERVIEW
Ray Tracing Overview
• Shooting-Bouncing Ray Tracing
Geometric Calculations
• Ray Generation
• Mesh Creation
Post Processing
• Sphere Intersections
• Double Counting
Parallelization of Ray Tracing
• GPU Acceleration
• Coalesced Memory Accesses
• Speedup from Parallelization
Results
• Comparison with another SBR algorithm
• Comparison with Image Theory
• Comparison with FMM-FFT
• Comparison with Commercial Software
Future Work
• Hybridization
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RAY TRACING
Applications of Ray
Tracing in CEM
Two types in
CEM
Image Theory
Shooting
Bouncing Rays
Time Complexity
Searching for Facet
Intersections
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RAY TRACING CONT.
• Maxwell’s Equations are linear in linear, homogenous, and anisotropic propagation domains
• Assume infinite planar facet interfaces
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IMAGE THEORY
• Exact Path Calculation
• O(Nk)
• N – Number of
observation points
• K – Number of facets
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SHOOTING-BOUNCING
RAYS(SBR)
• Intuitive implementation of ray tracing
• Rays launched from transmitting antenna source point
• Path of ray is traced until intersection with a facet
• Previous intersection next intersection
• Electric field is calculated once the ray has reached a reception point
• Advantages of SBR
• Computationally quick form of ray tracing
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THE SBR ALGORITHM
• Two Subsections
• Geometric Path Calculations
• Mesh Creation
• Ray Generation
• Post Processing
• Electric Field Calculations
• Double Count Removal
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SBR ALGORITHM INPUTS
• Number of Rays
• Limit on number of Reflections
• Lossy material vs. metallic
• Geometry definition (Mesh)
• OBJ file
• Location of observation points
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MESHES
• LiDAR Data
• Building Blueprint
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RAY GENERATION
• The Icosahedron
• Provides a consistent angle between the points distributed along each face.
• Enables easy computation of separation angle for each ray
• Batching
𝑛 ∗ (𝑛 + 1)
2
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RAY DENSITY
• Sampling Density of Rays
• Ideally the sampling density would rise to infinity
• Spatial Angle for Rays
• Rays approximate the field information of the volume that surrounds them
• Allows for conservation of power that all rays within that volume would contain provided infinite ray density
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Tubes Cones
Tracing of single ray
Double Count
Removal
Trouble with Curvature
Cover entire space without
overlap
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SPHERE INTERSECTIONS
• Intersection of the Rays
• Rays are received at spheres as opposed to planes or points
• Spheres model an omni-directional cross-section of the cone at an observation point.
• Reception sphere continuously grow
𝑅𝑎𝑑𝑖𝑢𝑠𝑆𝑝ℎ𝑒𝑟𝑒 = Τ𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∗ 𝛼 3
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SPHERE INTERSECTIONS
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SEPARATION ANGLE
• Angle across face of Icosahedron
• Same across all faces
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LOSSY DIELECTRIC WAVEGUIDE
• Image Theory Solution
• Long
• 1km
• Lossy Dielectric
• Dry Concrete (εr=5)
• Frequency = 1Ghz
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STATIC ALPHA PER-RAY ALPHA
EFFECT OF SEPARATION ANGLE
Reference results obtained here [1]
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MIN PER-RAY ALPHA MAX PER-RAY ALPHA
EFFECT OF SEPARATION ANGLE CONT.
Reference results obtained here [1]
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GEOMETRIC CALCULATIONS
• NVIDIA Ray-Tracing Application Programming Interface
• NVIDIA has invested much research in creating computationally quick ray tracing programs for use in rendering applications.
• We take advantage of the tools and software developed by NVIDIA
• Binary Space Partition Tree
• K-D treehttps://www.google.com/search?q=nvidia+optix&source=lnms&tbm=isch
&sa=X&ved=0ahUKEwjB6tmLl57jAhWPXM0KHXOTCTQQ_AUIEygE&
cshid=1562343531524818&biw=1280&bih=622#imgrc=sMPWGl7tpSmc
HM:
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ELECTRIC FIELD CALCULATIONS
• Attenuation of Electric Field
• Plane waves now interact by Fresnel
coefficients
• Loss due to distance traveled
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REFLECTED RAYS
• Decomposition into
normal and parallel
polarizations
• Angle in = Angle out
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DOUBLE COUNTING
• Ray’s that intersect the same triangles represent an approximation of rays with the same image theory path
• Reception spheres of the same image theory ray overlap at the observation point
• The electric field contribution is counted twice
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DOUBLE COUNT REMOVAL
• Removal based on
Adjacent Rays
• Rays stored in map
lookup
• Other techniques
• Removal based on check
of sphere size
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WITH DOUBLE COUNT
REMOVAL
WITHOUT DOUBLE
COUNT REMOVAL
EFFECTS OF DOUBLE COUNT REMOVAL
Reference results obtained here [1]
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ACCELERATION
• Yields efficient parallelization specifically on GPU’s.
Rays Propagate Independently
• Due to the independence of ray paths, field calculations for each ray are also independent
• GPU’s capable of handling the computing of the Fresnel coefficients
Electromagnetic Field Calculations
• Computationally intensive to re-compute the size of a sphere for each ray after each reflection.
• GPU’s efficiently handle this mathematically simple but extensive process.
Ray Sphere Intersections
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COALESCED MEMORY ACCESSES
• Access to global memory should be in a coalesced fashion for the threads located in each thread block.
• NVIDIA GeForce 1060 GPU’s have a warp size of 32
• Limits number of reads to global memory and increases speedup
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CONFIGURATION OPTIMIZATION
• Threads per block
• Rays per Thread
• Block size
Threads Per Block
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PARALLEL ICOSAHEDRON
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SPEEDUP
• Comparison between earlier iteration of
the algorithm
• No double count removal
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SBR AND SBR
Reference results obtained here [2]
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SBR AND IT
Reference results obtained here [1]
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REMCOM WIRELESS
INSITE
Option of shooting
bouncing ray
tracing
Exact Path
Corrections
GPU Acceleration
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OUR SBR AND REMCOM CONT.
Reference results obtained here [2]
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SBR AND FMM-FFT
• FMM-FFT
• Full-wave solver
• Supercomputer
• 4 hours and 54
minutes
Reference results obtained here [3]
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CONVERGENCE
• PEC Waveguide Tested
• Known Analytical Solution
• TE10 Mode
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RSS MAPS WITH SBR
• Received Signal Strength
• Laborious and time consuming process
• Simulated on Colorado School of Mines Edgar
Mine
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MEASUREMENTS
• Ground Plane Reflection
• Friis Formula
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MINE MEASUREMENTS
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FUTURE WORK
• SBR Hybridization
• Image theory - exact path adjustments
• MoM/FEM
• Diffraction
• More Real-world testing
• Adaptive sampling
• Adaptive observation point checks
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ACKNOWLEDGEMENTS/REFERENCES
• This work was supported by the National Science Foundation under grant ECCS-1646562.
1. D. Didascalou, Ray-optical wave propagation modeling in arbitrarily shaped tunnels, 2000.
2. Shin-Hon Chen and Shyh-Kang Jeng, "SBR image approach for radio wave propagation in tunnels with and without traffic," in IEEE Transactions on Vehicular Technology, vol. 45, no. 3, pp. 570-578, Aug. 1996.
3. A. C. Yucel, W. Sheng, C. Zhou, Y. Liu, H. Bagci and E. Michielssen, "An FMM-FFT Accelerated SIE Simulator for Analyzing EM Wave Propagation in Mine Environments Loaded With Conductors," in IEEE Journal on Multiscale and Multiphysics Computational Techniques, vol. 3, pp. 3-15, 2018.
4. M.F.Cátedra and J.Perez, Cell Planning for Wireless Communications. Norwood, MA, USA: Artech House, 1999.
5. B. M. Notaros, Electromagnetics, New Jersey : PEARSON Prentice Hall; 2010.
6. V. Mohtashami and A. A. Shishegar, "A new double—counting cancellation
technique for ray tracing using separation angle distribution," 2008 IEEE
International RF and Microwave Conference, Kuala Lumpur, 2008, pp. 306-310.
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THANK YOU
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SBR, FMM-FFT, REMCOM