GPU ACCELERATED CONE BASED SHOOTING BOUNCING

RAY TRACING

Masters Thesis Defense

Blake Troksa

Advisor: Dr. Branislav Notaros

Committee: Dr. Sudeep Pasricha

Dr. Hamid Chitsaz

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

RAY TRACING

Applications of Ray

Tracing in CEM

Two types in

CEM

Image Theory

Shooting

Bouncing Rays

Time Complexity

Searching for Facet

Intersections

RAY TRACING CONT.

• Maxwell’s Equations are linear in linear, homogenous, and anisotropic propagation domains

• Assume infinite planar facet interfaces

IMAGE THEORY

• Exact Path Calculation

• O(Nk)

• N – Number of

observation points

• K – Number of facets

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

THE SBR ALGORITHM

• Two Subsections

• Geometric Path Calculations

• Mesh Creation

• Ray Generation

• Post Processing

• Electric Field Calculations

• Double Count Removal

SBR ALGORITHM INPUTS

• Number of Rays

• Limit on number of Reflections

• Lossy material vs. metallic

• Geometry definition (Mesh)

• OBJ file

• Location of observation points

MESHES

• LiDAR Data

• Building Blueprint

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

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

Tubes Cones

Tracing of single ray

Double Count

Removal

Trouble with Curvature

Cover entire space without

overlap

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

SPHERE INTERSECTIONS

SEPARATION ANGLE

• Angle across face of Icosahedron

• Same across all faces

LOSSY DIELECTRIC WAVEGUIDE

• Image Theory Solution

• Long

• 1km

• Lossy Dielectric

• Dry Concrete (εr=5)

• Frequency = 1Ghz

STATIC ALPHA PER-RAY ALPHA

EFFECT OF SEPARATION ANGLE

Reference results obtained here [1]

MIN PER-RAY ALPHA MAX PER-RAY ALPHA

EFFECT OF SEPARATION ANGLE CONT.

Reference results obtained here [1]

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:

ELECTRIC FIELD CALCULATIONS

• Attenuation of Electric Field

• Plane waves now interact by Fresnel

coefficients

• Loss due to distance traveled

REFLECTED RAYS

• Decomposition into

normal and parallel

polarizations

• Angle in = Angle out

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

DOUBLE COUNT REMOVAL

• Removal based on

Adjacent Rays

• Rays stored in map

lookup

• Other techniques

• Removal based on check

of sphere size

WITH DOUBLE COUNT

REMOVAL

WITHOUT DOUBLE

COUNT REMOVAL

EFFECTS OF DOUBLE COUNT REMOVAL

Reference results obtained here [1]

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

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

CONFIGURATION OPTIMIZATION

• Threads per block

• Rays per Thread

• Block size

Threads Per Block

PARALLEL ICOSAHEDRON

SPEEDUP

• Comparison between earlier iteration of

the algorithm

• No double count removal

SBR AND SBR

Reference results obtained here [2]

SBR AND IT

Reference results obtained here [1]

REMCOM WIRELESS

INSITE

Option of shooting

bouncing ray

tracing

Exact Path

Corrections

GPU Acceleration

OUR SBR AND REMCOM CONT.

Reference results obtained here [2]

SBR AND FMM-FFT

• FMM-FFT

• Full-wave solver

• Supercomputer

• 4 hours and 54

minutes

Reference results obtained here [3]

CONVERGENCE

• PEC Waveguide Tested

• Known Analytical Solution

• TE10 Mode

RSS MAPS WITH SBR

• Received Signal Strength

• Laborious and time consuming process

• Simulated on Colorado School of Mines Edgar

Mine

MEASUREMENTS

• Ground Plane Reflection

• Friis Formula

MINE MEASUREMENTS

FUTURE WORK

• SBR Hybridization

• Image theory - exact path adjustments

• MoM/FEM

• Diffraction

• More Real-world testing

• Adaptive sampling

• Adaptive observation point checks

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.

THANK YOU

SBR, FMM-FFT, REMCOM