Presentation of one of my projects on computer graphics. It talks about Volume Rendering of Unstructured Tetrahedral Grids using Intel / nVidia OpenCL.

1. VOLUME RENDERING OF
UNSTRUCTURED TETRAHEDRAL GRIDS

2. Flow
• Introduction
• Problem Formulation
• Tetrahedral Interpolation
• Implementation
• Results
• Demo
• Endnotes
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3. Introduction: Volume Rendering
• Volume rendering is a technique that can
be used to visualize sampled 3D scalar
data as a continuous medium or extract
features.
Most algorithms for direct volume rendering
have assumed structured data in form of
rectilinear grid.
• In this project we worked on a method for
rendering unstructured volume; volume
represented by group of tetrahedrals.
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4. Problem Formulation
• The idea is to convert unstructured input tetrahedral grid
(UG) to output structured regular grid (SG) and render it
using existing ray casting system.
• The data represented in UG must be interpolated to
produce SG.
• The UG consists of tetrahedrals bounded by four vertices
numbered 1,2,3,4, the coordinates of ith vertex being (xi,
yi, zi) and associated data value is denoted fi.
• The data values are assumed to be the values of an
unknown locally smooth trivariate function
interpolate discussed in next heading.
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5. Problem Formulation
• Let P = (x,y,z) be the point at which the value of interpolation function is
to be estimated.
Two different interpolation schemes are followed here:
• Scheme 1: Map SG to UG
• For a given point P of SG and find the tetrahedral associated with P
in UG
• Estimate the function values for given cell based on interpolate.
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empty SG UG SG
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6. Problem Formulation
• Scheme 2: Map UG to SG
• Take a tetrahedral from UG and find points Ps lying on SG
• Estimate the function value at Ps based on interpolate.
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UG empty SG SG
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7. Tetrahedral Interpolation: interpolate
• Given a tetrahedron T with vertices v1, v2, v3, v4 and
function value associated with these vertices be f1, f2, f3
and f4, the problem is to find interpolated function value f
for any given point P.
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.P(f)
v1(f1)
v2(f2)v4(f4)
v3(f3)
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8. Tetrahedral Interpolation: interpolate
Geometric Solution
• Take ratio of perpendicular distance of P
to a face with perpendicular distance of
opposite vertex to that face.
• Find these ratios with all four faces and
name them l1, l2, l3 and l4.
• If the point P is lying inside tetrahedral
these ratios will come between 0 and 1.
• Sum of these ratios will always be 1.
• These l1,l2, l3 and l4 are known as
barycentric coordinates of point P with
respect to tetrahedral T.
• f = l1*f1 + l2*f2 + l3*f3 + l4*f4
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9. Tetrahedral Interpolation: interpolate
• Mathemetical Interpretation
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10. Tetrahedral Interpolation: interpolate
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11. Implementation
In implementation we are following 3 step approach
1. Load the vertices and tetrahedron information from
given .ts file into CPU memory
2. Based on two schemes presented, perform
computations using OpenCL (or OpenMP) to form a
regular grid
3. Display the grid by Ray Casting in OpenCL using CL-GL
Interoperability.
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12. Implementation: Description
Step1:
• The data set given .ts file is form of list of vertices with 3D
coordinates and associated function value and then a list of
tetrahedrons with asociated 4 vertices.
• We are first loading this information into memory.
• While loading the vertices we are computing minimum and
maximum values for (x,y,z) coordinates and storing it as minX,
minY, minZ, maxX, maxY, maxZ.
• We are then finding the difference between these minimum and
maximum values and storing it as diffX, diffY, diffZ.
• We are then computing diff equal to maximum of diffX, diffY
and diffZ.
• We are then finding dimensions of our bounding box with side
equal to diff.
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13. Step 2:
• Given
• We are computing A-1 for each tetrahedron
• We define a constant STEP_SIZE = 128 (or any other
value) which gives dimension of our volume as
128*128*128.
• We are setting the resolution (step size) of our volume as
res = diff / STEP_SIZE
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14. Scheme 1:
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1. Finding point lying
on SG
2. searching for
associated T in UG
and finding f value
using interpolation

15. • This scheme is implemented in both OpenCL and
OpenMP
• In OpenMP implementation we are adding following two
lines as compiler directive in starting of loop:
• #paragma omp set_num_threads(8)
• #paragma omp parallel for shared(i,j,k)
• In OpenCL implementation we are setting our dimensions
as 1D with
• size_t global_size = {STEP_SIZE * STEP_SIZE * STEP_SIZE}
• Here we are Parallelizing in terms of volume element
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16. Scheme2:
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1. Finding limits of
points lying inside
tetrahedral
2. For given limits finding f
values of points associated
with SG

17. • Scheme 2 is implemented in OpenCL. We are setting our
dimensions as 1D with
size_t global_size = tet_qty
• Here we are Parallelizing in terms of tetrahedral quantity
Step 3:
• We are then giving this 1D grid of function values to
existing ray tracer (provided by nVidia in their SDK) as
input.
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18. Results
• Hardware / Software for tests
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GPU
Model: nVidia Quadro FX 580
Cores: 32
Core Clock: 450 MHz
Memory: 512MB
Memory Bandwidth: 25.6 GiB/s
CPU
Model: Intel Core i7 860
Cores / Threads: 4/8
Clock Speed: 2.8GHz (3.0GHz when running on full load)
Memory: 8 GB
Memory Bandwidth: 21GB/s
OS / SDKs
Microsoft Windows 7 Professional 64Bit
Visual Studio 2010 32Bit
Microsoft OpenMP
nVidia CUDA SDK 3.2
nVidia OpenCL 1.1
Intel OpenCL 1.1 alpha
Input UG
Torus1.ts
Torusf1.ts
Torus8.ts
Engine.ts

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Scheme 1 Scheme 2
STEP_SIZE = 512
Time: 8.4 sec
STEP_SIZE = 512
Time: 2.5 sec

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Scheme 1 Scheme 2
STEP_SIZE = 512
Time: 2.5 sec
STEP_SIZE = 512
Time: 3.3 sec

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23. • Demo Video URL:
https://www.youtube.com/watch?v=CaBuZ7
se7-o
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24. Impressions
• Learning OpenCL was a challenging task but we it was
interesting.
• Debugging OpenCL is difficult task as stream output
(“printf” function) cannot be called in openCL kernel. In
Intel’s compiler is based on OpenCL 1.1 in which “printf” is
supported.
• Double precision computations are not supported on my
card.
• Graphic Driver Crash Problem
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25. “We now know a thousand ways not to
build a light bulb”
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THANKS !