Transcript ICVGIP-ppt - IIIT Hyderabad

Hybrid Ray Tracing and
Path Tracing of Bezier Surfaces
using a mixed hierarchy
Rohit Nigam, P. J. Narayanan
IIIT Hyderabad
CVIT, IIIT Hyderabad, Hyderabad, India
Representing a Scene
f>0
f<0
f=0
Triangular Mesh
Implicit Surface
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Parametric Surface
Parametric Surface: Motivation
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 Provide compact and effective representation.
 Remain curved and smooth at arbitrary level of
zooming.
 Memory efficient, in comparison with triangular mesh.
Bezier Surfaces
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• Bezier Surfaces are the most basic form of parametric
surfaces
• A Bezier Surface can be described as:
Q(u,v) = [U][M][P][M]T[V]T
where [U] = [u3 u2 u 1] and [V] = [v3 v2 v 1], 0 ≤ u,v ≤ 1
[M] is the Bezier Basis Matrix
[P] is the set of 16 Control Points defining the patch
Rendering Bezier Surfaces
• Tessellation based approches
– Eisenacher et al.(2009) :
View Dependent Adaptive Subdivision
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• Direct Ray Tracing
– Geimer et al.(2005) :
Newton Iteration
– Pabst et al.(2006) :
Bezier Clipping + Newton Iteration
Ray Tracing Bezier Surface
• Constructing an Accelaration Structure
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 Bounding Volume Hierarchy(BVH)
Ray Tracing Bezier Surface
• Ray Traversal through BVH
0 1 2 3 4 5 6 7 8 9
Ray List
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Outputs
Potential Ray-Patch intersections list
Initial parameter values
Ray Tracing Bezier Surface
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• Newton Iteration
Picture Courtesy : http://steadyserverpages.com
Geimer, Abert Approach
Original Curve
• Based on the flatness criteria, each
patch is divided into subpatches.
• BVH for original surfaces
– Bounding boxes of subpatches at leaf
nodes.
Subdivided Linear
Curve
• For each potential intersection
– Generate initial values for Newton Iteration
1
3
2
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Patch1
sp1 sp2
BVH Nodes
P2
sp1
sp2
P3
sp1 sp2
Subpatches at Leaf
Limitation of the Model for GPUs
• GPU Access time:
– High for global memory
– Comparatively less for shared memory and registers
When subdividing based on flatness criteria, we need to
– Store subpatches starting index
– Store total number of subpatches
– Store initial [u,v] pair for each potential intersection.
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Thus more global memory operations result in lower
throughput.
• Need to check every subpatch at leaf node
Our Approach
• Create a mixed hierarchy,
consisting of two hierarchical
structures.
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– The top level BVH tree is
constructed from the bounding
boxes of original patches.
– Leaf nodes represent the original
Bezier Surfaces.
– Each Patch is divided into fixed
size subpatches, hierarchically,
using De Casteljau algorithm.
– Make subtree for each patch from
bounding boxes of the subdivided
patches.
BVH for
Patches
BVH Nodes
Patches
Subtree Nodes
Subpatch
Hierarchy
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Sub-patches
1
2
3
4
Mixed Hierarchy Structure
• Newton Iteration applied to original patches
– No memory required to store subpatches
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• Fixed depth subtree
–
–
–
–
–
Utilize constant degree of bezier surfaces
Utilize shared memory
Apply early termination at subtree level
Leads to tighter bounds
A subdivision depth of 6 was found empirically sufficient.
Mixed Hierarchy Structure
• Newton Iteration applied on original patches.
– No memory required to store subpatches.
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• Fixed depth makes it possible utilize shared memory.
• A subtree at lower level leads to early termination at this
stage, reducing the (Ray, Bounding Box) intersections.
• Subdivision also leads to tighter bounds, which further
reduces the potential (Ray,Patch) intersections.
• A subdivision depth of 6 was found empirically sufficient
for our scenes.
GPU Traversal of
Mixed Hierarchy Structure
• A ‘traverse’ kernel traverses the first level of the BVH.
– Lists out Potential (Ray,Patch) intersections.
– We make use of atomic operations, to provide scalability.
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• ‘Recheck’ kernel parallely processes the generated
(ray,patch) list.
– This leads to further pruning of the list with tighter subpatch
bounding boxes.
– We make use of ‘t’ values computed here, to not traverse
subpatch nodes with higher values.
– This leads to reduced computation and in cases of false
positive, a little less accurate initial values.
– Lists out the reduced potential (Ray,Patch) intersections.
– Generates the initial values for each intersection.
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Secondary Rays
Hybrid Ray Tracing
GPU
Start
CPU
Preprocessing
Ray List
rayTraceGPU
rayTraceCPU
Point and Normal
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Generate Secondary Rays
Hybrid Ray Tracing
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Divide the Ray list between CPU and GPU
GPU algorithm comprises
of three kernels:
Traverse : Generate
Potential Ray-Patch
Intersections
Recheck : Further prune
intersections and get initial
values
Newton : Apply Newton
iteration to get hit-point
CPU stage comprises of:
1. Divide CPU Raylist into
2c threads, where c is
number of cores.
2. Intersect with main BVH
3. If intersects, intersect
with 2nd level subtree.
4. Apply Newton iteration
to get hit-point
Results
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Teapot Model
Fps : 64
2 Killeroos
Fps : 10.6
Bigguy Model
Fps : 28.6
Killeroo Model
Fps : 19.2
9 Bigguys
Fps : 5.2
System Specs
GTX 580 + i7 920
1024x1024
Path Tracing
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• We extend our ray tracing approach to Global
Illumination effects.
• We use Cook’s approach of Monte Carlo based
Stochastic Sampling, to sample the image at
appropriate non-uniformly spaced points.
• Each pixel is sampled for a user defined samples per
pixel
• We apply our data parallel approach to this massive ray
list to generate the desired effects.
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Path Tracing
Bigguy in a box: 400 spp, 512x512 resolution
Rendered in 28.5 minutes
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Path Tracing
Bigguy in a box: 1000 spp, 512x512 resolution
Rendered in 28.5 minutes
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Path Tracing
Bigguy in a box: 3000 spp, 512x512 resolution
Rendered in 28.5 minutes
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Path Tracing
Bigguy in a box: 5000 spp, 512x512 resolution
Rendered in 28.5 minutes
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Path Tracing
Bigguy in a box: 10000 spp, 512x512 resolution
Rendered in 28.5 minutes
Conclusion
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• A mixed hierarchy model is proposed to speed up Ray
Tracing process.
• GPU benefits greatly from fixed depth subtree.
• A hybrid model is proposed, to fully utilize compute
power of CPU and GPU.
• We demonstrate the capability of our method by
producing Global Illumination effects for Bezier patches.
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THANK YOU
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Hybrid Ray Tracing
• Divide the Ray list between CPU and GPU
 Ratio decided based on compute capabilities
• GPU algorithm comprises of three kernels:
 Traverse : Generate Potential Ray-Patch Intersections
 Recheck : Further prune intersections and get initial values
 Newton : Apply Newton iteration to get hit-point
• CPU stage comprises of:
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1.
2.
3.
4.
Divide CPU Raylist into 2c threads, where c is number of cores.
Intersection with main BVH
If intersects, further intersection with 2nd level subtree.
Finally, apply Newton iteration and generate hit-point
• CPU benefits from early ray termination.
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Hybrid Ray Tracing
Newton Iteration
• We represent a ray as intersection of two planes, (n1,d1)
and (n2,d2)
The ray patch intersection equation becomes
Q(u,v) represents the point on the patch.
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• We use Newton Iteration to solve for (u,v)
Here J is the inverse Jacobian matrix of R.
Results (Primary Rays, 1024x1024)
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Model
Patches
Ray-Patch
Intersections
Total Frame Time(ms)
CPU
GPU
Hybrid
Teapot
32
126589
74
8.71
8.01
Bigguy
3570
142779
110
14.59
13.18
Killeroo
11532
147116
193
22.38
20.43
2 Killeroos
23064
317494
356
42.29
38.58
9 Bigguys
32130
570136
2092
77.05
75.9
Results (Primary +Secondary)
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Model
Patches
Total Frame Time(ms)
CPU
GPU
Hybrid
Teapot
32
137
17.05
15.61
Bigguy
3570
232
39.45
34.92
Killeroo
11532
351
58.3
52.19
2 Killeroos
23064
726
106.03
94.55
9 Bigguys
32130
3107
196.79
191.81