difi: fast 3d distance field computation using graphics...
TRANSCRIPT
![Page 1: DiFi: Fast 3D Distance Field Computation using Graphics …gamma.cs.unc.edu/DIFI/Sud-EG04-DiFi-Presentation.pdf · 2009. 11. 3. · Robot Motion Planning Non-Photorealistic Rendering](https://reader035.vdocuments.mx/reader035/viewer/2022062604/5fc17e55e313233e040cc74b/html5/thumbnails/1.jpg)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
DiFi: Fast 3D Distance Field Computation using Graphics Hardware
Avneesh Sud, Miguel A. Otaduyand Dinesh Manocha
University of North Carolina at Chapel Hill
http://gamma.cs.unc.edu/DiFi
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Distance Field
Given a set of geometric primitives (sites), it is a scalar field representing the minimum distance from any point to the closest site
2D Distance field3 point sites
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Voronoi Diagram
Given a collection of sites, it is a subdivision of space into cells such that all points in a cell are closer to one site than to any other site
Voronoi Site Voronoi Region
3 point sites Voronoi diagram
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Distance Function
A scalar function f (x) representing minimum distance from a point x to a site
f (x,y)=√x2+y2 graph z = f (x,y)
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Voronoi Diagram and Distance FieldsRegion where distance function contributes to final distance field = Voronoi Region
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Why Should We Compute Them?Useful in a wide variety of applications
Collision DetectionSurface ReconstructionRobot Motion Planning
Non-Photorealistic RenderingSurface Simplification
Mesh GenerationShape Analysis
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Goal
Distance field algorithm:Fast computationApplicable to complex and generic modelsNo preprocessing
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)Applications and ResultsConclusions
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)Applications and ResultsConclusions
![Page 10: DiFi: Fast 3D Distance Field Computation using Graphics …gamma.cs.unc.edu/DIFI/Sud-EG04-DiFi-Presentation.pdf · 2009. 11. 3. · Robot Motion Planning Non-Photorealistic Rendering](https://reader035.vdocuments.mx/reader035/viewer/2022062604/5fc17e55e313233e040cc74b/html5/thumbnails/10.jpg)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Related Work
Geometric models: Polygonal dataVolumetric models: Image data
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Related Work
Geometric models: Polygonal dataAdaptive Grids [Vleugels97, Frisken00]Uniform Grids [Sethian96, Hoff99, Mauch00, Sigg03, Denny03, Furhmann03]
Volumetric models: Image data
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Related Work
Geometric models: Polygonal data
Volumetric models: Image dataApproximate Distance Fields [Danielsson80, Sethian96]Exact Distance Fields [Mulikin92, Breen00]Surveyed in [Cuisenaire99]Linear time algorithms for 2D [Breu95] and k-D [Maurer03]
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
GPU Based Computation
Accelerate using graphics hardware [Hoff99]Rasterization to compute distance valuesDepth test to perform minimum operator
Render distance functions Color buffer Depth buffer
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
GPU Based Computation
Graphics hardware can generate one 2D slice at a timeSweep along 3rd
dimension (Z-axis) computing 1 slice at a time
3D Voronoi Diagram
Slow for large number of sites and high grid resolutions
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
GPU Based Computation
For manifold objects, Voronoi regions bounded by prisms, wedges and cones [Mauch00, Sigg03]
Prism (Face)
Cone (Vertex)
Wedge (Edge)
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
GPU Based Computation
Compute distance functions inside Voronoi region bounds using programmable GPU [Sigg03]Best suited for computation in small neighborhood of the boundary
Not applicable to non-manifolds
Inefficient for global computation
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Contributions
A fast 3D distance field computation algorithm Reduces computation using geometric properties and spatial coherence
CullingClamping
Applicable to complex polygonal and image modelsNo preprocessing
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)
MotivationGeometric propertiesSite classificationCulling algorithmClamping algorithm
Applications and ResultsConclusions
![Page 19: DiFi: Fast 3D Distance Field Computation using Graphics …gamma.cs.unc.edu/DIFI/Sud-EG04-DiFi-Presentation.pdf · 2009. 11. 3. · Robot Motion Planning Non-Photorealistic Rendering](https://reader035.vdocuments.mx/reader035/viewer/2022062604/5fc17e55e313233e040cc74b/html5/thumbnails/19.jpg)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)
MotivationGeometric propertiesSite classificationCulling algorithmClamping algorithm
Applications and ResultsConclusions
![Page 20: DiFi: Fast 3D Distance Field Computation using Graphics …gamma.cs.unc.edu/DIFI/Sud-EG04-DiFi-Presentation.pdf · 2009. 11. 3. · Robot Motion Planning Non-Photorealistic Rendering](https://reader035.vdocuments.mx/reader035/viewer/2022062604/5fc17e55e313233e040cc74b/html5/thumbnails/20.jpg)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation
Not all sites contribute to distance field of a slice
zx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation
Not all sites contribute to distance field of a slice
zx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation
Not all sites contribute to distance field of a slice
zx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation
Not all sites contribute to distance field of a slice
zx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation
Not all sites contribute to distance field of a slice
zx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation
Sites whose Voronoi regions intersect the slice contribute to distance field
Small number of sites contributeCull remaining sites
zx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Motivation: Goals
Sites whose Voronoi regions intersect the slice contribute to distance field
Cull remaining sitesCompute distance function in domain where Voronoi region intersects slice
Clamp domain of computation
zx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)
MotivationGeometric propertiesSite classificationCulling algorithmClamping algorithm
Applications and ResultsConclusions
![Page 28: DiFi: Fast 3D Distance Field Computation using Graphics …gamma.cs.unc.edu/DIFI/Sud-EG04-DiFi-Presentation.pdf · 2009. 11. 3. · Robot Motion Planning Non-Photorealistic Rendering](https://reader035.vdocuments.mx/reader035/viewer/2022062604/5fc17e55e313233e040cc74b/html5/thumbnails/28.jpg)
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Geometric Properties
Connectivity: Voronoi regions are connected for all Lp norms
Used for culling
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Geometric Properties
Connectivity: Voronoi regions are connected for all Lp norms
Used for culling
Coherence: Change in distance field between adjacent slices is bounded
Used for clampingDistance functions for a point
site Pi to adjacent slices
Sk+1 Sk
P Z
X
δ
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)
MotivationGeometric propertiesSite classificationCulling algorithmClamping algorithm
Applications and ResultsConclusions
![Page 31: DiFi: Fast 3D Distance Field Computation using Graphics …gamma.cs.unc.edu/DIFI/Sud-EG04-DiFi-Presentation.pdf · 2009. 11. 3. · Robot Motion Planning Non-Photorealistic Rendering](https://reader035.vdocuments.mx/reader035/viewer/2022062604/5fc17e55e313233e040cc74b/html5/thumbnails/31.jpg)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice partition the set of sites
z
x
p1
p2
p3
p4
p5
slicek
p6
+Z
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice partition the set of sites using Voronoi region bounds:
z
x
p1
p2
p3
p4
p5
slicek
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice partition the set of sites using Voronoi region bounds:
Approaching
z
x
p1
p2
p3
p4
p5
slicek
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice partition the set of sites using Voronoi region bounds:
ApproachingIntersecting
x
p1
p2
p3
p4
p5
slicek
p6
z
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice partition the set of sites using Voronoi region bounds:
ApproachingIntersectingReceding
z
x
p1
p2
p3
p4
p5
slicek
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice partition the set of sites using Voronoi region bounds:
ApproachingIntersectingReceding
Only Intersecting sites contribute to distance field
z
x
p1
p2
p3
p4
p5
slicek
p6
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Site Classification
For each slice, also partition set of sites using sweep direction
z
x
p1
p2
p3
p4
p5
slicek
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice, also partition set of sites using sweep direction
Swept
z
x
p1
p2
p3
p4
p5
slicek
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Site Classification
For each slice, also partition set of sites using sweep direction
SweptUnswept
z
x
p1
p2
p3
p4
p5
slicek
p6
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Acceleration Techniques
Culling: Render distance functions for intersectingsites only
z
xp2
p3
p4
slicek
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Acceleration Techniques
Culling: Render distance functions for intersectingsites onlyClamping: For each intersecting site, clamp domain of computation
z
xp2
p3
p4
slicek
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)
MotivationGeometric propertiesSite classificationCulling algorithmClamping algorithm
Applications and ResultsConclusions
![Page 43: DiFi: Fast 3D Distance Field Computation using Graphics …gamma.cs.unc.edu/DIFI/Sud-EG04-DiFi-Presentation.pdf · 2009. 11. 3. · Robot Motion Planning Non-Photorealistic Rendering](https://reader035.vdocuments.mx/reader035/viewer/2022062604/5fc17e55e313233e040cc74b/html5/thumbnails/43.jpg)
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Goal
Render distance functions for intersecting sites only
z
xp2
p3
p4
slicek
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Culling: 2 Pass Algorithm
Render distance functions for intersecting swept sites: +Z pass
z
xp2
p3
p4
slicek
+Z
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Culling: 2 Pass Algorithm
Render distance functions for intersecting swept sites: -Z pass
z
xp2
p3
p4
slicek
-Z
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Culling: 2 Pass Algorithm
Render distance functions for intersecting sweptsitesFinal distance field obtained after both passes
z
xp2
p3
p4
slicek
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Culling
Computing exact intersecting set = Exact Voronoi computationSwept set easy to computeCompute a set of potentially intersecting swept (PIS) sitesUse hardware based occlusion queries to compute PIS
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Computing PIS
Given the potentially intersecting swept set for slice k
z
x
p1
p2
p3
p4
p5
slicek
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Computing PIS
For slice k+1:
z
x
p1
p2
p3
p4
p5
slicek+1
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Computing PIS
For slice k+1:Add newly swept sites to PIS
z
x
p1
p2
p3
p4
p5
slicek+1
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Computing PIS
For slice k+1:Add newly swept sites to PISDraw distance functions of new PIS
z
x
p1
p2
p3
p4
p5
slicek+1
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Computing PIS
For slice k+1:Add newly swept sites to intersecting setDraw distance functions of new intersecting setCheck visibility and update receding set
z
x
p1
p2
p3
p4
p5
slicek+1
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Computing PIS
For slice k+1:Add newly swept sites to intersecting setDraw distance functions of new intersecting setCheck visibility and update receding setGet final intersecting swept set for slice k+1
z
xp2
p4
p5
slicek+1
p6
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Culling: Conservative Sampling
Issue: Image space occlusion query may under sample a Voronoi region
Wrongly classifies a site as receding
Solution: “Grow” the Voronoi region by pixel size (details in paper)
p1
p2
p3
Sk
Sk+1
zx
p1 p2
p3
p4p5
yx
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)
Motivation Geometric propertiesSite classificationCulling algorithmClamping algorithm
Applications and ResultsConclusions
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clamping: Goal
Clamping: For each intersecting site, clamp domain of computation
z
xp2
p3
p4
slicek
Unclamped
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clamping: Goal
Clamping: For each intersecting site, clamp domain of computationDomain of computation = Intersection of Voronoi Region with slice
z
xp2
p3
p4
slicek
Clamped
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clamping
p4 p3
p2
zx
Sk
Dk(p3)
Exact Region
Distance function of each site is monotonicThe exact Voronoi region
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clamping
p4 p3
p2
zx
Sk
Dk(p3)
max(Dk(p3))
Bounded Region
Distance function of each site is monotonicThe exact Voronoi region is bounded by max of distance function
Exact Region
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clamping
p4 p3
p2
zx
Sk
Dk(p3)
max(Dk(p3))
max(Dk)
Distance function of each site is monotonicThe exact Voronoi region is bounded by max of distance function, which is bounded by max of distance field, max(Dk)
Exact RegionBounded Region
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Compute max(Dk+1) for slice k+1 incrementally using max(Dk)
Use max(Dk+1) for clamping
Clamping
Lemma: Let distance between adjacent slices be δz . Then change in maximum value of distance field between slices Sk and Sk+1 is given by:
max(Dk+1) ≤ max(Dk) + δz
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Clamping: Manifold Sites
Voronoi region bounded by prisms, wedges and cones [Mauch00, Sigg03]For each manifold site, refine Voronoi region bounds using prism, wedge or cone bounds
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)Applications and ResultsConclusions
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Implementation
Pentium4 2.8Ghz, 2GB RAMNVIDIA GeForce FX 5900 Ultra, 256MB Video RAMWindows XP, OpenGLHAVOC3D [Hoff99]
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results: Distance Field
Rotor Triceratops Head Cassini
log
time
(s)
DiFiCSC+HAVOCCSCHAVOC
0.1
1
10
100
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results: Distance Field
Rotor Triceratops Head Cassini
log
time
(s)
DiFiCSC+HAVOCHAVOCCSC
0.1
1
10
100 200x275x
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results: Distance Field
Rotor Triceratops Head Cassini
log
time
(s)
DiFiCSC+HAVOCHAVOCCSC
0.1
1
10
100
20x5x
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results: Distance Field
Rotor Triceratops Head Cassini
log
time
(s)
DiFiCSC+HAVOCHAVOCCSC
0.1
1
10
100
13x
2x
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results: Distance Field
Rotor Triceratops Head Cassini
log
time
(s)
DiFiCSC+HAVOCCSCHAVOC
0.1
1
10
100Non-Manifold
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results: Varying Resolution
20x26x32 40x53x64 78x105x128 156x210x256
Resolution
log
time
(s)
DiFiCSC+HAVOCHAVOCCSC
1
10
100
1000
Head Model: 21.6k polygons
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Results: Varying Polygon Count
Polygons
log
time
(s)
DiFiCSC+HAVOCHAVOCCSC
1
10
100
1000
10,882 21,764 43,528 87,056
Head Model: 79x105x128 grid size
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Applications: Medial Axis
Compute a simplified medial axis using gradient of distance field [Foskey03]Stable subset of exact medial axis
Head model
θ-simplified medial
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Applications: Medial Axis
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Applications: Motion Planning
DiFi used in a constraint-based planner [Garber02]
Voronoi diagram Estimated pathDistance field Proximity queries
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Live Demo
LaptopPentium4 3.2Ghz, 2GB RAMNVIDIA GeForce FX Go5700, 128MB Video RAMWindows XP, OpenGL
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Outline
Related WorkFast GPU based algorithm (DiFi)Applications and ResultsConclusions
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Conclusions
A fast 3D distance field computation algorithm with an order of magnitude speedup
Almost interactive for complex 3D models
Applicable to complex polygonal and image modelsNo preprocessing
Applicable to dynamic environments
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Conclusions
Use geometric properties to reduce computations
CullingClamping
Exploit spatial coherence for incremental computationPerform geometric tests efficiently on GPU
Overcome undersampling
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Limitations
Best suited for global distance field computation in complex environments
Culling involves occlusion query overheadClamping bounds depend on distribution of sites
Computes distance field on uniform grid
Size limited by GPU memoryApplication may require distance field readback to CPU
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Future Work
Efficient clamping for manifold sites [Sigg03]Explore temporal coherence for dynamic and deformable modelsExtend to k-th order Voronoi diagramsFurther applications like dynamic simulation, morphing and database queries
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Acknowledgments
ARONSFONRDARPAIntel CorporationAnonymous reviewersMing LinMark Foskey, Luv KohliMark Harris, Greg Coombe, Naga GovindarajuUNC GAMMA group
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Questions?
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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Questions?
DiFi: Fast 3D Distance Field Computation DiFi: Fast 3D Distance Field Computation using Graphics Hardwareusing Graphics Hardware
http://gamma.cs.unc.edu/DiFi