Geometric Computations on GPU: Proximity Queries

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Geometric Computations on GPU: Proximity Queries

Avneesh Sud & Dinesh Manocha


This LectureProximity Queries: OverviewVisibility computations using GPUsReliable GPU-based ComputationsCollision DetectionProximity Queries using Discrete Voronoi Diagram


Proximity QueriesCollision Detection

Collision Detection


Proximity QueriesPenetration Depth Contact

forces


Proximity QueriesSeparation Distance

Repulsive force, time of contact


Motivation: Driving Applications

Computer animationSurgical simulationRoboticsHapticsBioinformatics


MotivationInteractive proximity computation among general deformable models

Inter-object queries among multiple models


MotivationInteractive proximity computation among general deformable models

Intra-object (self-proximity) queries in cloth simulation




Graphics Processing Units (GPUs)

Well-designed for visibility computations

Rasterization – image-space visibilityMassively parallel

Render millions of polygons per secondWell suited for image-based algorithms

High growth rate


Recent growth rate of Graphics Processing Units

Card Million triangles/secRadeon 9700 Pro 325GeForce FX 5800 350Radeon 9800 XT 412GeForce FX 5950 356GeForce 6800 600GeForce 7950 1000GeForce 8800 ?


GPUs: Geometric Computations

Used for geometric applicationsMinkowski sums [Kim et al. 02]CSG rendering [Goldfeather et al. 89, Rossignac et al. 90]Voronoi computation [Hoff et al. 01, 02, Sud et al. 04]Isosurface computation [Pascucci 04]Map simplification [Mustafa et al. 01]Collision Detection [Govindaraju03, Govindaraju04]Proximity Computations [Sud06]


Graphics Processing Units (GPUs)

Well-designed for visibility computations

Rasterization – image-space visibilityMassively parallel

Render millions of polygons per secondWell suited for image-based algorithms

High growth rate


Setup EngineStream of transformed vertices

Setup of setup commands and state

Vertex Processing Engines

Pixel Processing Engines

Stream of visible pixels

Alpha test

Stencil test

Depth test

Stream of vertices

IEEE Floating Point (32-bit)

IEEE Floating Point (32-bit) Limited Resolution!

Draw stream of triangles CPUGPU

Visibility of triangles

GPU


Draw stream of triangles CPUGPU

Visibility of triangles

Vertex Processing Engines Setup Engine

Stream of vertices


Alpha test


Stencil test

Depth test

Stream of transformed vertices

Setup of setup commands and state

count of visible pixels

GPU


GPUs for Geometric Computations: Issues

PrecisionFrame-buffer readbacks




Limited Resolution!

Resolution along X, Y,Z

X – 13 bits fixed precision

Y – 13 bits fixed precision

Z – 24 bits fixed precision*

On CPU – 32-bit or 64-bit floating-point precision

Frame-Buffer Precision


Frame-Buffer ReadbackInvolve stalls

Affect throughputSlow!


Frame-Buffer Readback Performance

Data Courtesy: www.techreport.comJune 2004

Readback of 1Kx1K frame-buffer takes 18 ms over PCI-Express

http://www.techreport.com/


GPU Growth Rate

CPU Growth Rate

AGP Bandwidth Growth Rate

Courtesy: Anselmo Lastra


SolutionsFrame-Buffer Readbacks Minimize readback data (eg Visibility information)Precision Refine answer on CPU


NV Occlusion QueryExtension name: NV_occlusion_queryReturns pixel count – the no. of pixels that passProvides an interface to issue multiple queries at once before asking for the result of any oneApplications can now overlap the time it takes for the queries to return with other work increasing the parallelism between CPU and GPU


NV Occlusion Query – How to Use (1)(Optional) Disable Depth/Color Buffers(Optional) Disable any other irrelevant non-geometric stateGenerate occlusion queriesBegin ith occlusion queryRender ith (bounding) geometryEnd occlusion queryDo other CPU computation while queries are being made(Optional) Enable Depth/Color Buffers(Optional) Re-enable other stateGet pixel count of ith queryIf (count > MAX_COUNT) render ith geometry


NV Occlusion Query – How to Use (2)Generate occlusion queriesGluint queries[N];GLuint pixelCount;glGenOcclusionQueriesNV(N, queries);Loop over queriesfor (i = 0; i < N; i++) {

glBeginOcclusionQueryNV(queries[i]); // render ith geometry glEndOcclusionQueryNV(); }

Get pixel countsfor (i = 0; i < N; i++) {

glGetOcclusionQueryuivNV(queries[i], GL_PIXEL_COUNT_NV, &pixelCount); if (pixelCount > MAX_COUNT) // do work for ith geometry }




GPU: Culling Coprocessor

AABB Culling

Exact Tests2.5D Overlap

Tests

Voronoi-Based Culling

Collision

Distance Potential Neighbor Set

N-ObjectsGPU-Based Culling

Potential Colliding Set


Inaccuracies in GPU-Based Algorithms

Image samplingDepth buffer precision

[Govindaraju, Lin, Manocha,Special Issue on Best Papers of ACM

VRST’04in IEEE TVCG]


Image SamplingOccurs when a primitive does not cover any pixels


Image SamplingPrimitives are rasterized but no intersecting points are sampled by hardware

Viewport

C = pixel center

Intersecting point


Depth Buffer PrecisionIntersecting points are sampled but precision is not sufficient

Viewport

C = pixel center

Intersecting point

T1


Overcome Image Sampling

Sufficiently fatten the trianglesUse Minkowski sums

Minkowski Sum AB = A B = {a + b: a A, b

B}


PL

Minkowski Sum: Example

P L




Goal Interactive collision detection

between complex objectsLarge number of objectsHigh primitive countNon-convex objectsOpen and closed objects


Non-rigid MotionDeformable objectsChanging topologySelf-collisions


CULLIDE: Overview

Potentially Colliding Set (PCS) computationExact collision tests on the PCS

[Govindaraju, Redon, Lin, Manocha, ACM Graphics Hardware 2003]


Algorithm

Object-LevelPruning

Subobject-Level

PruningExact Tests

GPU-based PCS computation Using CPU


Potentially Colliding Set (PCS)

PCS


Potentially Colliding Set (PCS)

PCS


Algorithm

Object-LevelPruning

Subobject- Level

PruningExact Tests


Visibility of ObjectsAn object is fully visible if it is completely in front of the remaining objects

O1

O

View

O2


Visibility for Collisions: Geometric Interpretation

Sufficient but not a necessary condition for existence of separating surface with unit depth complexity

O1

O

View

O2


PCS Pruning

Prune objects that do not collide


PCS Pruning

O1 O2 … Oi-1 Oi Oi+1 … On-1 OnO1 O2 … Oi-1 Oi Oi+1 … On-1 OnO1 O2 … Oi-1 Oi Oi+1 … On-1 On


PCS ComputationEach object tested against all objects but itselfNaive algorithm is O(n2)Linear time algorithm

Uses two pass rendering approachConservative solution


PCS Computation: First Pass

O1 O2 … Oi-1 Oi Oi+1 … On-1 On

Render


O1 O2 … Oi-1 Oi


Fully Visible?

Render Yes. Does not collide withO1,O2,…,Oi-1




Render

Fully Visible?


PCS Computation: Second Pass


Render



Render

Fully Visible?

Oi Oi+1 … On-1 On

Yes. Does not collide with Oi+1,…,On-1,On



Render

Fully Visible?



PCS Computation


Fully VisibleFully Visible


PCS Computation

O1 O2 O3 … Oi-1 Oi Oi+1 … On-2 On-1 On

O1 O3 … Oi-1 Oi+1 … On-1


Algorithm

Object-LevelPruning

Subobject- Level

PruningExact Tests


CULLIDE Algorithm

Object-LevelPruning

Subobject-Level

PruningExact Tests

Exact overlap tests using CPU


Full Visibility Queries on GPUs

We require a queryTests if a primitive is fully visible or not

Current hardware supports occlusion queries

Test if only part of a primitive is visible or not

Our solutionChange the sign of the depth function


Full Visibility Queries on GPUs

Depth functionGEQUAL LESS

All fragments Pass FailPassFail

FailPassFail PassFail

Query not supported

Occlusion query

Examples - HP_Occlusion_test, NV_occlusion_query


Bandwidth AnalysisRead back only integer identifiers

Computation at high screen resolutions


Demo: CULLIDE


Quick-CULLIDE

Improved two-pass algorithmUtilize visibility relationships among objects across different viewsHandle intra-object collisions

[Govindaraju, Lin, Manocha,IEEE Virtual Reality 2005]


Quick-CULLIDE: Visibility Sets

Decompose PCS into four disjoint sets

FFV (First pass Fully Visible)SFV (Second pass Fully Visible)NFV (Not Fully Visible in either passes)BFV (Both passes Fully Visible)

Visibility sets have five interesting properties!


Visibility Sets: Properties

FFV and SFV are collision-free sets



O1 O2 … Oi-1 Oi … Oj … On-1 On

Render



O1 O2 … Oi-1 Oi … Oj … On-1 On

Render

Fully Visible


Visibility Sets: PropertiesIt is sufficient to test visibility of

objects in FFV in second pass only





O1 O2 … Oi-1 Oi


Render



O1 O2 … Oi-1 Oi Oi+1 … On-1 OnNot Colliding

Collision tested in Second pass


Visibility Sets: PropertiesIt is sufficient to render objects in

FFV in first pass only!





O1 O2 … Oi-1 Oi


Render


PCS Computation

O1 O2 … Oi-1 Oi Oi+1 … On-1 OnNot Colliding

Render


Visibility Sets: PropertiesIt is sufficient to test the visibility

of objects in SFV in first pass only!


Visibility Sets: Properties

It is sufficient to render objects in SFV in second pass only!


Quick-CULLIDE: Advantages

Better culling efficiency Lower depth complexity than CULLIDEAlways better than CULLIDE

Faster computational performanceLower number of visibility queries and rendering operations

Can handle self-collisions


Demo: Quick-CULLIDE


Reliability

z

x

Given a primitive P

P


Reliability

z

x

Px is the portion of P projecting inside pixel X

Pixel X

Px


S

Reliability

z

x

S is a sphere centered at origin bounding pixel X

Pixel X

Px


Reliability

z

x

If we compute Minkowski sum PxS= Px S,

Pixel X

PxS

Px


Reliability

z

x

Px

then the rasterization of the Minkowski sum PxS

generates two fragments

Pixel X

PxS

Sample Depths


Reliability

z

x

Px

and the fragments bound depth values in Px

Pixel X

PxS

Sample Depths


Reliability

z

x

P1

Given two primitives P1 and P2

Pixel X

P2


Reliability

d

x

P1

If P1 and P2 intersect in 3-D,

Pixel X

P2

P1 and P2 intersect in 3-D


Reliability

d

x

P1

and we compute their Minkowski sums with a pixel-sized sphere centered at origin

Pixel X

P2


Reliability

z

x

P1

rasterization of the Minkowski sums overlap in image-space

Pixel X

P2


z

x

Pixel X

P1

P2

P1S

P2S


Bounding Offsets of a Triangle

Exact OffsetsThree edge-aligned cylinders, three spheres, two trianglesCan be rendered using fragment programsExpensive!

Oriented Bounding Box (OBB)


Union of OBBs


Demo: R-CULLIDE




N-Body Distance QueryGiven a set of sites, find all closest pairsNearest-neighbor for each site1 5

2 1

3 1

4 1

5 1

6 5

1

2

3

4

5

6


GoalCompute N-Body distance efficiently

CullingFor each site, compute Potential Neighbor Set (PNS) of sites

1

2

3

4

5

6

1 5


GoalCompute N-Body distance efficientlyFor each site, compute Potential Neighbor Set (PNS) of sites

Contains nearest neighbor

1

2

3

4

5

6

PNS(1) = {5,3}


OutlineRelated workN-Body distance queriesCulling using second order discrete Voronoi diagramsResults


Voronoi Culling for N-Body Query

AABB Culling

Voronoi-based Culling

N-ObjectsStage I Stage II

Exact Distance Tests

Potential Neighbor Set

Stage III


Second-order Voronoi Diagram

1

2

3

4

5

6

Governors = 2 closest sites


Benefit of Second-order Voronoi Diagram

Voronoi diagram: Spatial partition based on proximitySecond-order Voronoi diagram: Proximity to two sites

Nearest neighbor information


Culling using Second-order Voronoi Diagram

12 3

9

9 Polygonal Objects



PNS(1) = Sites whose second order Voronoi regions intersect 1

12 3

9

Second order Voronoi Diagram

8 7

4 56



PNS(1) = Sites whose second order Voronoi regions intersect 1

PNS(1) = {2,3}Second order Voronoi diagram provides PNS for all sites

12 3

PNS(1)



PNS(1) = Sites whose second order Voronoi regions intersect 1Second order Voronoi diagram provides PNS for all sitesPNS(1) = {2,3}PNS(2) = {1,4,9}

12

PNS(2)

9

4



PNS(1) = Sites whose second order Voronoi regions intersect 1Second order Voronoi diagram provides PNS for all sitesPNS(1) = {2,3}PNS(2) = {1,4,9}…PNS(9) = {2,8}

2

PNS(9)

9 8


Proximity Culling using Discrete Voronoi Diagram

Computing exact Voronoi diagram difficult


Proximity Culling using Discrete Voronoi Diagram

Computing exact Voronoi diagram difficultCompute Discrete Voronoi Diagram (DVD)

Interactive computation using GPU

Second order details in thesis

Discrete Voronoi Diagram


Distance Bounds for Conservative Computation

Under-sampling errorsProvides approximate separation distance (SD)

SD’SD



Theorem (Distance bounds):

SD’


Distance Bounds for Conservative ComputationTheorem (Distance bounds):

SD’ - < SD < SD’ +

SD’ = Approximate Separation DistanceSD = Exact Separation Distance = Grid resolution

SD



Compute PNS using distance boundsExact tests on CPU

Documents

Geometric Computations on GPU: Proximity Queries