GS-4150, Bullet 3 OpenCL Rigid Body Simulation, by Erwin Coumans

BULLET 3 OPENCL™ RIGID BODY SIMULATION
ERWIN COUMANS, AMD

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2 | BULLET 3 OpenCL™ RIGID BODY SIMULATION | NOVEMBER 21, 2013 | CONFIDENTIAL

AGENDA

Introduction, Particles, Rigid Bodies

GPU Collision Detection

GPU Constraint Solving


BULLET 2.82 AND BULLET 3 OPENCL™ ALPHA
 Real-time C++ collision detection and rigid body dynamics library
 Used in movies
‒ Maya, Houdini, Cinema 4D, Blender, Lightwave, Carrara, Posed 3D, thinking Particles, etc
‒ Disney Animation (Bolt), PDI Dreamworks (Shrek, How to train your dragon), Sony Imageworks (2012),

 Games
‒ GTA IV, Disney Toystory 3, Cars 2, Riptide GP, GP2

 Industrial applications, Robotics
‒ Siemens NX9 MCD, Gazebo


PARTICLES AND RIGID BODIES

 Position (Center of mass, float3)
 Orientation
‒ (Inertia basis frame, float4)


UPDATING THE TRANSFORM

 Linear velocity (float3)

 Angular velocity (float3)


C/C++ VERSUS OPENCL™
void integrateTransforms(Body* bodies, int numNodes, float timeStep)
{
for (int nodeID=0;nodeId<numNodes;nodeID++) {
if( bodies[nodeID].m_invMass != 0.f) {
bodies[nodeID].m_pos += bodies[nodeID].m_linVel * timeStep;
}
}
__kernel void integrateTransformsKernel( __global Body* bodies, int numNodes, float timeStep)
{
int nodeID = get_global_id(0);
if( nodeID < numNodes && (bodies[nodeID].m_invMass != 0.f)) {
}
}


One to One mapping

Read Compute Write

OPENCL™ PARTICLES


UPDATE ORIENTATION
__kernel void integrateTransformsKernel( __global Body* bodies,const int numNodes, float timeStep, float angularDamping, float4 gravityAcceleration)
{
if( nodeID < numNodes && (bodies[nodeID].m_invMass != 0.f))
{
//linear velocity
bodies[nodeID].m_linVel += gravityAcceleration * timeStep;
//apply gravity
float4 angvel = bodies[nodeID].m_angVel;
//angular velocity
bodies[nodeID].m_angVel *= angularDamping;
//add some angular damping
float4 axis;
float fAngle = native_sqrt(dot(angvel, angvel));
if(fAngle*timeStep> BT_GPU_ANGULAR_MOTION_THRESHOLD)
//limit the angular motion
fAngle = BT_GPU_ANGULAR_MOTION_THRESHOLD / timeStep;
if(fAngle < 0.001f)
axis = angvel * (0.5f*timeStep-(timeStep*timeStep*timeStep)*0.020833333333f * fAngle * fAngle);
else
axis = angvel * ( native_sin(0.5f * fAngle * timeStep) / fAngle);
float4 dorn = axis;
dorn.w = native_cos(fAngle * timeStep * 0.5f);
float4 orn0 = bodies[nodeID].m_quat;
float4 predictedOrn = quatMult(dorn, orn0);
predictedOrn = quatNorm(predictedOrn);
bodies[nodeID].m_quat=predictedOrn;
//update the orientation
}
}

See opencl/gpu_rigidbody/kernels/integrateKernel.cl

UPDATE TRANSFORMS, HOST SETUP

ciErrNum = clSetKernelArg(g_integrateTransformsKernel, 0, sizeof(cl_mem), &bodies);
ciErrNum = clSetKernelArg(g_integrateTransformsKernel, 1, sizeof(int), &numBodies);
ciErrNum = clSetKernelArg(g_integrateTransformsKernel, 1, sizeof(float), &deltaTime);
ciErrNum = clSetKernelArg(g_integrateTransformsKernel, 1, sizeof(float), &angularDamping);
ciErrNum = clSetKernelArg(g_integrateTransformsKernel, 1, sizeof(float4), &gravityAcceleration);
size_t workGroupSize = 64;
size_t
numWorkItems = workGroupSize*((m_numPhysicsInstances + (workGroupSize)) / workGroupSize);
if (workGroupSize>numWorkItems)
workGroupSize=numWorkItems;
ciErrNum = clEnqueueNDRangeKernel(g_cqCommandQue, g_integrateTransformsKernel, 1, NULL, &numWorkItems, &workGroupSize,0 ,0 ,0);


MOVING THE CODE TO GPU
 Create an OpenCL™ wrapper
‒ Easier use, fits code style, extra features, learn the API

 Replace C++ by C
 Move data to contiguous memory
 Replace pointers by indices
 Exploit the GPU hardware…


SHARING DATA STRUCTURES AND CODE BETWEEN OPENCL™ AND C/C++
#include "Bullet3Collision/NarrowPhaseCollision/shared/b3RigidBodyData.h"
#include "Bullet3Dynamics/shared/b3IntegrateTransforms.h"
__kernel void integrateTransformsKernel( __global b3RigidBodyData_t* bodies,const int numNodes, float timeStep, float angularDamping,
float4 gravityAcceleration)
{
if( nodeID < numNodes)
{
integrateSingleTransform(bodies,nodeID, timeStep, angularDamping,gravityAcceleration);
}

}


PREPROCESSING OF KERNELS WITH INCLUDES IN SINGLE HEADER FILE
 We want the option of embedding kernels in our C/C++ program
 Expand all #include files, recursively into a single stringified header file
‒ This header can be used in OpenCL™ kernels and in regular C/C++ files too
‒ Kernel binary is cached and cached version is unvalidated based on time stamp of embedded kernel file

 Premake, Lua and a lcpp: very small and simple C pre-processor written in Lua
‒ See https://github.com/willsteel/lcpp


HOST, DEVICE, KERNELS, WORK ITEMS
Host

Device (GPU)

CPU

L2 cache

Global Host
Memory


Global Device Memory

RIGID BODY PIPELINE

Collision Data
Collision
shapes

Compute
world space
Object AABB

Object
AABB

Object
local space
BVH

Detect
pairs

Broad Phase
Collision Detection (CD)

Dynamics Data
Overlapping
pairs

Contact
points

Cull complex
shapes
local space

Mid Phase
CD

Start


Compute
contact
points

Narrow
Phase CD

time

Constraints
(contacts,
joints)

Setup
constraints

Mass
Inertia

Forces,
Gravity

Solve
constraints

Constraint
Solving

World
transforms
velocities

Integrate
position

Integration

End

BOUNDING VOLUMES AND DETECT PAIRS
X min
Y min
Z min
*

MAX (X,Y,Z)

X max
Y max
Z max
Object ID
MIN (X,Y,Z)

Output pairs
Object ID A
Object ID A
Object ID A

Object ID B
Object ID B
Object ID B

COMPUTE PAIRS BRUTE FORCE
__kernel void computePairsKernelOriginal( __global const btAabbCL* aabbs,
__global int2* pairsOut, volatile __global int* pairCount,
int numObjects, int axis, int maxPairs)
{
int i = get_global_id(0);
if (i>=numObjects)
return;
for (int j=0;j<numObjects;j++)
{
if ( i != j && TestAabbAgainstAabb2GlobalGlobal(&aabbs[i],&aabbs[j])) {
int2 myPair;
myPair.x = aabbs[i].m_minIndices[3]; myPair.y = aabbs[j].m_minIndices[3];
int curPair = atomic_inc (pairCount);
if (curPair<maxPairs)
pairsOut[curPair] = myPair; //flush to main memory
}
}


Scatter operation

DETECT PAIRS
 Uniform Grid
‒ Very fast
‒ Suitable for GPU
‒ Object size restrictions

0

1

2

F

C

E

5

D

B

A

8

3

10

7

11

 Can be mixed with other algorithms
12

13

 See bullet3srcBullet3OpenCLBroadphaseCollisionb3GpuGridBroadphase.cpp


14

15

UNIFORM GRID AND PARALLEL PRIMITIVES

 Radix Sort the particles based on their cell index
 Use a prefix scan to compute the cell size and offset

 Fast OpenCL™ and DirectX® 11 Direct Compute implementation

1 AXIS SORT, SWEEP AND PRUNE

 Find best sap axis
 Sort aabbs along this axis

 For each object, find and add overlapping pairs


COMPUTE PAIRS 1-AXIS SORT
__kernel void computePairsKernelOriginal( __global const btAabbCL* aabbs,
__global int2* pairsOut, volatile __global int* pairCount,
int numObjects, int axis, int maxPairs)
{
int i = get_global_id(0);
if (i>=numObjects)
return;
for (int j=i+1;j<numObjects;j++)
{
if(aabbs[i].m_maxElems[axis] < (aabbs[j].m_minElems[axis]))
break;
if (TestAabbAgainstAabb2GlobalGlobal(&aabbs[i],&aabbs[j])) {
int2 myPair;
myPair.x = aabbs[i].m_minIndices[3]; myPair.y = aabbs[j].m_minIndices[3];
int curPair = atomic_inc (pairCount);
if (curPair<maxPairs)
pairsOut[curPair] = myPair; //flush to main memory
}
}


GPU MEMORY HIERARCHY

Private
Memory
(registers)

Shared Local Memory

Compute Unit

Shared Local Memory

Shared Local Memory

Global Device Memory


BARRIER

A point in the program where all threads stop and wait
When all threads in the Work Group have reached the barrier,
they can proceed

Barrier


KERNEL OPTIMIZATIONS FOR 1-AXIS SORT
CONTENT SUBHEADER

LOCAL MEMORY

block to fetch AABBs and re-use them within a workgroup (barrier)

AVOID GLOBAL
ATOMICS

Use private memory to accumulate overlapping pairs (append buffer)

LOCAL ATOMICS

Determine early exit condition for all work items within a workgroup


KERNEL OPTIMIZATIONS (1-AXIS SORT)
 Load balancing
‒ One work item per object, multiple work items for large objects

 See opencl/gpu_broadphase/kernels/sapFast.cl and sap.cl

(contains un-optimized and optimized version of the kernel for comparison)


SEQUENTIAL INCREMENTAL 3-AXIS SAP


PARALLEL INCREMENTAL 3-AXIS SAP

Parallel sort 3 axis
Keep old and new sorted axis
‒6 sorted axis in total


PARALLEL INCREMENTAL 3-AXIS SAP

Sorted x-axis old
Sorted x-axis new

 If begin or endpoint has same index do nothing
 Otherwise, range scan on old AND new axis
‒adding or removing pairs, similar to original SAP

 Read-only scan is embarrassingly parallel

HYBRID CPU/GPU PAIR SEARCH

0

1

2

F

C
D

12

E

5

B
A

8

13

3

Small Large
Small GPU either
Large either CPU

10

14

7

11

15


TRIANGLE MESH COLLISION DETECTION


GPU BVH TRAVERSAL
 Create skip indices for
faster traversal
 Create subtrees that
fit in Local Memory
 Stream subtrees for
entire wavefront/warp

 Quantize Nodes
‒ 16 bytes/node


COMPOUND VERSUS COMPOUND COLLISION DETECTION


TREE VERSUS TREE: TANDEM TRAVERSAL
for (int p=0;p<numSubTreesA;p++) {
for (int q=0;q<numSubTreesB;q++) {
b3Int2 node0; node0.x = startNodeIndexA;node0.y = startNodeIndexB;
nodeStack[depth++]=node0; depth = 1;
do {
b3Int2 node = nodeStack[--depth];
if (nodeOverlap){
if(isInternalA && isInternalB){
nodeStack[depth++] = b3MakeInt2(nodeAleftChild, nodeBleftChild);
nodeStack[depth++] = b3MakeInt2(nodeArightChild, nodeBleftChild);
nodeStack[depth++] = b3MakeInt2(nodeAleftChild, nodeBrightChild);
nodeStack[depth++] = b3MakeInt2(nodeArightChild, nodeBrightChild);
} else {
if (isLeafA && isLeafB) processLeaf(…)
else { …} //see actual code
}
} while (depth);

 See __kernel void findCompoundPairsKernel( __global const int4* pairs … in
‒ in bullet3srcBullet3OpenCLNarrowphaseCollisionkernels/sat.cl

CONTACT GENERATION: GPU CONVEX HEIGHTFIELD
 Dual representation

 SATHE, R. 2006. Collision detection shader using cube-maps. In ShaderX5, Charles River Media


SEPARATING AXIS TEST
 Face normal A

 Face normal B
 Edge-edge normal
plane

A

B

axis

 Uniform work suits GPU very well: one work unit processes all SAT tests for one pair
 Precise solution and faster than height field approximation for low-resolution convex shapes
 See opencl/gpu_sat/kernels/sat.cl

COMPUTING CONTACT POSITIONS
clipping planes
 Given the separating normal find incident face
 Clip incident face using Sutherland Hodgman clipping

incident

n
n

reference face

 One work unit performs clipping for one pair, reduces contacts and appends to contact buffer
 See opencl/gpu_sat/kernels/satClipHullContacts.cl

SAT ON GPU
 Break the algorithm into pipeline stages, separated into many kernels
‒ findSeparatingAxisKernel
‒ findClippingFacesKernel
‒ clipFacesKernel
‒ contactReductionKernel

 Concave and compound cases produce even more stages
‒ bvhTraversalKernel,findConcaveSeparatingAxisKernel,findCompoundPairsKernel,processCompoundPairsPrimitiv
esKernel,processCompoundPairsKernel,findConcaveSphereContactsKernel,clipHullHullConcaveConvexKernel


GPU CONTACT REDUCTION

 See newContactReductionKernel in opencl/gpu_sat/kernels/satClipHullContacts.cl

REORDERING CONSTRAINTS REVISITED

B

1

A

B

1

1
2

C

A

4

D

A

B

C

D

Batch 0

1

1

3

3

Batch 1

4

2

2

4

2
3

4

D

3

4


CPU SEQUENTIAL BATCH CREATION
while( nIdxSrc ) {
nIdxDst = 0;
int nCurrentBatch = 0;
for(int i=0; i<N_FLG/32; i++) flg[i] = 0; //clear flag
for(int i=0; i<nIdxSrc; i++)
{
int idx = idxSrc[i]; btAssert( idx < n );
//check if it can go
int aIdx = cs[idx].m_bodyAPtr & FLG_MASK;
int bIdx = cs[idx].m_bodyBPtr & FLG_MASK;
u32 aUnavailable = flg[ aIdx/32 ] & (1<<(aIdx&31));u32 bUnavailable = flg[ bIdx/32 ] & (1<<(bIdx&31));
if( aUnavailable==0 && bUnavailable==0 )
{
flg[ aIdx/32 ] |= (1<<(aIdx&31));
flg[ bIdx/32 ] |= (1<<(bIdx&31));
cs[idx].getBatchIdx() = batchIdx;
sortData[idx].m_key = batchIdx; sortData[idx].m_value = idx;
nCurrentBatch++;
if( nCurrentBatch == simdWidth ) {
nCurrentBatch = 0;
for(int i=0; i<N_FLG/32; i++) flg[i] = 0;
}
}
else {
idxDst[nIdxDst++] = idx;
}
}
swap2( idxSrc, idxDst ); swap2( nIdxSrc, nIdxDst );
batchIdx ++;
}

GPU ITERATIVE BATCHING

D

1

4

A

For each unassigned constraint

B

B

C

D

unused

For each batch

A

unused

unused

unused

Try to reserve bodies
1

1

A

B

Batch 0 1

1

 Before locking attempt, first check if bodies are already used in previous iterations
 See “A parallel constraint solver for a rigid body simulation”, Takahiro Harada,
http://dl.acm.org/citation.cfm?id=2077378.2077406

3

Append constraint to batch

 Parallel threads in workgroup (same SIMD) use local atomics to lock rigid bodies

and openclgpu_rigidbodykernelsbatchingKernels.cl

2

C

D

GPU PARALLEL TWO STAGE BATCH CREATION

 Cell size > maximum dynamic object size
 Constraint are assigned to a cell
‒ based on the center-of-mass location of the first active rigid body of the pair-wise constraint

 Non-neighboring cells can be processed in parallel


MASS SPLITTING+JACOBI ~= PGS
2

3

B
1

D
4
A

A

B0

B1

C0

C1

D1

D1

A

1

1

2

2

3

3

4

4

C

B

B1

C0

C0

B0

Averaging velocities

D

C1

Parallel Jacobi

C1

 See “Mass Splitting for Jitter-Free Parallel Rigid Body Simulation” by Tonge et. al.

GPU NON-CONTACT CONSTRAINTS, JOINTS


GPU NON-CONTACT CONSTRAINTS, JOINTS
__kernel void getInfo1Kernel(__global unsigned int* infos, __global b3GpuGenericConstraint* constraints, int numConstraints)
__kernel void getInfo2Kernel(__global b3SolverConstraint* solverConstraintRows, ..
switch (constraint->m_constraintType)
{
case B3_GPU_POINT2POINT_CONSTRAINT_TYPE:
case B3_GPU_FIXED_CONSTRAINT_TYPE:
}

 getInfo1Kernel and getInfo2Kernel with switch statement replaces virtual methods in Bullet 2.x
 See bullet3srcBullet3OpenCLRigidBodykernelsjointSolver.cl


DETERMINISTIC RESULTS
 Projected Gauss Seidel requires solving rows in the same order
 Sort the constraint rows (contacts, joints)

 Solve constraint batches in the same order


DYNAMICA PLUGIN FOR MAYA WITH OPENCL™


AMD CODEXL OPENCL™ DEBUGGER AND PROFILER


STACKING TEST


FUTURE WORK
 DirectX®11 DirectCompute port
 Multi GPU, multi-core, MPI

 Move over Bullet 2 to Bullet 3, hybrid of CPU and GPU
‒ Featherstone, direct solvers on CPU

 Cloth and Fluid simulation, TressFX hair, with two-way interaction
 Extend GPU-PGS solver to GPU-NNCG
‒ Non-smooth non-linear conjugate gradient solver

 Improve GPU Ray intersection tests


THANK YOU!
Visit http://bulletphysics.org for more information. All source code is available:
 http://github.com/erwincoumans/bullet3
‒ Lets you fork, report issues and request features

 Windows®, Linux®, Mac OSX
 AMD and NVIDIA GPU
‒ Preferably high-end desktop GPU


GS-4150, Bullet 3 OpenCL Rigid Body Simulation, by Erwin Coumans

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