bool calcPenDepth()
{
// Ryn Hybrid Pen Depth and EPA if necessary
SimdVector3 v( 1, 0, 0 );
SimdScalar squaredDistance = SIMD_INFINITY;
SimdScalar delta = 0.f;
const SimdScalar margin = g_pConvexShapes[ 0 ]->GetMargin() + g_pConvexShapes[ 1 ]->GetMargin();
const SimdScalar marginSqrd = margin * margin;
SimdScalar maxRelErrorSqrd = 1e-3 * 1e-3;
simplexSolver.reset();
while ( true )
{
assert( ( v.length2() > 0 ) && "Warning: v is the zero vector!" );
SimdVector3 seperatingAxisInA = -v * g_convexShapesTransform[ 0 ].getBasis();
SimdVector3 seperatingAxisInB = v * g_convexShapesTransform[ 1 ].getBasis();
SimdVector3 pInA = g_pConvexShapes[ 0 ]->LocalGetSupportingVertexWithoutMargin( seperatingAxisInA );
SimdVector3 qInB = g_pConvexShapes[ 1 ]->LocalGetSupportingVertexWithoutMargin( seperatingAxisInB );
SimdPoint3 pWorld = g_convexShapesTransform[ 0 ]( pInA );
SimdPoint3 qWorld = g_convexShapesTransform[ 1 ]( qInB );
SimdVector3 w = pWorld - qWorld;
delta = v.dot( w );
// potential exit, they don't overlap
if ( ( delta > 0 ) && ( ( delta * delta / squaredDistance ) > marginSqrd ) )
{
// Convex shapes do not overlap
return false;
}
//exit 0: the new point is already in the simplex, or we didn't come any closer
if ( ( squaredDistance - delta <= squaredDistance * maxRelErrorSqrd ) || simplexSolver.inSimplex( w ) )
{
simplexSolver.compute_points( g_wWitnesses[ 0 ], g_wWitnesses[ 1 ] );
assert( ( squaredDistance > 0 ) && "squaredDistance is zero!" );
SimdScalar vLength = sqrt( squaredDistance );
g_wWitnesses[ 0 ] -= v * ( g_pConvexShapes[ 0 ]->GetMargin() / vLength );
g_wWitnesses[ 1 ] += v * ( g_pConvexShapes[ 1 ]->GetMargin() / vLength );
return true;
}
//add current vertex to simplex
simplexSolver.addVertex( w, pWorld, qWorld );
//calculate the closest point to the origin (update vector v)
if ( !simplexSolver.closest( v ) )
{
simplexSolver.compute_points( g_wWitnesses[ 0 ], g_wWitnesses[ 1 ] );
assert( ( squaredDistance > 0 ) && "squaredDistance is zero!" );
SimdScalar vLength = sqrt( squaredDistance );
g_wWitnesses[ 0 ] -= v * ( g_pConvexShapes[ 0 ]->GetMargin() / vLength );
g_wWitnesses[ 1 ] += v * ( g_pConvexShapes[ 1 ]->GetMargin() / vLength );
return true;
}
SimdScalar previousSquaredDistance = squaredDistance;
squaredDistance = v.length2();
//are we getting any closer ?
if ( previousSquaredDistance - squaredDistance <= SIMD_EPSILON * previousSquaredDistance )
{
simplexSolver.backup_closest( v );
squaredDistance = v.length2();
simplexSolver.compute_points( g_wWitnesses[ 0 ], g_wWitnesses[ 1 ] );
assert( ( squaredDistance > 0 ) && "squaredDistance is zero!" );
SimdScalar vLength = sqrt( squaredDistance );
g_wWitnesses[ 0 ] -= v * ( g_pConvexShapes[ 0 ]->GetMargin() / vLength );
g_wWitnesses[ 1 ] += v * ( g_pConvexShapes[ 1 ]->GetMargin() / vLength );
return true;
}
if ( simplexSolver.fullSimplex() || ( squaredDistance <= SIMD_EPSILON * simplexSolver.maxVertex() ) )
{
// Run EPA
break;
}
}
return epaPenDepthSolver.CalcPenDepth( simplexSolver, g_pConvexShapes[ 0 ], g_pConvexShapes[ 1 ],
g_convexShapesTransform[ 0 ], g_convexShapesTransform[ 1 ], v,
g_wWitnesses[ 0 ], g_wWitnesses[ 1 ], 0 );
}
bool EpaPenetrationDepthSolver::HybridPenDepth( SimplexSolverInterface& simplexSolver,
ConvexShape* pConvexA, ConvexShape* pConvexB,
const SimdTransform& transformA, const SimdTransform& transformB,
SimdPoint3& wWitnessOnA, SimdPoint3& wWitnessOnB,
SimdScalar& penDepth, SimdVector3& v )
{
SimdScalar squaredDistance = SIMD_INFINITY;
SimdScalar delta = 0.f;
const SimdScalar margin = pConvexA->GetMargin() + pConvexB->GetMargin();
const SimdScalar marginSqrd = margin * margin;
simplexSolver.reset();
int nbIterations = 0;
while ( true )
{
assert( ( v.length2() > 0 ) && "Warning: v is the zero vector!" );
SimdVector3 seperatingAxisInA = -v * transformA.getBasis();
SimdVector3 seperatingAxisInB = v * transformB.getBasis();
SimdVector3 pInA = pConvexA->LocalGetSupportingVertexWithoutMargin( seperatingAxisInA );
SimdVector3 qInB = pConvexB->LocalGetSupportingVertexWithoutMargin( seperatingAxisInB );
SimdPoint3 pWorld = transformA( pInA );
SimdPoint3 qWorld = transformB( qInB );
SimdVector3 w = pWorld - qWorld;
delta = v.dot( w );
// potential exit, they don't overlap
if ( ( delta > 0 ) && ( ( delta * delta / squaredDistance ) > marginSqrd ) )
{
// Convex shapes do not overlap
// Returning true means that Hybrid's result is ok and there's no need to run EPA
penDepth = 0;
return true;
}
//exit 0: the new point is already in the simplex, or we didn't come any closer
if ( ( squaredDistance - delta <= squaredDistance * g_GJKMaxRelErrorSqrd ) || simplexSolver.inSimplex( w ) )
{
simplexSolver.compute_points( wWitnessOnA, wWitnessOnB );
assert( ( squaredDistance > 0 ) && "squaredDistance is zero!" );
SimdScalar vLength = sqrt( squaredDistance );
wWitnessOnA -= v * ( pConvexA->GetMargin() / vLength );
wWitnessOnB += v * ( pConvexB->GetMargin() / vLength );
penDepth = pConvexA->GetMargin() + pConvexB->GetMargin() - vLength;
// Returning true means that Hybrid's result is ok and there's no need to run EPA
return true;
}
//add current vertex to simplex
simplexSolver.addVertex( w, pWorld, qWorld );
//calculate the closest point to the origin (update vector v)
if ( !simplexSolver.closest( v ) )
{
simplexSolver.compute_points( wWitnessOnA, wWitnessOnB );
assert( ( squaredDistance > 0 ) && "squaredDistance is zero!" );
SimdScalar vLength = sqrt( squaredDistance );
wWitnessOnA -= v * ( pConvexA->GetMargin() / vLength );
wWitnessOnB += v * ( pConvexB->GetMargin() / vLength );
penDepth = pConvexA->GetMargin() + pConvexB->GetMargin() - vLength;
// Returning true means that Hybrid's result is ok and there's no need to run EPA
return true;
}
SimdScalar previousSquaredDistance = squaredDistance;
squaredDistance = v.length2();
//are we getting any closer ?
if ( previousSquaredDistance - squaredDistance <= SIMD_EPSILON * previousSquaredDistance )
{
simplexSolver.backup_closest( v );
squaredDistance = v.length2();
simplexSolver.compute_points( wWitnessOnA, wWitnessOnB );
assert( ( squaredDistance > 0 ) && "squaredDistance is zero!" );
SimdScalar vLength = sqrt( squaredDistance );
wWitnessOnA -= v * ( pConvexA->GetMargin() / vLength );
wWitnessOnB += v * ( pConvexB->GetMargin() / vLength );
penDepth = pConvexA->GetMargin() + pConvexB->GetMargin() - vLength;
// Returning true means that Hybrid's result is ok and there's no need to run EPA
return true;
}
if ( simplexSolver.fullSimplex() || ( squaredDistance <= SIMD_EPSILON * simplexSolver.maxVertex() ) )
{
// Convex Shapes intersect - we need to run EPA
// Returning false means that Hybrid couldn't do anything for us
// and that we need to run EPA to calculate the pen depth
return false;
}
++nbIterations;
}
}
bool Epa::Initialize( SimplexSolverInterface& simplexSolver )
{
// Run GJK on the enlarged shapes to obtain a simplex of the enlarged CSO
SimdVector3 v( 1, 0, 0 );
SimdScalar squaredDistance = SIMD_INFINITY;
SimdScalar delta = 0.f;
simplexSolver.reset();
int nbIterations = 0;
while ( true )
{
EPA_DEBUG_ASSERT( ( v.length2() > 0 ) ,"Warning : v has zero magnitude!" );
SimdVector3 seperatingAxisInA = -v * m_transformA.getBasis();
SimdVector3 seperatingAxisInB = v * m_transformB.getBasis();
SimdVector3 pInA = m_pConvexShapeA->LocalGetSupportingVertex( seperatingAxisInA );
SimdVector3 qInB = m_pConvexShapeB->LocalGetSupportingVertex( seperatingAxisInB );
SimdPoint3 pWorld = m_transformA( pInA );
SimdPoint3 qWorld = m_transformB( qInB );
SimdVector3 w = pWorld - qWorld;
delta = v.dot( w );
EPA_DEBUG_ASSERT( ( delta <= 0 ) ,"Shapes are disjoint, EPA should have never been called!" );
if ( delta > 0.f )
return false;
EPA_DEBUG_ASSERT( !simplexSolver.inSimplex( w ) ,"Shapes are disjoint, EPA should have never been called!" );
if (simplexSolver.inSimplex( w ))
return false;
// Add support point to simplex
simplexSolver.addVertex( w, pWorld, qWorld );
bool closestOk = simplexSolver.closest( v );
EPA_DEBUG_ASSERT( closestOk ,"Shapes are disjoint, EPA should have never been called!" );
if (!closestOk)
return false;
SimdScalar prevVSqrd = squaredDistance;
squaredDistance = v.length2();
// Is v converging to v(A-B) ?
EPA_DEBUG_ASSERT( ( ( prevVSqrd - squaredDistance ) > SIMD_EPSILON * prevVSqrd ) ,
"Shapes are disjoint, EPA should have never been called!" );
if (( ( prevVSqrd - squaredDistance ) <= SIMD_EPSILON * prevVSqrd ))
return false;
if ( simplexSolver.fullSimplex() || ( squaredDistance <= SIMD_EPSILON * simplexSolver.maxVertex() ) )
{
break;
}
++nbIterations;
}
SimdPoint3 simplexPoints[ 5 ];
SimdPoint3 wSupportPointsOnA[ 5 ];
SimdPoint3 wSupportPointsOnB[ 5 ];
int nbSimplexPoints = simplexSolver.getSimplex( wSupportPointsOnA, wSupportPointsOnB, simplexPoints );
// nbSimplexPoints can't be one because cases where the origin is on the boundary are handled
// by hybrid penetration depth
EPA_DEBUG_ASSERT( ( ( nbSimplexPoints > 1 ) ,( nbSimplexPoints <= 4 ) ) ,
"Hybrid Penetration Depth algorithm failed!" );
int nbPolyhedronPoints = nbSimplexPoints;
#ifndef EPA_POLYHEDRON_USE_PLANES
int initTetraIndices[ 4 ] = { 0, 1, 2, 3 };
#endif
// Prepare initial polyhedron to start EPA from
if ( nbSimplexPoints == 1 )
{
return false;
}
else if ( nbSimplexPoints == 2 )
{
// We have a line segment inside the CSO that contains the origin
// Create an hexahedron ( two tetrahedron glued together ) by adding 3 new points
SimdVector3 d = simplexPoints[ 0 ] - simplexPoints[ 1 ];
d.normalize();
SimdVector3 v1;
SimdVector3 v2;
SimdVector3 v3;
SimdVector3 e1;
SimdScalar absx = abs( d.getX() );
SimdScalar absy = abs( d.getY() );
SimdScalar absz = abs( d.getZ() );
if ( absx < absy )
{
if ( absx < absz )
{
e1.setX( 1 );
}
else
{
e1.setZ( 1 );
}
}
else
{
if ( absy < absz )
{
e1.setY( 1 );
}
else
{
e1.setZ( 1 );
}
}
v1 = d.cross( e1 );
v1.normalize();
v2 = v1.rotate( d, 120 * SIMD_RADS_PER_DEG );
v3 = v2.rotate( d, 120 * SIMD_RADS_PER_DEG );
nbPolyhedronPoints = 5;
SimdVector3 seperatingAxisInA = v1 * m_transformA.getBasis();
SimdVector3 seperatingAxisInB = -v1 * m_transformB.getBasis();
SimdVector3 p = m_pConvexShapeA->LocalGetSupportingVertex( seperatingAxisInA );
SimdVector3 q = m_pConvexShapeB->LocalGetSupportingVertex( seperatingAxisInB );
SimdPoint3 pWorld = m_transformA( p );
SimdPoint3 qWorld = m_transformB( q );
wSupportPointsOnA[ 2 ] = pWorld;
wSupportPointsOnB[ 2 ] = qWorld;
simplexPoints[ 2 ] = wSupportPointsOnA[ 2 ] - wSupportPointsOnB[ 2 ];
seperatingAxisInA = v2 * m_transformA.getBasis();
seperatingAxisInB = -v2 * m_transformB.getBasis();
p = m_pConvexShapeA->LocalGetSupportingVertex( seperatingAxisInA );
q = m_pConvexShapeB->LocalGetSupportingVertex( seperatingAxisInB );
pWorld = m_transformA( p );
qWorld = m_transformB( q );
wSupportPointsOnA[ 3 ] = pWorld;
wSupportPointsOnB[ 3 ] = qWorld;
simplexPoints[ 3 ] = wSupportPointsOnA[ 3 ] - wSupportPointsOnB[ 3 ];
seperatingAxisInA = v3 * m_transformA.getBasis();
seperatingAxisInB = -v3 * m_transformB.getBasis();
p = m_pConvexShapeA->LocalGetSupportingVertex( seperatingAxisInA );
q = m_pConvexShapeB->LocalGetSupportingVertex( seperatingAxisInB );
pWorld = m_transformA( p );
qWorld = m_transformB( q );
wSupportPointsOnA[ 4 ] = pWorld;
wSupportPointsOnB[ 4 ] = qWorld;
simplexPoints[ 4 ] = wSupportPointsOnA[ 4 ] - wSupportPointsOnB[ 4 ];
#ifndef EPA_POLYHEDRON_USE_PLANES
if ( TetrahedronContainsOrigin( simplexPoints[ 0 ], simplexPoints[ 2 ], simplexPoints[ 3 ], simplexPoints[ 4 ] ) )
{
initTetraIndices[ 1 ] = 2;
initTetraIndices[ 2 ] = 3;
initTetraIndices[ 3 ] = 4;
}
else
{
if ( TetrahedronContainsOrigin( simplexPoints[ 1 ], simplexPoints[ 2 ], simplexPoints[ 3 ], simplexPoints[ 4 ] ) )
{
initTetraIndices[ 0 ] = 1;
initTetraIndices[ 1 ] = 2;
initTetraIndices[ 2 ] = 3;
initTetraIndices[ 3 ] = 4;
}
else
{
// No tetrahedron contains the origin
assert( false && "Unable to find an initial tetrahedron that contains the origin!" );
return false;
}
}
#endif
}
else if ( nbSimplexPoints == 3 )
{
// We have a triangle inside the CSO that contains the origin
// Create an hexahedron ( two tetrahedron glued together ) by adding 2 new points
SimdVector3 v0 = simplexPoints[ 2 ] - simplexPoints[ 0 ];
SimdVector3 v1 = simplexPoints[ 1 ] - simplexPoints[ 0 ];
SimdVector3 triangleNormal = v0.cross( v1 );
triangleNormal.normalize();
nbPolyhedronPoints = 5;
SimdVector3 seperatingAxisInA = triangleNormal * m_transformA.getBasis();
SimdVector3 seperatingAxisInB = -triangleNormal * m_transformB.getBasis();
SimdVector3 p = m_pConvexShapeA->LocalGetSupportingVertex( seperatingAxisInA );
SimdVector3 q = m_pConvexShapeB->LocalGetSupportingVertex( seperatingAxisInB );
SimdPoint3 pWorld = m_transformA( p );
SimdPoint3 qWorld = m_transformB( q );
wSupportPointsOnA[ 3 ] = pWorld;
wSupportPointsOnB[ 3 ] = qWorld;
simplexPoints[ 3 ] = wSupportPointsOnA[ 3 ] - wSupportPointsOnB[ 3 ];
#ifndef EPA_POLYHEDRON_USE_PLANES
// We place this check here because if the tetrahedron contains the origin
// there is no need to sample another support point
if ( !TetrahedronContainsOrigin( simplexPoints[ 0 ], simplexPoints[ 1 ], simplexPoints[ 2 ], simplexPoints[ 3 ] ) )
{
#endif
seperatingAxisInA = -triangleNormal * m_transformA.getBasis();
seperatingAxisInB = triangleNormal * m_transformB.getBasis();
p = m_pConvexShapeA->LocalGetSupportingVertex( seperatingAxisInA );
q = m_pConvexShapeB->LocalGetSupportingVertex( seperatingAxisInB );
pWorld = m_transformA( p );
qWorld = m_transformB( q );
wSupportPointsOnA[ 4 ] = pWorld;
wSupportPointsOnB[ 4 ] = qWorld;
simplexPoints[ 4 ] = wSupportPointsOnA[ 4 ] - wSupportPointsOnB[ 4 ];
#ifndef EPA_POLYHEDRON_USE_PLANES
if ( TetrahedronContainsOrigin( simplexPoints[ 0 ], simplexPoints[ 1 ], simplexPoints[ 2 ], simplexPoints[ 4 ] ) )
{
initTetraIndices[ 3 ] = 4;
}
else
{
// No tetrahedron contains the origin
assert( false && "Unable to find an initial tetrahedron that contains the origin!" );
return false;
}
}
#endif
}
#ifdef _DEBUG
else if ( nbSimplexPoints == 4 )
{
EPA_DEBUG_ASSERT( TetrahedronContainsOrigin( simplexPoints ) ,"Initial tetrahedron does not contain the origin!" );
}
#endif
#ifndef EPA_POLYHEDRON_USE_PLANES
SimdPoint3 wTetraPoints[ 4 ] = { simplexPoints[ initTetraIndices[ 0 ] ],
simplexPoints[ initTetraIndices[ 1 ] ],
simplexPoints[ initTetraIndices[ 2 ] ],
simplexPoints[ initTetraIndices[ 3 ] ] };
SimdPoint3 wTetraSupportPointsOnA[ 4 ] = { wSupportPointsOnA[ initTetraIndices[ 0 ] ],
wSupportPointsOnA[ initTetraIndices[ 1 ] ],
wSupportPointsOnA[ initTetraIndices[ 2 ] ],
wSupportPointsOnA[ initTetraIndices[ 3 ] ] };
SimdPoint3 wTetraSupportPointsOnB[ 4 ] = { wSupportPointsOnB[ initTetraIndices[ 0 ] ],
wSupportPointsOnB[ initTetraIndices[ 1 ] ],
wSupportPointsOnB[ initTetraIndices[ 2 ] ],
wSupportPointsOnB[ initTetraIndices[ 3 ] ] };
#endif
#ifdef EPA_POLYHEDRON_USE_PLANES
if ( !m_polyhedron.Create( simplexPoints, wSupportPointsOnA, wSupportPointsOnB, nbPolyhedronPoints ) )
#else
if ( !m_polyhedron.Create( wTetraPoints, wTetraSupportPointsOnA, wTetraSupportPointsOnB, 4 ) )
#endif
{
// Failed to create initial polyhedron
EPA_DEBUG_ASSERT( false ,"Failed to create initial polyhedron!" );
return false;
}
// Add initial faces to priority queue
#ifdef _DEBUG
//m_polyhedron._dbgSaveToFile( "epa_start.dbg" );
#endif
std::list< EpaFace* >& faces = m_polyhedron.GetFaces();
std::list< EpaFace* >::iterator facesItr( faces.begin() );
while ( facesItr != faces.end() )
{
EpaFace* pFace = *facesItr;
if ( !pFace->m_deleted )
{
//#ifdef EPA_POLYHEDRON_USE_PLANES
// if ( pFace->m_planeDistance >= 0 )
// {
// m_polyhedron._dbgSaveToFile( "epa_start.dbg" );
// assert( false && "Face's plane distance equal or greater than 0!" );
// }
//#endif
if ( pFace->IsAffinelyDependent() )
{
EPA_DEBUG_ASSERT( false ,"One initial face is affinely dependent!" );
return false;
}
if ( pFace->m_vSqrd <= 0 )
{
EPA_DEBUG_ASSERT( false ,"Face containing the origin!" );
return false;
}
if ( pFace->IsClosestPointInternal() )
{
m_faceEntries.push_back( pFace );
std::push_heap( m_faceEntries.begin(), m_faceEntries.end(), CompareEpaFaceEntries );
}
}
++facesItr;
}
#ifdef _DEBUG
//m_polyhedron._dbgSaveToFile( "epa_start.dbg" );
#endif
EPA_DEBUG_ASSERT( !m_faceEntries.empty() ,"No faces added to heap!" );
return true;
}
