Example #1
0
        public static void Contacts(int particleIndex,
                                    float4 position,
                                    quaternion orientation,
                                    float4 radii,
                                    int colliderIndex,
                                    BurstAffineTransform transform,
                                    BurstColliderShape shape,
                                    NativeQueue <BurstContact> .ParallelWriter contacts)
        {
            float4 center = shape.center * transform.scale;

            position = transform.InverseTransformPointUnscaled(position) - center;

            float radius           = shape.size.x * math.cmax(transform.scale.xyz);
            float distanceToCenter = math.length(position);

            float4 normal = position / distanceToCenter;

            BurstContact c = new BurstContact
            {
                entityA = particleIndex,
                entityB = colliderIndex,
                point   = center + normal * radius,
                normal  = normal,
            };

            c.point  = transform.TransformPointUnscaled(c.point);
            c.normal = transform.TransformDirection(c.normal);

            c.distance = distanceToCenter - radius - (shape.contactOffset + BurstMath.EllipsoidRadius(c.normal, orientation, radii.xyz));

            contacts.Enqueue(c);
        }
            public void Execute(int workItemIndex)
            {
                int start, end;

                batchData.GetConstraintRange(workItemIndex, out start, out end);

                for (int i = start; i < end; ++i)
                {
                    var contact = contacts[i];

                    // update contact basis:
                    contact.CalculateBasis(velocities[contact.entityA] - velocities[contact.entityB]);

                    // update contact masses:
                    int  aMaterialIndex  = particleMaterialIndices[contact.entityA];
                    int  bMaterialIndex  = particleMaterialIndices[contact.entityB];
                    bool rollingContacts = (aMaterialIndex >= 0 ? collisionMaterials[aMaterialIndex].rollingContacts > 0 : false) |
                                           (bMaterialIndex >= 0 ? collisionMaterials[bMaterialIndex].rollingContacts > 0 : false);

                    contact.CalculateContactMassesA(ref invMasses, ref prevPositions, ref prevOrientations, ref invInertiaTensors, rollingContacts);
                    contact.CalculateContactMassesB(ref invMasses, ref prevPositions, ref prevOrientations, ref invInertiaTensors, rollingContacts);

                    // update contact distance:
                    float dAB = math.dot(prevPositions[contact.entityA] - prevPositions[contact.entityB], contact.normal);
                    float dA  = BurstMath.EllipsoidRadius(contact.normal, prevOrientations[contact.entityA], radii[contact.entityA].xyz);
                    float dB  = BurstMath.EllipsoidRadius(contact.normal, prevOrientations[contact.entityB], radii[contact.entityB].xyz);
                    contact.distance = dAB - (dA + dB);

                    contacts[i] = contact;
                }
            }
            public void Execute(int i)
            {
                var contact = contacts[i];

                int simplexStart = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSize);

                // get the material from the first particle in the simplex:
                int  aMaterialIndex  = particleMaterialIndices[simplices[simplexStart]];
                bool rollingContacts = aMaterialIndex >= 0 ? collisionMaterials[aMaterialIndex].rollingContacts > 0 : false;

                float4     relativeVelocity       = float4.zero;
                float4     simplexPrevPosition    = float4.zero;
                quaternion simplexPrevOrientation = new quaternion(0, 0, 0, 0);
                float      simplexInvMass         = 0;
                float4     simplexInvInertia      = float4.zero;
                float      simplexRadius          = 0;

                for (int j = 0; j < simplexSize; ++j)
                {
                    int particleIndex = simplices[simplexStart + j];
                    relativeVelocity             += velocities[particleIndex] * contact.pointA[j];
                    simplexPrevPosition          += prevPositions[particleIndex] * contact.pointA[j];
                    simplexPrevOrientation.value += prevOrientations[particleIndex].value * contact.pointA[j];
                    simplexInvMass    += invMasses[particleIndex] * contact.pointA[j];
                    simplexInvInertia += invInertiaTensors[particleIndex] * contact.pointA[j];
                    simplexRadius     += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
                }

                // if there's a rigidbody present, subtract its velocity from the relative velocity:
                int rigidbodyIndex = shapes[contact.bodyB].rigidbodyIndex;

                if (rigidbodyIndex >= 0)
                {
                    relativeVelocity -= BurstMath.GetRigidbodyVelocityAtPoint(rigidbodyIndex, contact.pointB, rigidbodies, rigidbodyLinearDeltas, rigidbodyAngularDeltas, inertialFrame.frame);

                    int bMaterialIndex = shapes[contact.bodyB].materialIndex;
                    rollingContacts |= bMaterialIndex >= 0 ? collisionMaterials[bMaterialIndex].rollingContacts > 0 : false;
                }

                // update contact distance
                contact.distance = math.dot(simplexPrevPosition - contact.pointB, contact.normal) - simplexRadius;

                // calculate contact point in A's surface:
                float4 contactPoint = contact.pointB + contact.normal * contact.distance;

                // update contact orthonormal basis:
                contact.CalculateBasis(relativeVelocity);

                // calculate A's contact mass.
                contact.CalculateContactMassesA(simplexInvMass, simplexInvInertia, simplexPrevPosition, simplexPrevOrientation, contactPoint, rollingContacts);

                // calculate B's contact mass.
                if (rigidbodyIndex >= 0)
                {
                    contact.CalculateContactMassesB(rigidbodies[rigidbodyIndex], inertialFrame.frame);
                }

                contacts[i] = contact;
            }
Example #4
0
            public void Execute(int i)
            {
                var contact = contacts[i];

                int  aMaterialIndex  = particleMaterialIndices[contact.entityA];
                bool rollingContacts = aMaterialIndex >= 0 ? collisionMaterials[aMaterialIndex].rollingContacts > 0 : false;

                int rigidbodyIndex = shapes[contact.entityB].rigidbodyIndex;

                if (rigidbodyIndex >= 0)
                {
                    // update contact basis:
                    float4 relativeVelocity = velocities[contact.entityA] - BurstMath.GetRigidbodyVelocityAtPoint(rigidbodies[rigidbodyIndex], contact.ContactPointB, rigidbodyLinearDeltas[rigidbodyIndex], rigidbodyAngularDeltas[rigidbodyIndex], inertialFrame.frame);
                    contact.CalculateBasis(relativeVelocity);

                    int bMaterialIndex = shapes[contact.entityB].materialIndex;
                    rollingContacts |= bMaterialIndex >= 0 ? collisionMaterials[bMaterialIndex].rollingContacts > 0 : false;

                    // update contact masses:
                    contact.CalculateContactMassesA(ref invMasses, ref prevPositions, ref prevOrientations, ref invInertiaTensors, rollingContacts);
                    contact.CalculateContactMassesB(rigidbodies[rigidbodyIndex], false);
                }
                else
                {
                    // update contact basis:
                    contact.CalculateBasis(velocities[contact.entityA]);

                    // update contact masses:
                    contact.CalculateContactMassesA(ref invMasses, ref prevPositions, ref prevOrientations, ref invInertiaTensors, rollingContacts);
                }

                // update contact distance
                float dAB = math.dot(prevPositions[contact.entityA] - contact.point, contact.normal);
                float dA  = BurstMath.EllipsoidRadius(contact.normal, prevOrientations[contact.entityA], radii[contact.entityA].xyz);
                float dB  = shapes[contact.entityB].contactOffset;

                contact.distance = dAB - (dA + dB);

                contacts[i] = contact;
            }
Example #5
0
        private static void BIHTraverse(int particleIndex,
                                        int colliderIndex,
                                        float4 particlePosition,
                                        quaternion particleOrientation,
                                        float4 particleVelocity,
                                        float4 particleRadii,
                                        ref BurstAabb particleBounds,
                                        int nodeIndex,
                                        ref NativeArray <BIHNode> bihNodes,
                                        ref NativeArray <Edge> edges,
                                        ref NativeArray <float2> vertices,
                                        ref EdgeMeshHeader header,
                                        ref BurstAffineTransform colliderToSolver,
                                        ref BurstColliderShape shape,
                                        NativeQueue <BurstContact> .ParallelWriter contacts)
        {
            var node = bihNodes[header.firstNode + nodeIndex];

            // amount by which we should inflate aabbs:
            float offset = shape.contactOffset + particleRadii.x;

            if (node.firstChild >= 0)
            {
                // visit min node:
                if (particleBounds.min[node.axis] - offset <= node.min)
                {
                    BIHTraverse(particleIndex, colliderIndex,
                                particlePosition, particleOrientation, particleVelocity, particleRadii, ref particleBounds,
                                node.firstChild, ref bihNodes, ref edges, ref vertices, ref header,
                                ref colliderToSolver, ref shape, contacts);
                }

                // visit max node:
                if (particleBounds.max[node.axis] + offset >= node.max)
                {
                    BIHTraverse(particleIndex, colliderIndex,
                                particlePosition, particleOrientation, particleVelocity, particleRadii, ref particleBounds,
                                node.firstChild + 1, ref bihNodes, ref edges, ref vertices, ref header,
                                ref colliderToSolver, ref shape, contacts);
                }
            }
            else
            {
                // precalculate inverse of velocity vector for ray/aabb intersections:
                float4 invDir = math.rcp(particleVelocity);

                // contacts against all triangles:
                for (int i = node.start; i < node.start + node.count; ++i)
                {
                    Edge t = edges[header.firstEdge + i];

                    float4 v1 = new float4(vertices[header.firstVertex + t.i1], 0, 0) * colliderToSolver.scale;
                    float4 v2 = new float4(vertices[header.firstVertex + t.i2], 0, 0) * colliderToSolver.scale;

                    BurstAabb aabb = new BurstAabb(v1, v2, 0.01f);
                    aabb.Expand(new float4(offset));

                    // only generate a contact if the particle trajectory intersects its inflated aabb:
                    if (aabb.IntersectsRay(particlePosition, invDir, true))
                    {
                        float4 point      = BurstMath.NearestPointOnEdge(v1, v2, particlePosition);
                        float4 pointToTri = particlePosition - point;
                        float  distance   = math.length(pointToTri);

                        if (distance > BurstMath.epsilon)
                        {
                            BurstContact c = new BurstContact()
                            {
                                entityA = particleIndex,
                                entityB = colliderIndex,
                                point   = colliderToSolver.TransformPointUnscaled(point),
                                normal  = colliderToSolver.TransformDirection(pointToTri / distance),
                            };

                            c.distance = distance - (shape.contactOffset + BurstMath.EllipsoidRadius(c.normal, particleOrientation, particleRadii.xyz));

                            contacts.Enqueue(c);
                        }
                    }
                }
            }
        }
            public void InteractionTest(int A, int B)
            {
                bool samePhase     = (phases[A] & (int)Oni.ParticleFlags.GroupMask) == (phases[B] & (int)Oni.ParticleFlags.GroupMask);
                bool noSelfCollide = (phases[A] & (int)Oni.ParticleFlags.SelfCollide) == 0 || (phases[B] & (int)Oni.ParticleFlags.SelfCollide) == 0;

                // only particles of a different phase or set to self-collide can interact.
                if (samePhase && noSelfCollide)
                {
                    return;
                }

                // Predict positions at the end of the whole step:
                float4 predictedPositionA = positions[A] + velocities[A] * dt;
                float4 predictedPositionB = positions[B] + velocities[B] * dt;

                // Calculate particle center distance:
                float4 dab = predictedPositionA - predictedPositionB;
                float  d2  = math.lengthsq(dab);

                // if both particles are fluid, check their smoothing radii:
                if ((phases[A] & (int)Oni.ParticleFlags.Fluid) != 0 &&
                    (phases[B] & (int)Oni.ParticleFlags.Fluid) != 0)
                {
                    float fluidDistance = math.max(fluidRadii[A], fluidRadii[B]);
                    if (d2 <= fluidDistance * fluidDistance)
                    {
                        fluidInteractionsQueue.Enqueue(new FluidInteraction {
                            particleA = A, particleB = B
                        });
                    }
                }
                else // at least one solid particle
                {
                    float solidDistance = radii[A].x + radii[B].x;

                    // if these particles are self-colliding (have same phase), see if they intersect at rest.
                    if (samePhase &&
                        restPositions[A].w > 0.5f &&
                        restPositions[B].w > 0.5f)
                    {
                        // if rest positions intersect, return too.
                        float sqr_rest_distance = math.lengthsq(restPositions[A] - restPositions[B]);
                        if (sqr_rest_distance < solidDistance * solidDistance)
                        {
                            return;
                        }
                    }

                    // calculate distance at which particles are able to interact:
                    int   matIndexA           = particleMaterialIndices[A];
                    int   matIndexB           = particleMaterialIndices[B];
                    float interactionDistance = solidDistance * 1.2f + (matIndexA >= 0 ? collisionMaterials[matIndexA].stickDistance : 0) +
                                                (matIndexB >= 0 ? collisionMaterials[matIndexB].stickDistance : 0);

                    // if the distance between their predicted positions is smaller than the interaction distance:
                    if (math.lengthsq(dab) <= interactionDistance * interactionDistance)
                    {
                        // calculate contact normal and distance:
                        float4 normal   = positions[A] - positions[B];
                        float  distance = math.length(normal);

                        if (distance > BurstMath.epsilon)
                        {
                            normal /= distance;

                            float rA = BurstMath.EllipsoidRadius(normal, orientations[A], radii[A].xyz);
                            float rB = BurstMath.EllipsoidRadius(normal, orientations[B], radii[B].xyz);

                            // adapt normal for one-sided particles:
                            if ((phases[A] & (int)Oni.ParticleFlags.OneSided) != 0 &&
                                (phases[B] & (int)Oni.ParticleFlags.OneSided) != 0)
                            {
                                float3 adjustment = float3.zero;
                                if (rA < rB)
                                {
                                    adjustment = math.mul(orientations[A], new float3(0, 0, -1));
                                }
                                else
                                {
                                    adjustment = math.mul(orientations[B], new float3(0, 0, 1));
                                }

                                float dot = math.dot(normal.xyz, adjustment);
                                if (dot < 0)
                                {
                                    normal -= 2 * dot * new float4(adjustment, 0);
                                }
                            }

                            contactsQueue.Enqueue(new BurstContact
                            {
                                entityA  = A,
                                entityB  = B,
                                point    = positions[B] + normal * rB,
                                normal   = normal,
                                distance = distance - (rA + rB)
                            });
                        }
                    }
                }
            }
            public void Execute(int workItemIndex)
            {
                int start, end;

                batchData.GetConstraintRange(workItemIndex, out start, out end);

                for (int i = start; i < end; ++i)
                {
                    var contact = contacts[i];

                    int simplexStartA = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSizeA);
                    int simplexStartB = simplexCounts.GetSimplexStartAndSize(contact.bodyB, out int simplexSizeB);


                    // Combine collision materials:
                    BurstCollisionMaterial material = CombineCollisionMaterials(simplices[simplexStartA], simplices[simplexStartB]);

                    float4 simplexPositionA = float4.zero, simplexPositionB = float4.zero;
                    float  simplexRadiusA = 0, simplexRadiusB = 0;

                    for (int j = 0; j < simplexSizeA; ++j)
                    {
                        int particleIndex = simplices[simplexStartA + j];
                        simplexPositionA += positions[particleIndex] * contact.pointA[j];
                        simplexRadiusA   += BurstMath.EllipsoidRadius(contact.normal, orientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
                    }
                    for (int j = 0; j < simplexSizeB; ++j)
                    {
                        int particleIndex = simplices[simplexStartB + j];
                        simplexPositionB += positions[particleIndex] * contact.pointB[j];
                        simplexRadiusB   += BurstMath.EllipsoidRadius(contact.normal, orientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
                    }

                    float4 posA = simplexPositionA - contact.normal * simplexRadiusA;
                    float4 posB = simplexPositionB + contact.normal * simplexRadiusB;

                    // adhesion:
                    float lambda = contact.SolveAdhesion(posA, posB, material.stickDistance, material.stickiness, substepTime);

                    // depenetration:
                    lambda += contact.SolvePenetration(posA, posB, solverParameters.maxDepenetration * substepTime);

                    // Apply normal impulse to both particles (w/ shock propagation):
                    if (math.abs(lambda) > BurstMath.epsilon)
                    {
                        float  shock = solverParameters.shockPropagation * math.dot(contact.normal, math.normalizesafe(gravity));
                        float4 delta = lambda * contact.normal;

                        float baryScale = BurstMath.BaryScale(contact.pointA);
                        for (int j = 0; j < simplexSizeA; ++j)
                        {
                            int particleIndex = simplices[simplexStartA + j];
                            deltas[particleIndex] += delta * invMasses[particleIndex] * contact.pointA[j] * baryScale * (1 - shock);
                            counts[particleIndex]++;
                        }

                        baryScale = BurstMath.BaryScale(contact.pointB);
                        for (int j = 0; j < simplexSizeB; ++j)
                        {
                            int particleIndex = simplices[simplexStartB + j];
                            deltas[particleIndex] -= delta * invMasses[particleIndex] * contact.pointB[j] * baryScale * (1 + shock);
                            counts[particleIndex]++;
                        }
                    }

                    // Apply position deltas immediately, if using sequential evaluation:
                    if (constraintParameters.evaluationOrder == Oni.ConstraintParameters.EvaluationOrder.Sequential)
                    {
                        for (int j = 0; j < simplexSizeA; ++j)
                        {
                            int particleIndex = simplices[simplexStartA + j];
                            BurstConstraintsBatchImpl.ApplyPositionDelta(particleIndex, constraintParameters.SORFactor, ref positions, ref deltas, ref counts);
                        }

                        for (int j = 0; j < simplexSizeB; ++j)
                        {
                            int particleIndex = simplices[simplexStartB + j];
                            BurstConstraintsBatchImpl.ApplyPositionDelta(particleIndex, constraintParameters.SORFactor, ref positions, ref deltas, ref counts);
                        }
                    }

                    contacts[i] = contact;
                }
            }
            public void Execute(int workItemIndex)
            {
                int start, end;

                batchData.GetConstraintRange(workItemIndex, out start, out end);

                for (int i = start; i < end; ++i)
                {
                    var contact = contacts[i];

                    int simplexStartA = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSizeA);
                    int simplexStartB = simplexCounts.GetSimplexStartAndSize(contact.bodyB, out int simplexSizeB);

                    float4     simplexVelocityA        = float4.zero;
                    float4     simplexPrevPositionA    = float4.zero;
                    quaternion simplexPrevOrientationA = new quaternion(0, 0, 0, 0);
                    float      simplexRadiusA          = 0;
                    float      simplexInvMassA         = 0;
                    float4     simplexInvInertiaA      = float4.zero;

                    float4     simplexVelocityB        = float4.zero;
                    float4     simplexPrevPositionB    = float4.zero;
                    quaternion simplexPrevOrientationB = new quaternion(0, 0, 0, 0);
                    float      simplexRadiusB          = 0;
                    float      simplexInvMassB         = 0;
                    float4     simplexInvInertiaB      = float4.zero;

                    for (int j = 0; j < simplexSizeA; ++j)
                    {
                        int particleIndex = simplices[simplexStartA + j];
                        simplexVelocityA              += velocities[particleIndex] * contact.pointA[j];
                        simplexPrevPositionA          += prevPositions[particleIndex] * contact.pointA[j];
                        simplexPrevOrientationA.value += prevOrientations[particleIndex].value * contact.pointA[j];
                        simplexInvMassA    += invMasses[particleIndex] * contact.pointA[j];
                        simplexInvInertiaA += invInertiaTensors[particleIndex] * contact.pointA[j];
                        simplexRadiusA     += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
                    }

                    for (int j = 0; j < simplexSizeB; ++j)
                    {
                        int particleIndex = simplices[simplexStartB + j];
                        simplexVelocityB              += velocities[particleIndex] * contact.pointB[j];
                        simplexPrevPositionB          += prevPositions[particleIndex] * contact.pointB[j];
                        simplexPrevOrientationB.value += prevOrientations[particleIndex].value * contact.pointB[j];
                        simplexInvMassB    += invMasses[particleIndex] * contact.pointB[j];
                        simplexInvInertiaB += invInertiaTensors[particleIndex] * contact.pointB[j];
                        simplexRadiusB     += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointB[j];
                    }

                    // update contact distance
                    float dAB = math.dot(simplexPrevPositionA - simplexPrevPositionB, contact.normal);
                    contact.distance = dAB - (simplexRadiusA + simplexRadiusB);

                    // calculate contact points:
                    float4 contactPointA = simplexPrevPositionB + contact.normal * (contact.distance + simplexRadiusB);
                    float4 contactPointB = simplexPrevPositionA - contact.normal * (contact.distance + simplexRadiusA);

                    // update contact basis:
                    contact.CalculateBasis(simplexVelocityA - simplexVelocityB);

                    // update contact masses:
                    int  aMaterialIndex  = particleMaterialIndices[simplices[simplexStartA]];
                    int  bMaterialIndex  = particleMaterialIndices[simplices[simplexStartB]];
                    bool rollingContacts = (aMaterialIndex >= 0 ? collisionMaterials[aMaterialIndex].rollingContacts > 0 : false) |
                                           (bMaterialIndex >= 0 ? collisionMaterials[bMaterialIndex].rollingContacts > 0 : false);

                    contact.CalculateContactMassesA(simplexInvMassA, simplexInvInertiaA, simplexPrevPositionA, simplexPrevOrientationA, contactPointA, rollingContacts);
                    contact.CalculateContactMassesB(simplexInvMassB, simplexInvInertiaB, simplexPrevPositionB, simplexPrevOrientationB, contactPointB, rollingContacts);

                    contacts[i] = contact;
                }
            }
        public static void Contacts(int particleIndex,
                                    int colliderIndex,
                                    float4 position,
                                    quaternion orientation,
                                    float4 radii,
                                    ref NativeArray <float> heightMap,
                                    HeightFieldHeader header,
                                    BurstAffineTransform colliderToSolver,
                                    BurstColliderShape shape,
                                    NativeQueue <BurstContact> .ParallelWriter contacts)
        {
            float4 pos = colliderToSolver.InverseTransformPoint(position);

            BurstContact c = new BurstContact
            {
                entityA = particleIndex,
                entityB = colliderIndex,
            };

            int resolutionU = (int)shape.center.x;
            int resolutionV = (int)shape.center.y;

            // calculate terrain cell size:
            float cellWidth  = shape.size.x / (resolutionU - 1);
            float cellHeight = shape.size.z / (resolutionV - 1);

            // calculate particle bounds min/max cells:
            int2 min = new int2((int)math.floor((pos[0] - radii[0]) / cellWidth), (int)math.floor((pos[2] - radii[0]) / cellHeight));
            int2 max = new int2((int)math.floor((pos[0] + radii[0]) / cellWidth), (int)math.floor((pos[2] + radii[0]) / cellHeight));

            for (int su = min[0]; su <= max[0]; ++su)
            {
                if (su >= 0 && su < resolutionU - 1)
                {
                    for (int sv = min[1]; sv <= max[1]; ++sv)
                    {
                        if (sv >= 0 && sv < resolutionV - 1)
                        {
                            // calculate neighbor sample indices:
                            int csu1 = math.clamp(su + 1, 0, resolutionU - 1);
                            int csv1 = math.clamp(sv + 1, 0, resolutionV - 1);

                            // sample heights:
                            float h1 = heightMap[header.firstSample + sv * resolutionU + su] * shape.size.y;
                            float h2 = heightMap[header.firstSample + sv * resolutionU + csu1] * shape.size.y;
                            float h3 = heightMap[header.firstSample + csv1 * resolutionU + su] * shape.size.y;
                            float h4 = heightMap[header.firstSample + csv1 * resolutionU + csu1] * shape.size.y;

                            float min_x = su * shape.size.x / (resolutionU - 1);
                            float max_x = csu1 * shape.size.x / (resolutionU - 1);
                            float min_z = sv * shape.size.z / (resolutionV - 1);
                            float max_z = csv1 * shape.size.z / (resolutionV - 1);

                            // contact with the first triangle:
                            float4 pointOnTri = BurstMath.NearestPointOnTri(new float4(min_x, h3, max_z, 0),
                                                                            new float4(max_x, h4, max_z, 0),
                                                                            new float4(min_x, h1, min_z, 0),
                                                                            pos);
                            float4 normal   = pos - pointOnTri;
                            float  distance = math.length(normal);

                            if (distance > BurstMath.epsilon)
                            {
                                c.normal = normal / distance;
                                c.point  = pointOnTri;

                                c.normal = colliderToSolver.TransformDirection(c.normal);
                                c.point  = colliderToSolver.TransformPoint(c.point);

                                c.distance = distance - (shape.contactOffset + BurstMath.EllipsoidRadius(c.normal, orientation, radii.xyz));
                                contacts.Enqueue(c);
                            }

                            // contact with the second triangle:
                            pointOnTri = BurstMath.NearestPointOnTri(new float4(min_x, h1, min_z, 0),
                                                                     new float4(max_x, h4, max_z, 0),
                                                                     new float4(max_x, h2, min_z, 0),
                                                                     pos);
                            normal   = pos - pointOnTri;
                            distance = math.length(normal);

                            if (distance > BurstMath.epsilon)
                            {
                                c.normal = normal / distance;
                                c.point  = pointOnTri;

                                c.normal = colliderToSolver.TransformDirection(c.normal);
                                c.point  = colliderToSolver.TransformPoint(c.point);

                                c.distance = distance - (shape.contactOffset + BurstMath.EllipsoidRadius(c.normal, orientation, radii.xyz));
                                contacts.Enqueue(c);
                            }
                        }
                    }
                }
            }
        }
Example #10
0
        public static void Contacts(int particleIndex,
                                    float4 position,
                                    quaternion orientation,
                                    float4 radii,
                                    int colliderIndex,
                                    BurstAffineTransform transform,
                                    BurstColliderShape shape,
                                    NativeQueue <BurstContact> .ParallelWriter contacts)
        {
            BurstContact c = new BurstContact()
            {
                entityA = particleIndex,
                entityB = colliderIndex,
            };

            float4 center = shape.center * transform.scale;

            position = transform.InverseTransformPointUnscaled(position) - center;

            int    direction = (int)shape.size.z;
            float  radius    = shape.size.x * math.max(transform.scale[(direction + 1) % 3], transform.scale[(direction + 2) % 3]);
            float  height    = math.max(radius, shape.size.y * 0.5f * transform.scale[direction]);
            float  d         = position[direction];
            float4 axisProj  = float4.zero;
            float4 cap       = float4.zero;

            axisProj[direction] = d;
            cap[direction]      = height - radius;

            float4 centerToPoint;
            float  centerToPointNorm;

            if (d > height - radius)
            { //one cap
                centerToPoint     = position - cap;
                centerToPointNorm = math.length(centerToPoint);

                c.distance = centerToPointNorm - radius;
                c.normal   = (centerToPoint / (centerToPointNorm + math.FLT_MIN_NORMAL));
                c.point    = cap + c.normal * radius;
            }
            else if (d < -height + radius)
            { // other cap
                centerToPoint     = position + cap;
                centerToPointNorm = math.length(centerToPoint);

                c.distance = centerToPointNorm - radius;
                c.normal   = (centerToPoint / (centerToPointNorm + math.FLT_MIN_NORMAL));
                c.point    = -cap + c.normal * radius;
            }
            else
            {//cylinder
                centerToPoint     = position - axisProj;
                centerToPointNorm = math.length(centerToPoint);

                c.distance = centerToPointNorm - radius;
                c.normal   = (centerToPoint / (centerToPointNorm + math.FLT_MIN_NORMAL));
                c.point    = axisProj + c.normal * radius;
            }

            c.point += center;
            c.point  = transform.TransformPointUnscaled(c.point);
            c.normal = transform.TransformDirection(c.normal);

            c.distance -= shape.contactOffset + BurstMath.EllipsoidRadius(c.normal, orientation, radii.xyz);

            contacts.Enqueue(c);
        }
Example #11
0
            public void Execute(int workItemIndex)
            {
                int start, end;

                batchData.GetConstraintRange(workItemIndex, out start, out end);

                for (int i = start; i < end; ++i)
                {
                    var contact = contacts[i];

                    int simplexStartA = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSizeA);
                    int simplexStartB = simplexCounts.GetSimplexStartAndSize(contact.bodyB, out int simplexSizeB);

                    // Combine collision materials:
                    BurstCollisionMaterial material = CombineCollisionMaterials(simplices[simplexStartA], simplices[simplexStartB]);

                    float4     prevPositionA     = float4.zero;
                    float4     linearVelocityA   = float4.zero;
                    float4     angularVelocityA  = float4.zero;
                    float4     invInertiaTensorA = float4.zero;
                    quaternion orientationA      = new quaternion(0, 0, 0, 0);
                    float      simplexRadiusA    = 0;

                    float4     prevPositionB     = float4.zero;
                    float4     linearVelocityB   = float4.zero;
                    float4     angularVelocityB  = float4.zero;
                    float4     invInertiaTensorB = float4.zero;
                    quaternion orientationB      = new quaternion(0, 0, 0, 0);
                    float      simplexRadiusB    = 0;

                    for (int j = 0; j < simplexSizeA; ++j)
                    {
                        int particleIndex = simplices[simplexStartA + j];
                        prevPositionA      += prevPositions[particleIndex] * contact.pointA[j];
                        linearVelocityA    += BurstIntegration.DifferentiateLinear(positions[particleIndex], prevPositions[particleIndex], substepTime) * contact.pointA[j];
                        angularVelocityA   += BurstIntegration.DifferentiateAngular(orientations[particleIndex], prevOrientations[particleIndex], substepTime) * contact.pointA[j];
                        invInertiaTensorA  += invInertiaTensors[particleIndex] * contact.pointA[j];
                        orientationA.value += orientations[particleIndex].value * contact.pointA[j];
                        simplexRadiusA     += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
                    }
                    for (int j = 0; j < simplexSizeB; ++j)
                    {
                        int particleIndex = simplices[simplexStartB + j];
                        prevPositionB      += prevPositions[particleIndex] * contact.pointB[j];
                        linearVelocityB    += BurstIntegration.DifferentiateLinear(positions[particleIndex], prevPositions[particleIndex], substepTime) * contact.pointB[j];
                        angularVelocityB   += BurstIntegration.DifferentiateAngular(orientations[particleIndex], prevOrientations[particleIndex], substepTime) * contact.pointB[j];
                        invInertiaTensorB  += invInertiaTensors[particleIndex] * contact.pointB[j];
                        orientationB.value += orientations[particleIndex].value * contact.pointB[j];
                        simplexRadiusB     += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointB[j];
                    }

                    float4 rA = float4.zero, rB = float4.zero;

                    // Consider angular velocities if rolling contacts are enabled:
                    if (material.rollingContacts > 0)
                    {
                        rA = -contact.normal * simplexRadiusA;
                        rB = contact.normal * simplexRadiusB;

                        linearVelocityA += new float4(math.cross(angularVelocityA.xyz, rA.xyz), 0);
                        linearVelocityB += new float4(math.cross(angularVelocityB.xyz, rB.xyz), 0);
                    }

                    // Calculate relative velocity:
                    float4 relativeVelocity = linearVelocityA - linearVelocityB;

                    // Calculate friction impulses (in the tangent and bitangent ddirections):
                    float2 impulses         = contact.SolveFriction(relativeVelocity, material.staticFriction, material.dynamicFriction, substepTime);

                    // Apply friction impulses to both particles:
                    if (math.abs(impulses.x) > BurstMath.epsilon || math.abs(impulses.y) > BurstMath.epsilon)
                    {
                        float4 tangentImpulse   = impulses.x * contact.tangent;
                        float4 bitangentImpulse = impulses.y * contact.bitangent;
                        float4 totalImpulse     = tangentImpulse + bitangentImpulse;

                        float baryScale = BurstMath.BaryScale(contact.pointA);
                        for (int j = 0; j < simplexSizeA; ++j)
                        {
                            int particleIndex = simplices[simplexStartA + j];
                            deltas[particleIndex] += (tangentImpulse * contact.tangentInvMassA + bitangentImpulse * contact.bitangentInvMassA) * substepTime * contact.pointA[j] * baryScale;
                            counts[particleIndex]++;
                        }

                        baryScale = BurstMath.BaryScale(contact.pointB);
                        for (int j = 0; j < simplexSizeB; ++j)
                        {
                            int particleIndex = simplices[simplexStartB + j];
                            deltas[particleIndex] -= (tangentImpulse * contact.tangentInvMassB + bitangentImpulse * contact.bitangentInvMassB) * substepTime * contact.pointB[j] * baryScale;
                            counts[particleIndex]++;
                        }

                        // Rolling contacts:
                        if (material.rollingContacts > 0)
                        {
                            // Calculate angular velocity deltas due to friction impulse:
                            float4x4 solverInertiaA = BurstMath.TransformInertiaTensor(invInertiaTensorA, orientationA);
                            float4x4 solverInertiaB = BurstMath.TransformInertiaTensor(invInertiaTensorB, orientationB);

                            float4 angVelDeltaA = math.mul(solverInertiaA, new float4(math.cross(rA.xyz, totalImpulse.xyz), 0));
                            float4 angVelDeltaB = -math.mul(solverInertiaB, new float4(math.cross(rB.xyz, totalImpulse.xyz), 0));

                            // Final angular velocities, after adding the deltas:
                            angularVelocityA += angVelDeltaA;
                            angularVelocityB += angVelDeltaB;

                            // Calculate weights (inverse masses):
                            float invMassA = math.length(math.mul(solverInertiaA, math.normalizesafe(angularVelocityA)));
                            float invMassB = math.length(math.mul(solverInertiaB, math.normalizesafe(angularVelocityB)));

                            // Calculate rolling axis and angular velocity deltas:
                            float4 rollAxis       = float4.zero;
                            float  rollingImpulse = contact.SolveRollingFriction(angularVelocityA, angularVelocityB, material.rollingFriction, invMassA, invMassB, ref rollAxis);
                            angVelDeltaA += rollAxis * rollingImpulse * invMassA;
                            angVelDeltaB -= rollAxis * rollingImpulse * invMassB;

                            // Apply orientation deltas to particles:
                            quaternion orientationDeltaA = BurstIntegration.AngularVelocityToSpinQuaternion(orientationA, angVelDeltaA, substepTime);
                            quaternion orientationDeltaB = BurstIntegration.AngularVelocityToSpinQuaternion(orientationB, angVelDeltaB, substepTime);

                            for (int j = 0; j < simplexSizeA; ++j)
                            {
                                int        particleIndex = simplices[simplexStartA + j];
                                quaternion qA            = orientationDeltas[particleIndex];
                                qA.value += orientationDeltaA.value;
                                orientationDeltas[particleIndex] = qA;
                                orientationCounts[particleIndex]++;
                            }

                            for (int j = 0; j < simplexSizeB; ++j)
                            {
                                int        particleIndex = simplices[simplexStartB + j];
                                quaternion qB            = orientationDeltas[particleIndex];
                                qB.value += orientationDeltaB.value;
                                orientationDeltas[particleIndex] = qB;
                                orientationCounts[particleIndex]++;
                            }
                        }
                    }

                    contacts[i] = contact;
                }
            }
Example #12
0
        public static void Contacts(int particleIndex,
                                    int colliderIndex,
                                    float4 position,
                                    quaternion orientation,
                                    float4 radii,
                                    ref NativeArray <BurstDFNode> dfNodes,
                                    DistanceFieldHeader header,
                                    BurstAffineTransform colliderToSolver,
                                    BurstColliderShape shape,
                                    NativeQueue <BurstContact> .ParallelWriter contacts)
        {
            float4 pos = colliderToSolver.InverseTransformPoint(position);

            BurstContact c = new BurstContact
            {
                entityA = particleIndex,
                entityB = colliderIndex,
            };

            float4 sample = DFTraverse(pos, 0, ref header, ref dfNodes);

            c.normal = new float4(math.normalize(sample.xyz), 0);
            c.point  = pos - c.normal * sample[3];

            c.normal = colliderToSolver.TransformDirection(c.normal);
            c.point  = colliderToSolver.TransformPoint(c.point);

            c.distance = sample[3] * math.cmax(colliderToSolver.scale.xyz) - (shape.contactOffset + BurstMath.EllipsoidRadius(c.normal, orientation, radii.xyz));
            contacts.Enqueue(c);
        }
        public static void Contacts(int particleIndex,
                                    float4 position,
                                    quaternion orientation,
                                    float4 radii,
                                    int colliderIndex,
                                    BurstAffineTransform transform,
                                    BurstColliderShape shape,
                                    NativeQueue <BurstContact> .ParallelWriter contacts)
        {
            BurstContact c = new BurstContact()
            {
                entityA = particleIndex,
                entityB = colliderIndex,
            };

            float4 center = shape.center * transform.scale;
            float4 size   = shape.size * transform.scale * 0.5f;

            position = transform.InverseTransformPointUnscaled(position) - center;

            // Get minimum distance for each axis:
            float4 distances = size - math.abs(position);

            // if we are inside the box:
            if (distances.x >= 0 && distances.y >= 0 && distances.z >= 0)
            {
                // find minimum distance in all three axes and the axis index:
                float min  = float.MaxValue;
                int   axis = 0;
                for (int i = 0; i < 3; ++i)
                {
                    if (distances[i] < min)
                    {
                        min  = distances[i];
                        axis = i;
                    }
                }

                c.normal = float4.zero;
                c.point  = position;

                c.distance     = -distances[axis];
                c.normal[axis] = position[axis] > 0 ? 1 : -1;
                c.point[axis]  = size[axis] * c.normal[axis];
            }
            else // we are outside the box:
            {
                // clamp point to be inside the box:
                c.point = math.clamp(position, -size, size);

                // find distance and direction to clamped point:
                float4 diff = position - c.point;
                c.distance = math.length(diff);
                c.normal   = diff / (c.distance + math.FLT_MIN_NORMAL);
            }

            c.point += center;
            c.point  = transform.TransformPointUnscaled(c.point);
            c.normal = transform.TransformDirection(c.normal);

            c.distance -= shape.contactOffset + BurstMath.EllipsoidRadius(c.normal, orientation, radii.xyz);

            contacts.Enqueue(c);
        }
Example #14
0
            public void Execute()
            {
                for (int i = 0; i < contacts.Length; ++i)
                {
                    var contact = contacts[i];

                    // Get the indices of the particle and collider involved in this contact:
                    int simplexStart  = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSize);
                    int colliderIndex = contact.bodyB;

                    // Skip contacts involving triggers:
                    if (shapes[colliderIndex].flags > 0)
                    {
                        continue;
                    }

                    // Get the rigidbody index (might be < 0, in that case there's no rigidbody present)
                    int rigidbodyIndex = shapes[colliderIndex].rigidbodyIndex;

                    // Combine collision materials (use material from first particle in simplex)
                    BurstCollisionMaterial material = CombineCollisionMaterials(simplices[simplexStart], colliderIndex);

                    // Calculate relative velocity:
                    float4 rA = float4.zero, rB = float4.zero;

                    float4     prevPositionA     = float4.zero;
                    float4     linearVelocityA   = float4.zero;
                    float4     angularVelocityA  = float4.zero;
                    float4     invInertiaTensorA = float4.zero;
                    quaternion orientationA      = new quaternion(0, 0, 0, 0);
                    float      simplexRadiusA    = 0;

                    for (int j = 0; j < simplexSize; ++j)
                    {
                        int particleIndex = simplices[simplexStart + j];
                        prevPositionA      += prevPositions[particleIndex] * contact.pointA[j];
                        linearVelocityA    += BurstIntegration.DifferentiateLinear(positions[particleIndex], prevPositions[particleIndex], substepTime) * contact.pointA[j];
                        angularVelocityA   += BurstIntegration.DifferentiateAngular(orientations[particleIndex], prevOrientations[particleIndex], substepTime) * contact.pointA[j];
                        invInertiaTensorA  += invInertiaTensors[particleIndex] * contact.pointA[j];
                        orientationA.value += orientations[particleIndex].value * contact.pointA[j];
                        simplexRadiusA     += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
                    }

                    float4 relativeVelocity      = linearVelocityA;

                    // Add particle angular velocity if rolling contacts are enabled:
                    if (material.rollingContacts > 0)
                    {
                        rA = -contact.normal * simplexRadiusA;
                        relativeVelocity += new float4(math.cross(angularVelocityA.xyz, rA.xyz), 0);
                    }

                    // Subtract rigidbody velocity:
                    if (rigidbodyIndex >= 0)
                    {
                        // Note: unlike rA, that is expressed in solver space, rB is expressed in world space.
                        rB = inertialFrame.frame.TransformPoint(contact.pointB) - rigidbodies[rigidbodyIndex].com;
                        relativeVelocity -= BurstMath.GetRigidbodyVelocityAtPoint(rigidbodyIndex, contact.pointB, rigidbodies, rigidbodyLinearDeltas, rigidbodyAngularDeltas, inertialFrame.frame);
                    }

                    // Determine impulse magnitude:
                    float2 impulses              = contact.SolveFriction(relativeVelocity, material.staticFriction, material.dynamicFriction, stepTime);

                    if (math.abs(impulses.x) > BurstMath.epsilon || math.abs(impulses.y) > BurstMath.epsilon)
                    {
                        float4 tangentImpulse   = impulses.x * contact.tangent;
                        float4 bitangentImpulse = impulses.y * contact.bitangent;
                        float4 totalImpulse     = tangentImpulse + bitangentImpulse;

                        float baryScale = BurstMath.BaryScale(contact.pointA);
                        for (int j = 0; j < simplexSize; ++j)
                        {
                            int particleIndex = simplices[simplexStart + j];
                            //(tangentImpulse * contact.tangentInvMassA + bitangentImpulse * contact.bitangentInvMassA) * dt;
                            deltas[particleIndex] += (tangentImpulse * contact.tangentInvMassA + bitangentImpulse * contact.bitangentInvMassA) * substepTime * contact.pointA[j] * baryScale;
                            counts[particleIndex]++;
                        }

                        if (rigidbodyIndex >= 0)
                        {
                            BurstMath.ApplyImpulse(rigidbodyIndex, -totalImpulse, contact.pointB, rigidbodies, rigidbodyLinearDeltas, rigidbodyAngularDeltas, inertialFrame.frame);
                        }

                        // Rolling contacts:
                        if (material.rollingContacts > 0)
                        {
                            // Calculate angular velocity deltas due to friction impulse:
                            float4x4 solverInertiaA = BurstMath.TransformInertiaTensor(invInertiaTensorA, orientationA);

                            float4 angVelDeltaA = math.mul(solverInertiaA, new float4(math.cross(rA.xyz, totalImpulse.xyz), 0));
                            float4 angVelDeltaB = float4.zero;

                            // Final angular velocities, after adding the deltas:
                            angularVelocityA += angVelDeltaA;
                            float4 angularVelocityB = float4.zero;

                            // Calculate weights (inverse masses):
                            float invMassA = math.length(math.mul(solverInertiaA, math.normalizesafe(angularVelocityA)));
                            float invMassB = 0;

                            if (rigidbodyIndex >= 0)
                            {
                                angVelDeltaB     = math.mul(-rigidbodies[rigidbodyIndex].inverseInertiaTensor, new float4(math.cross(rB.xyz, totalImpulse.xyz), 0));
                                angularVelocityB = rigidbodies[rigidbodyIndex].angularVelocity + angVelDeltaB;
                                invMassB         = math.length(math.mul(rigidbodies[rigidbodyIndex].inverseInertiaTensor, math.normalizesafe(angularVelocityB)));
                            }

                            // Calculate rolling axis and angular velocity deltas:
                            float4 rollAxis       = float4.zero;
                            float  rollingImpulse = contact.SolveRollingFriction(angularVelocityA, angularVelocityB, material.rollingFriction, invMassA, invMassB, ref rollAxis);
                            angVelDeltaA += rollAxis * rollingImpulse * invMassA;
                            angVelDeltaB -= rollAxis * rollingImpulse * invMassB;

                            // Apply orientation delta to particles:
                            quaternion orientationDelta = BurstIntegration.AngularVelocityToSpinQuaternion(orientationA, angVelDeltaA, substepTime);

                            for (int j = 0; j < simplexSize; ++j)
                            {
                                int        particleIndex = simplices[simplexStart + j];
                                quaternion qA            = orientationDeltas[particleIndex];
                                qA.value += orientationDelta.value;
                                orientationDeltas[particleIndex] = qA;
                                orientationCounts[particleIndex]++;
                            }

                            // Apply angular velocity delta to rigidbody:
                            if (rigidbodyIndex >= 0)
                            {
                                float4 angularDelta = rigidbodyAngularDeltas[rigidbodyIndex];
                                angularDelta += angVelDeltaB;
                                rigidbodyAngularDeltas[rigidbodyIndex] = angularDelta;
                            }
                        }
                    }

                    contacts[i] = contact;
                }
            }
            public void Execute()
            {
                for (int i = 0; i < contacts.Length; ++i)
                {
                    var contact = contacts[i];

                    int simplexStart  = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSize);
                    int colliderIndex = contact.bodyB;

                    // Skip contacts involving triggers:
                    if (shapes[colliderIndex].flags > 0)
                    {
                        continue;
                    }

                    // Get the rigidbody index (might be < 0, in that case there's no rigidbody present)
                    int rigidbodyIndex = shapes[colliderIndex].rigidbodyIndex;

                    // Combine collision materials (use material from first particle in simplex)
                    BurstCollisionMaterial material = CombineCollisionMaterials(simplices[simplexStart], colliderIndex);

                    // Get relative velocity at contact point.
                    // As we do not consider true ellipses for collision detection, particle contact points are never off-axis.
                    // So particle angular velocity does not contribute to normal impulses, and we can skip it.
                    float4 simplexPosition     = float4.zero;
                    float4 simplexPrevPosition = float4.zero;
                    float  simplexRadius       = 0;

                    for (int j = 0; j < simplexSize; ++j)
                    {
                        int particleIndex = simplices[simplexStart + j];
                        simplexPosition     += positions[particleIndex] * contact.pointA[j];
                        simplexPrevPosition += prevPositions[particleIndex] * contact.pointA[j];
                        simplexRadius       += BurstMath.EllipsoidRadius(contact.normal, orientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
                    }

                    // project position to the end of the full step:
                    float4 posA = math.lerp(simplexPrevPosition, simplexPosition, substeps);
                    posA += -contact.normal * simplexRadius;

                    float4 posB = contact.pointB;

                    if (rigidbodyIndex >= 0)
                    {
                        posB += BurstMath.GetRigidbodyVelocityAtPoint(rigidbodyIndex, contact.pointB, rigidbodies, rigidbodyLinearDeltas, rigidbodyAngularDeltas, inertialFrame.frame) * stepTime;
                    }

                    // adhesion:
                    float lambda = contact.SolveAdhesion(posA, posB, material.stickDistance, material.stickiness, stepTime);

                    // depenetration:
                    lambda += contact.SolvePenetration(posA, posB, solverParameters.maxDepenetration * stepTime);

                    // Apply normal impulse to both simplex and rigidbody:
                    if (math.abs(lambda) > BurstMath.epsilon)
                    {
                        float4 delta = lambda * contact.normal * BurstMath.BaryScale(contact.pointA) / substeps;
                        for (int j = 0; j < simplexSize; ++j)
                        {
                            int particleIndex = simplices[simplexStart + j];
                            deltas[particleIndex] += delta * invMasses[particleIndex] * contact.pointA[j];
                            counts[particleIndex]++;
                        }

                        // Apply position deltas immediately, if using sequential evaluation:
                        if (constraintParameters.evaluationOrder == Oni.ConstraintParameters.EvaluationOrder.Sequential)
                        {
                            for (int j = 0; j < simplexSize; ++j)
                            {
                                int particleIndex = simplices[simplexStart + j];
                                BurstConstraintsBatchImpl.ApplyPositionDelta(particleIndex, constraintParameters.SORFactor, ref positions, ref deltas, ref counts);
                            }
                        }

                        if (rigidbodyIndex >= 0)
                        {
                            BurstMath.ApplyImpulse(rigidbodyIndex, -lambda / stepTime * contact.normal, contact.pointB, rigidbodies, rigidbodyLinearDeltas, rigidbodyAngularDeltas, inertialFrame.frame);
                        }
                    }

                    contacts[i] = contact;
                }
            }