예제 #1
0
        // Sequential position solver for position constraints.
        public bool SolveTOIPositionConstraints(int toiIndexA, int toiIndexB)
        {
            float minSeparation = 0.0f;

            for (int i = 0; i < _count; ++i)
            {
                ContactPositionConstraint pc = _positionConstraints[i];

                int     indexA       = pc.indexA;
                int     indexB       = pc.indexB;
                Vector2 localCenterA = pc.localCenterA;
                Vector2 localCenterB = pc.localCenterB;
                int     pointCount   = pc.pointCount;

                float mA = 0.0f;
                float iA = 0.0f;
                if (indexA == toiIndexA || indexA == toiIndexB)
                {
                    mA = pc.invMassA;
                    iA = pc.invIA;
                }

                float mB = 0.0f;
                float iB = 0.0f;
                if (indexB == toiIndexA || indexB == toiIndexB)
                {
                    mB = pc.invMassB;
                    iB = pc.invIB;
                }

                Vector2 cA = _positions[indexA].c;
                float   aA = _positions[indexA].a;

                Vector2 cB = _positions[indexB].c;
                float   aB = _positions[indexB].a;

                // Solve normal constraints
                for (int j = 0; j < pointCount; ++j)
                {
                    Transform xfA = new Transform();
                    Transform xfB = new Transform();
                    xfA.q.Set(aA);
                    xfB.q.Set(aB);
                    xfA.p = cA - MathUtils.Mul(xfA.q, localCenterA);
                    xfB.p = cB - MathUtils.Mul(xfB.q, localCenterB);

                    Vector2 normal;
                    Vector2 point;
                    float   separation;

                    PositionSolverManifold.Initialize(pc, xfA, xfB, j, out normal, out point, out separation);

                    Vector2 rA = point - cA;
                    Vector2 rB = point - cB;

                    // Track max constraint error.
                    minSeparation = Math.Min(minSeparation, separation);

                    // Prevent large corrections and allow slop.
                    float C = MathUtils.Clamp(Settings.Baumgarte * (separation + Settings.LinearSlop), -Settings.MaxLinearCorrection, 0.0f);

                    // Compute the effective mass.
                    float rnA = MathUtils.Cross(rA, normal);
                    float rnB = MathUtils.Cross(rB, normal);
                    float K   = mA + mB + iA * rnA * rnA + iB * rnB * rnB;

                    // Compute normal impulse
                    float impulse = K > 0.0f ? -C / K : 0.0f;

                    Vector2 P = impulse * normal;

                    cA -= mA * P;
                    aA -= iA * MathUtils.Cross(rA, P);

                    cB += mB * P;
                    aB += iB * MathUtils.Cross(rB, P);
                }

                _positions[indexA].c = cA;
                _positions[indexA].a = aA;

                _positions[indexB].c = cB;
                _positions[indexB].a = aB;
            }

            // We can't expect minSpeparation >= -b2_linearSlop because we don't
            // push the separation above -b2_linearSlop.
            return(minSeparation >= -1.5f * Settings.LinearSlop);
        }
예제 #2
0
        public void Reset(TimeStep step, int count, Contact[] contacts, Position[] positions, Velocity[] velocities, bool warmstarting = Settings.EnableWarmstarting)
        {
            _step       = step;
            _count      = count;
            _positions  = positions;
            _velocities = velocities;
            _contacts   = contacts;

            // grow the array
            if (_velocityConstraints == null || _velocityConstraints.Length < count)
            {
                _velocityConstraints = new ContactVelocityConstraint[count * 2];
                _positionConstraints = new ContactPositionConstraint[count * 2];

                for (int i = 0; i < _velocityConstraints.Length; i++)
                {
                    _velocityConstraints[i] = new ContactVelocityConstraint();
                }

                for (int i = 0; i < _positionConstraints.Length; i++)
                {
                    _positionConstraints[i] = new ContactPositionConstraint();
                }
            }

            // Initialize position independent portions of the constraints.
            for (int i = 0; i < _count; ++i)
            {
                Contact contact = contacts[i];

                Fixture  fixtureA = contact.FixtureA;
                Fixture  fixtureB = contact.FixtureB;
                Shape    shapeA   = fixtureA.Shape;
                Shape    shapeB   = fixtureB.Shape;
                float    radiusA  = shapeA.Radius;
                float    radiusB  = shapeB.Radius;
                Body     bodyA    = fixtureA.Body;
                Body     bodyB    = fixtureB.Body;
                Manifold manifold = contact.Manifold;

                int pointCount = manifold.PointCount;
                Debug.Assert(pointCount > 0);

                ContactVelocityConstraint vc = _velocityConstraints[i];
                vc.friction     = contact.Friction;
                vc.restitution  = contact.Restitution;
                vc.tangentSpeed = contact.TangentSpeed;
                vc.indexA       = bodyA.IslandIndex;
                vc.indexB       = bodyB.IslandIndex;
                vc.invMassA     = bodyA._invMass;
                vc.invMassB     = bodyB._invMass;
                vc.invIA        = bodyA._invI;
                vc.invIB        = bodyB._invI;
                vc.contactIndex = i;
                vc.pointCount   = pointCount;
                vc.K.SetZero();
                vc.normalMass.SetZero();

                ContactPositionConstraint pc = _positionConstraints[i];
                pc.indexA       = bodyA.IslandIndex;
                pc.indexB       = bodyB.IslandIndex;
                pc.invMassA     = bodyA._invMass;
                pc.invMassB     = bodyB._invMass;
                pc.localCenterA = bodyA._sweep.LocalCenter;
                pc.localCenterB = bodyB._sweep.LocalCenter;
                pc.invIA        = bodyA._invI;
                pc.invIB        = bodyB._invI;
                pc.localNormal  = manifold.LocalNormal;
                pc.localPoint   = manifold.LocalPoint;
                pc.pointCount   = pointCount;
                pc.radiusA      = radiusA;
                pc.radiusB      = radiusB;
                pc.type         = manifold.Type;

                for (int j = 0; j < pointCount; ++j)
                {
                    ManifoldPoint           cp  = manifold.Points[j];
                    VelocityConstraintPoint vcp = vc.points[j];

                    if (Settings.EnableWarmstarting)
                    {
                        vcp.normalImpulse  = _step.dtRatio * cp.NormalImpulse;
                        vcp.tangentImpulse = _step.dtRatio * cp.TangentImpulse;
                    }
                    else
                    {
                        vcp.normalImpulse  = 0.0f;
                        vcp.tangentImpulse = 0.0f;
                    }

                    vcp.rA           = Vector2.Zero;
                    vcp.rB           = Vector2.Zero;
                    vcp.normalMass   = 0.0f;
                    vcp.tangentMass  = 0.0f;
                    vcp.velocityBias = 0.0f;

                    pc.localPoints[j] = cp.LocalPoint;
                }
            }
        }
예제 #3
0
        public void InitializeVelocityConstraints()
        {
            for (int i = 0; i < _count; ++i)
            {
                ContactVelocityConstraint vc = _velocityConstraints[i];
                ContactPositionConstraint pc = _positionConstraints[i];

                float    radiusA  = pc.radiusA;
                float    radiusB  = pc.radiusB;
                Manifold manifold = _contacts[vc.contactIndex].Manifold;

                int indexA = vc.indexA;
                int indexB = vc.indexB;

                float   mA           = vc.invMassA;
                float   mB           = vc.invMassB;
                float   iA           = vc.invIA;
                float   iB           = vc.invIB;
                Vector2 localCenterA = pc.localCenterA;
                Vector2 localCenterB = pc.localCenterB;

                Vector2 cA = _positions[indexA].c;
                float   aA = _positions[indexA].a;
                Vector2 vA = _velocities[indexA].v;
                float   wA = _velocities[indexA].w;

                Vector2 cB = _positions[indexB].c;
                float   aB = _positions[indexB].a;
                Vector2 vB = _velocities[indexB].v;
                float   wB = _velocities[indexB].w;

                Debug.Assert(manifold.PointCount > 0);

                Transform xfA = new Transform();
                Transform xfB = new Transform();
                xfA.q.Set(aA);
                xfB.q.Set(aB);
                xfA.p = cA - MathUtils.Mul(xfA.q, localCenterA);
                xfB.p = cB - MathUtils.Mul(xfB.q, localCenterB);

                Vector2 normal;
                FixedArray2 <Vector2> points;
                WorldManifold.Initialize(ref manifold, ref xfA, radiusA, ref xfB, radiusB, out normal, out points);

                vc.normal = normal;

                int pointCount = vc.pointCount;
                for (int j = 0; j < pointCount; ++j)
                {
                    VelocityConstraintPoint vcp = vc.points[j];

                    vcp.rA = points[j] - cA;
                    vcp.rB = points[j] - cB;

                    float rnA = MathUtils.Cross(vcp.rA, vc.normal);
                    float rnB = MathUtils.Cross(vcp.rB, vc.normal);

                    float kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;

                    vcp.normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;

                    Vector2 tangent = MathUtils.Cross(vc.normal, 1.0f);

                    float rtA = MathUtils.Cross(vcp.rA, tangent);
                    float rtB = MathUtils.Cross(vcp.rB, tangent);

                    float kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;

                    vcp.tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f;

                    // Setup a velocity bias for restitution.
                    vcp.velocityBias = 0.0f;
                    float vRel = Vector2.Dot(vc.normal, vB + MathUtils.Cross(wB, vcp.rB) - vA - MathUtils.Cross(wA, vcp.rA));
                    if (vRel < -Settings.VelocityThreshold)
                    {
                        vcp.velocityBias = -vc.restitution * vRel;
                    }
                }

                // If we have two points, then prepare the block solver.
                if (vc.pointCount == 2)
                {
                    VelocityConstraintPoint vcp1 = vc.points[0];
                    VelocityConstraintPoint vcp2 = vc.points[1];

                    float rn1A = MathUtils.Cross(vcp1.rA, vc.normal);
                    float rn1B = MathUtils.Cross(vcp1.rB, vc.normal);
                    float rn2A = MathUtils.Cross(vcp2.rA, vc.normal);
                    float rn2B = MathUtils.Cross(vcp2.rB, vc.normal);

                    float k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
                    float k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
                    float k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;

                    // Ensure a reasonable condition number.
                    const float k_maxConditionNumber = 1000.0f;
                    if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
                    {
                        // K is safe to invert.
                        vc.K.ex       = new Vector2(k11, k12);
                        vc.K.ey       = new Vector2(k12, k22);
                        vc.normalMass = vc.K.Inverse;
                    }
                    else
                    {
                        // The constraints are redundant, just use one.
                        // TODO_ERIN use deepest?
                        vc.pointCount = 1;
                    }
                }
            }
        }