예제 #1
0
        public void SolveVelocityConstraints()
        {
            for (int i = 0; i < _count; ++i)
            {
                ContactVelocityConstraint vc = _velocityConstraints[i];

                int   indexA     = vc.indexA;
                int   indexB     = vc.indexB;
                float mA         = vc.invMassA;
                float iA         = vc.invIA;
                float mB         = vc.invMassB;
                float iB         = vc.invIB;
                int   pointCount = vc.pointCount;

                Vector2 vA = _velocities[indexA].v;
                float   wA = _velocities[indexA].w;
                Vector2 vB = _velocities[indexB].v;
                float   wB = _velocities[indexB].w;

                Vector2 normal   = vc.normal;
                Vector2 tangent  = Vectex.Cross(normal, 1.0f);
                float   friction = vc.friction;

                //Debug.Assert(pointCount == 1 || pointCount == 2);

                // Solve tangent constraints first because non-penetration is more important
                // than friction.
                for (int j = 0; j < pointCount; ++j)
                {
                    VelocityConstraintPoint vcp = vc.points[j];

                    // Relative velocity at contact
                    Vector2 dv = vB + Vectex.Cross(wB, vcp.rB) - vA - Vectex.Cross(wA, vcp.rA);

                    // Compute tangent force
                    float vt     = Vector2.Dot(dv, tangent) - vc.tangentSpeed;
                    float lambda = vcp.tangentMass * (-vt);

                    // b2Clamp the accumulated force
                    float maxFriction = friction * vcp.normalImpulse;
                    float newImpulse  = Math.Clamp(vcp.tangentImpulse + lambda, -maxFriction, maxFriction);
                    lambda             = newImpulse - vcp.tangentImpulse;
                    vcp.tangentImpulse = newImpulse;

                    // Apply contact impulse
                    Vector2 P = lambda * tangent;

                    vA -= mA * P;
                    wA -= iA * Vectex.Cross(vcp.rA, P);

                    vB += mB * P;
                    wB += iB * Vectex.Cross(vcp.rB, P);
                }

                // Solve normal constraints
                if (pointCount == 1 || Settings.BlockSolve == false)
                {
                    for (int j = 0; j < pointCount; ++j)
                    {
                        VelocityConstraintPoint vcp = vc.points[j];

                        // Relative velocity at contact
                        Vector2 dv = vB + Vectex.Cross(wB, vcp.rB) - vA - Vectex.Cross(wA, vcp.rA);

                        // Compute normal impulse
                        float vn     = Vector2.Dot(dv, normal);
                        float lambda = -vcp.normalMass * (vn - vcp.velocityBias);

                        // b2Clamp the accumulated impulse
                        float newImpulse = MathF.Max(vcp.normalImpulse + lambda, 0.0f);
                        lambda            = newImpulse - vcp.normalImpulse;
                        vcp.normalImpulse = newImpulse;

                        // Apply contact impulse
                        Vector2 P = lambda * normal;
                        vA -= mA * P;
                        wA -= iA * Vectex.Cross(vcp.rA, P);

                        vB += mB * P;
                        wB += iB * Vectex.Cross(vcp.rB, P);
                    }
                }
                else
                {
                    // Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
                    // Build the mini LCP for this contact patch
                    //
                    // vn = A * x + b, vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
                    //
                    // A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
                    // b = vn0 - velocityBias
                    //
                    // The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
                    // implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
                    // vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be tested. The first valid
                    // solution that satisfies the problem is chosen.
                    //
                    // In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
                    // that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
                    //
                    // Substitute:
                    //
                    // x = a + d
                    //
                    // a := old total impulse
                    // x := new total impulse
                    // d := incremental impulse
                    //
                    // For the current iteration we extend the formula for the incremental impulse
                    // to compute the new total impulse:
                    //
                    // vn = A * d + b
                    //    = A * (x - a) + b
                    //    = A * x + b - A * a
                    //    = A * x + b'
                    // b' = b - A * a;

                    VelocityConstraintPoint cp1 = vc.points[0];
                    VelocityConstraintPoint cp2 = vc.points[1];

                    Vector2 a = new Vector2(cp1.normalImpulse, cp2.normalImpulse);
                    //Debug.Assert(a.X >= 0.0f && a.Y >= 0.0f);

                    // Relative velocity at contact
                    Vector2 dv1 = vB + Vectex.Cross(wB, cp1.rB) - vA - Vectex.Cross(wA, cp1.rA);
                    Vector2 dv2 = vB + Vectex.Cross(wB, cp2.rB) - vA - Vectex.Cross(wA, cp2.rA);

                    // Compute normal velocity
                    float vn1 = Vector2.Dot(dv1, normal);
                    float vn2 = Vector2.Dot(dv2, normal);

                    Vector2 b = new Vector2((float)(vn1 - cp1.velocityBias),
                                            (float)(vn2 - cp2.velocityBias));

                    // Compute b'
                    b -= Vector2.Transform(a, vc.K); // Common.Math.Mul(vc.K, a);

                    //const float k_errorTol = 1e-3f;
                    //B2_NOT_USED(k_errorTol);

                    for (; ;)
                    {
                        //
                        // Case 1: vn = 0
                        //
                        // 0 = A * x + b'
                        //
                        // Solve for x:
                        //
                        // x = - inv(A) * b'
                        //
                        Vector2 x = -Vector2.Transform(b, vc.normalMass); //Common.Math.Mul(vc.normalMass, b);

                        if (x.X >= 0.0f && x.Y >= 0.0f)
                        {
                            // Get the incremental impulse
                            Vector2 d = x - a;

                            // Apply incremental impulse
                            Vector2 P1 = d.X * normal;
                            Vector2 P2 = d.Y * normal;
                            vA -= mA * (P1 + P2);
                            wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));

                            vB += mB * (P1 + P2);
                            wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(cp2.rB, P2));

                            // Accumulate
                            cp1.normalImpulse = x.X;
                            cp2.normalImpulse = x.Y;

                            break;
                        }

                        //
                        // Case 2: vn1 = 0 and x2 = 0
                        //
                        //   0 = a11 * x1 + a12 * 0 + b1'
                        // vn2 = a21 * x1 + a22 * 0 + b2'
                        //
                        x.X = -cp1.normalMass * b.X;
                        x.Y = 0.0f;
                        vn1 = 0.0f;
                        vn2 = vc.K.M22 * x.X + b.Y;
                        if (x.X >= 0.0f && vn2 >= 0.0f)
                        {
                            // Get the incremental impulse
                            Vector2 d = x - a;

                            // Apply incremental impulse
                            Vector2 P1 = d.X * normal;
                            Vector2 P2 = d.Y * normal;
                            vA -= mA * (P1 + P2);
                            wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));

                            vB += mB * (P1 + P2);
                            wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(cp2.rB, P2));

                            // Accumulate
                            cp1.normalImpulse = x.X;
                            cp2.normalImpulse = x.Y;

                            break;
                        }


                        //
                        // Case 3: vn2 = 0 and x1 = 0
                        //
                        // vn1 = a11 * 0 + a12 * x2 + b1'
                        //   0 = a21 * 0 + a22 * x2 + b2'
                        //
                        x.X = 0.0f;
                        x.Y = -cp2.normalMass * b.Y;
                        vn1 = vc.K.M12 * x.Y + b.X;
                        vn2 = 0.0f;

                        if (x.Y >= 0.0f && vn1 >= 0.0f)
                        {
                            // Resubstitute for the incremental impulse
                            Vector2 d = x - a;

                            // Apply incremental impulse
                            Vector2 P1 = d.X * normal;
                            Vector2 P2 = d.Y * normal;
                            vA -= mA * (P1 + P2);
                            wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));

                            vB += mB * (P1 + P2);
                            wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(cp2.rB, P2));

                            // Accumulate
                            cp1.normalImpulse = x.X;
                            cp2.normalImpulse = x.Y;

                            break;
                        }

                        //
                        // Case 4: x1 = 0 and x2 = 0
                        //
                        // vn1 = b1
                        // vn2 = b2;
                        x.X = 0.0f;
                        x.Y = 0.0f;
                        vn1 = b.X;
                        vn2 = b.Y;

                        if (vn1 >= 0.0f && vn2 >= 0.0f)
                        {
                            // Resubstitute for the incremental impulse
                            Vector2 d = x - a;

                            // Apply incremental impulse
                            Vector2 P1 = d.X * normal;
                            Vector2 P2 = d.Y * normal;
                            vA -= mA * (P1 + P2);
                            wA -= iA * (Vectex.Cross(cp1.rA, P1) + Vectex.Cross(cp2.rA, P2));

                            vB += mB * (P1 + P2);
                            wB += iB * (Vectex.Cross(cp1.rB, P1) + Vectex.Cross(cp2.rB, P2));

                            // Accumulate
                            cp1.normalImpulse = x.X;
                            cp2.normalImpulse = x.Y;

                            break;
                        }

                        // No solution, give up. This is hit sometimes, but it doesn't seem to matter.
                        break;
                    }
                }

                _velocities[indexA].v = vA;
                _velocities[indexA].w = wA;
                _velocities[indexB].v = vB;
                _velocities[indexB].w = wB;
            }
        }
예제 #2
0
        public ContactSolver(ContactSolverDef def)
        {
            _step  = def.step;
            _count = def.count;
            _positionConstraints = new ContactPositionConstraint[_count];
            _velocityConstraints = new ContactVelocityConstraint[_count];
            _positions           = def.positions;
            _velocities          = def.velocities;
            _contacts            = def.contacts;

            for (int i = 0; i < _count; ++i)
            {
                Contact contact = _contacts[i];

                Fixture  fixtureA = contact.m_fixtureA;
                Fixture  fixtureB = contact.m_fixtureB;
                Shape    shapeA   = fixtureA.Shape;
                Shape    shapeB   = fixtureB.Shape;
                float    radiusA  = shapeA.m_radius;
                float    radiusB  = shapeB.m_radius;
                Body     bodyA    = fixtureA.Body;
                Body     bodyB    = fixtureB.Body;
                Manifold manifold = contact.Manifold;

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

                _velocityConstraints[i] = new ContactVelocityConstraint();
                ContactVelocityConstraint vc = _velocityConstraints[i];
                vc.friction     = contact.m_friction;
                vc.restitution  = contact.m_restitution;
                vc.tangentSpeed = contact.m_tangentSpeed;
                vc.indexA       = bodyA.m_islandIndex;
                vc.indexB       = bodyB.m_islandIndex;
                vc.invMassA     = bodyA.m_invMass;
                vc.invMassB     = bodyB.m_invMass;
                vc.invIA        = bodyA.m_invI;
                vc.invIB        = bodyB.m_invI;
                vc.contactIndex = i;
                vc.pointCount   = pointCount;
                vc.K            = new Matrix3x2(); // .SetZero();
                vc.normalMass   = new Matrix3x2(); // .SetZero();

                _positionConstraints[i] = new ContactPositionConstraint();
                ContactPositionConstraint pc = _positionConstraints[i];
                pc.indexA       = bodyA.m_islandIndex;
                pc.indexB       = bodyB.m_islandIndex;
                pc.invMassA     = bodyA.m_invMass;
                pc.invMassB     = bodyB.m_invMass;
                pc.localCenterA = bodyA.m_sweep.localCenter;
                pc.localCenterB = bodyB.m_sweep.localCenter;
                pc.invIA        = bodyA.m_invI;
                pc.invIB        = bodyB.m_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];
                    vc.points[j] = new VelocityConstraintPoint();
                    VelocityConstraintPoint vcp = vc.points[j];

                    if (_step.warmStarting)
                    {
                        vcp.normalImpulse  = _step.dtRatio * cp.normalImpulse;
                        vcp.tangentImpulse = _step.dtRatio * cp.tangentImpulse;
                    }
                    else
                    {
                        vcp.normalImpulse  = 0f;
                        vcp.tangentImpulse = 0f;
                    }

                    vcp.rA           = Vector2.Zero;
                    vcp.rB           = Vector2.Zero;
                    vcp.normalMass   = 0f;
                    vcp.tangentMass  = 0f;
                    vcp.velocityBias = 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 = Matrex.CreateRotation(aA);                   // Actually about twice as fast to use our own function
                xfB.q = Matrex.CreateRotation(aB);                   // Actually about twice as fast to use our own function
                xfA.p = cA - Vector2.Transform(localCenterA, xfA.q); // Common.Math.Mul(xfA.q, localCenterA);
                xfB.p = cB - Vector2.Transform(localCenterB, xfB.q); // Common.Math.Mul(xfB.q, localCenterB);

                WorldManifold worldManifold = new WorldManifold();
                worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);

                vc.normal = worldManifold.normal;

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

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

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

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

                    vcp.normalMass = kNormal > 0f ? 1f / kNormal : 0f;

                    Vector2 tangent = Vectex.Cross(vc.normal, 1f);

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

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

                    vcp.tangentMass = kTangent > 0f ? 1f / kTangent : 0f;

                    vcp.velocityBias = 0f;
                    float vRel = Vector2.Dot(vc.normal, vB + Vectex.Cross(wB, vcp.rB) - vA - Vectex.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 && Settings.BlockSolve)
                {
                    VelocityConstraintPoint vcp1 = vc.points[0];
                    VelocityConstraintPoint vcp2 = vc.points[1];

                    float rn1A = Vectex.Cross(vcp1.rA, vc.normal);
                    float rn1B = Vectex.Cross(vcp1.rB, vc.normal);
                    float rn2A = Vectex.Cross(vcp2.rA, vc.normal);
                    float rn2B = Vectex.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 = new Matrix3x2(k11, k12, k12, k22, 0, 0);

                        // vc.K.ex       = new Vector2(k11, k12);
                        // vc.K.ey       = new Vector2(k12, k22);
                        /*Matrix3x2*/
                        Matrex.Invert(vc.K, out Matrix3x2 KT);
                        vc.normalMass = KT;
                    }
                    else
                    {
                        // The constraints are redundant, just use one.
                        // TODO_ERIN use deepest?
                        vc.pointCount = 1;
                    }
                }
            }
        }