internal override bool SolvePositionConstraints(float baumgarte) { if (_frequencyHz > 0.0f) { // There is no position correction for soft distance raints. return(true); } Body b1 = _bodyA; Body b2 = _bodyB; XForm xf1, xf2; b1.GetXForm(out xf1); b2.GetXForm(out xf2); Vector2 r1 = MathUtils.Multiply(ref xf1.R, _localAnchor1 - b1.GetLocalCenter()); Vector2 r2 = MathUtils.Multiply(ref xf2.R, _localAnchor2 - b2.GetLocalCenter()); Vector2 d = b2._sweep.c + r2 - b1._sweep.c - r1; float length = d.Length(); d /= length; float C = length - _length; C = MathUtils.Clamp(C, -Settings.b2_maxLinearCorrection, Settings.b2_maxLinearCorrection); float impulse = -_mass * C; _u = d; Vector2 P = impulse * _u; b1._sweep.c -= b1._invMass * P; b1._sweep.a -= b1._invI * MathUtils.Cross(r1, P); b2._sweep.c += b2._invMass * P; b2._sweep.a += b2._invI * MathUtils.Cross(r2, P); b1.SynchronizeTransform(); b2.SynchronizeTransform(); return(Math.Abs(C) < Settings.b2_linearSlop); }
internal override bool SolvePositionConstraints(float baumgarte) { float linearError = 0.0f; Body b1 = _bodyA; Body b2 = _bodyB; float coordinate1, coordinate2; if (_revolute1 != null) { coordinate1 = _revolute1.GetJointAngle(); } else { coordinate1 = _prismatic1.GetJointTranslation(); } if (_revolute2 != null) { coordinate2 = _revolute2.GetJointAngle(); } else { coordinate2 = _prismatic2.GetJointTranslation(); } float C = _ant - (coordinate1 + _ratio * coordinate2); float impulse = _mass * (-C); b1._sweep.c += b1._invMass * impulse * _J.linear1; b1._sweep.a += b1._invI * impulse * _J.angular1; b2._sweep.c += b2._invMass * impulse * _J.linear2; b2._sweep.a += b2._invI * impulse * _J.angular2; b1.SynchronizeTransform(); b2.SynchronizeTransform(); // TODO_ERIN not implemented return(linearError < Settings.b2_linearSlop); }
internal override bool SolvePositionConstraints(float baumgarte) { Body b1 = _bodyA; Body b2 = _bodyB; Vector2 c1 = b1._sweep.c; float a1 = b1._sweep.a; Vector2 c2 = b2._sweep.c; float a2 = b2._sweep.a; // Solve linear limit raint. float linearError = 0.0f, angularError = 0.0f; bool active = false; float C2 = 0.0f; Mat22 R1 = new Mat22(a1); Mat22 R2 = new Mat22(a2); Vector2 r1 = MathUtils.Multiply(ref R1, _localAnchor1 - _localCenter1); Vector2 r2 = MathUtils.Multiply(ref R2, _localAnchor2 - _localCenter2); Vector2 d = c2 + r2 - c1 - r1; if (_enableLimit) { _axis = MathUtils.Multiply(ref R1, _localXAxis1); _a1 = MathUtils.Cross(d + r1, _axis); _a2 = MathUtils.Cross(r2, _axis); float translation = Vector2.Dot(_axis, d); if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.b2_linearSlop) { // Prevent large angular corrections C2 = MathUtils.Clamp(translation, -Settings.b2_maxLinearCorrection, Settings.b2_maxLinearCorrection); linearError = Math.Abs(translation); active = true; } else if (translation <= _lowerTranslation) { // Prevent large linear corrections and allow some slop. C2 = MathUtils.Clamp(translation - _lowerTranslation + Settings.b2_linearSlop, -Settings.b2_maxLinearCorrection, 0.0f); linearError = _lowerTranslation - translation; active = true; } else if (translation >= _upperTranslation) { // Prevent large linear corrections and allow some slop. C2 = MathUtils.Clamp(translation - _upperTranslation - Settings.b2_linearSlop, 0.0f, Settings.b2_maxLinearCorrection); linearError = translation - _upperTranslation; active = true; } } _perp = MathUtils.Multiply(ref R1, _localYAxis1); _s1 = MathUtils.Cross(d + r1, _perp); _s2 = MathUtils.Cross(r2, _perp); Vector3 impulse; Vector2 C1 = new Vector2(Vector2.Dot(_perp, d), a2 - a1 - _refAngle); linearError = Math.Max(linearError, Math.Abs(C1.X)); angularError = Math.Abs(C1.Y); if (active) { float m1 = _invMass1, m2 = _invMass2; float i1 = _invI1, i2 = _invI2; float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2; float k12 = i1 * _s1 + i2 * _s2; float k13 = i1 * _s1 * _a1 + i2 * _s2 * _a2; float k22 = i1 + i2; float k23 = i1 * _a1 + i2 * _a2; float k33 = m1 + m2 + i1 * _a1 * _a1 + i2 * _a2 * _a2; _K.col1 = new Vector3(k11, k12, k13); _K.col2 = new Vector3(k12, k22, k23); _K.col3 = new Vector3(k13, k23, k33); Vector3 C = new Vector3(-C1.X, -C1.Y, -C2); impulse = _K.Solve33(C); // negated above } else { float m1 = _invMass1, m2 = _invMass2; float i1 = _invI1, i2 = _invI2; float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2; float k12 = i1 * _s1 + i2 * _s2; float k22 = i1 + i2; _K.col1 = new Vector3(k11, k12, 0.0f); _K.col2 = new Vector3(k12, k22, 0.0f); Vector2 impulse1 = _K.Solve22(-C1); impulse.X = impulse1.X; impulse.Y = impulse1.Y; impulse.Z = 0.0f; } Vector2 P = impulse.X * _perp + impulse.Z * _axis; float L1 = impulse.X * _s1 + impulse.Y + impulse.Z * _a1; float L2 = impulse.X * _s2 + impulse.Y + impulse.Z * _a2; c1 -= _invMass1 * P; a1 -= _invI1 * L1; c2 += _invMass2 * P; a2 += _invI2 * L2; // TODO_ERIN remove need for this. b1._sweep.c = c1; b1._sweep.a = a1; b2._sweep.c = c2; b2._sweep.a = a2; b1.SynchronizeTransform(); b2.SynchronizeTransform(); return(linearError <= Settings.b2_linearSlop && angularError <= Settings.b2_angularSlop); }
internal override bool SolvePositionConstraints(float baumgarte) { Body b1 = _bodyA; Body b2 = _bodyB; Vector2 s1 = _groundAnchor1; Vector2 s2 = _groundAnchor2; float linearError = 0.0f; if (_state == LimitState.AtUpper) { XForm xf1, xf2; b1.GetXForm(out xf1); b2.GetXForm(out xf2); Vector2 r1 = MathUtils.Multiply(ref xf1.R, _localAnchor1 - b1.GetLocalCenter()); Vector2 r2 = MathUtils.Multiply(ref xf2.R, _localAnchor2 - b2.GetLocalCenter()); Vector2 p1 = b1._sweep.c + r1; Vector2 p2 = b2._sweep.c + r2; // Get the pulley axes. _u1 = p1 - s1; _u2 = p2 - s2; float length1 = _u1.Length(); float length2 = _u2.Length(); if (length1 > Settings.b2_linearSlop) { _u1 *= 1.0f / length1; } else { _u1 = Vector2.Zero; } if (length2 > Settings.b2_linearSlop) { _u2 *= 1.0f / length2; } else { _u2 = Vector2.Zero; } float C = _ant - length1 - _ratio * length2; linearError = Math.Max(linearError, -C); C = MathUtils.Clamp(C + Settings.b2_linearSlop, -Settings.b2_maxLinearCorrection, 0.0f); float impulse = -_pulleyMass * C; Vector2 P1 = -impulse * _u1; Vector2 P2 = -_ratio * impulse * _u2; b1._sweep.c += b1._invMass * P1; b1._sweep.a += b1._invI * MathUtils.Cross(r1, P1); b2._sweep.c += b2._invMass * P2; b2._sweep.a += b2._invI * MathUtils.Cross(r2, P2); b1.SynchronizeTransform(); b2.SynchronizeTransform(); } if (_limitState1 == LimitState.AtUpper) { XForm xf1; b1.GetXForm(out xf1); Vector2 r1 = MathUtils.Multiply(ref xf1.R, _localAnchor1 - b1.GetLocalCenter()); Vector2 p1 = b1._sweep.c + r1; _u1 = p1 - s1; float length1 = _u1.Length(); if (length1 > Settings.b2_linearSlop) { _u1 *= 1.0f / length1; } else { _u1 = Vector2.Zero; } float C = _maxLength1 - length1; linearError = Math.Max(linearError, -C); C = MathUtils.Clamp(C + Settings.b2_linearSlop, -Settings.b2_maxLinearCorrection, 0.0f); float impulse = -_limitMass1 * C; Vector2 P1 = -impulse * _u1; b1._sweep.c += b1._invMass * P1; b1._sweep.a += b1._invI * MathUtils.Cross(r1, P1); b1.SynchronizeTransform(); } if (_limitState2 == LimitState.AtUpper) { XForm xf2; b2.GetXForm(out xf2); Vector2 r2 = MathUtils.Multiply(ref xf2.R, _localAnchor2 - b2.GetLocalCenter()); Vector2 p2 = b2._sweep.c + r2; _u2 = p2 - s2; float length2 = _u2.Length(); if (length2 > Settings.b2_linearSlop) { _u2 *= 1.0f / length2; } else { _u2 = Vector2.Zero; } float C = _maxLength2 - length2; linearError = Math.Max(linearError, -C); C = MathUtils.Clamp(C + Settings.b2_linearSlop, -Settings.b2_maxLinearCorrection, 0.0f); float impulse = -_limitMass2 * C; Vector2 P2 = -impulse * _u2; b2._sweep.c += b2._invMass * P2; b2._sweep.a += b2._invI * MathUtils.Cross(r2, P2); b2.SynchronizeTransform(); } return(linearError < Settings.b2_linearSlop); }
public bool SolvePositionConstraints(float baumgarte) { float minSeparation = 0.0f; int constraintCount = _constraints.Count; for (int i = 0; i < constraintCount; ++i) { ContactConstraint c = _constraints[i]; Body bodyA = c.bodyA; Body bodyB = c.bodyB; float invMassA = bodyA._mass * bodyA._invMass; float invIA = bodyA._mass * bodyA._invI; float invMassB = bodyB._mass * bodyB._invMass; float invIB = bodyB._mass * bodyB._invI; PositionSolverManifold psm = new PositionSolverManifold(ref c); Vector2 normal = psm._normal; // Solve normal constraints for (int j = 0; j < c.pointCount; ++j) { ContactConstraintPoint ccp = c.points[j]; Vector2 point = psm._points[j]; float separation = psm._separations[j]; Vector2 rA = point - bodyA._sweep.c; Vector2 rB = point - bodyB._sweep.c; // Track max raint error. minSeparation = Math.Min(minSeparation, separation); // Prevent large corrections and allow slop. float C = baumgarte * MathUtils.Clamp(separation + Settings.b2_linearSlop, -Settings.b2_maxLinearCorrection, 0.0f); // Compute normal impulse float impulse = -ccp.equalizedMass * C; #if MATH_OVERLOADS Vector2 P = impulse * normal; bodyA._sweep.c -= invMassA * P; bodyA._sweep.a -= invIA * MathUtils.Cross(rA, P); bodyB._sweep.c += invMassB * P; bodyB._sweep.a += invIB * MathUtils.Cross(rB, P); #else Vector2 P = new Vector2(impulse * normal.X, impulse * normal.Y); bodyA._sweep.c.X -= invMassA * P.X; bodyA._sweep.c.Y -= invMassA * P.Y; bodyA._sweep.a -= invIA * (rA.X * P.Y - rA.Y * P.X); bodyB._sweep.c.X += invMassB * P.X; bodyB._sweep.c.Y += invMassB * P.Y; bodyB._sweep.a += invIB * (rB.X * P.Y - rB.Y * P.X); #endif bodyA.SynchronizeTransform(); bodyB.SynchronizeTransform(); } } // We can't expect minSpeparation >= -Settings.b2_linearSlop because we don't // push the separation above -Settings.b2_linearSlop. return(minSeparation >= -1.5f * Settings.b2_linearSlop); }
public void Solve(ref TimeStep step, Vector2 gravity, bool allowSleep) { // Integrate velocities and apply damping. for (int i = 0; i < _bodyCount; ++i) { Body b = _bodies[i]; if (b.IsStatic) { continue; } // Integrate velocities. b._linearVelocity += step.dt * (gravity + b._invMass * b._force); b._angularVelocity += step.dt * b._invI * b._torque; // Reset forces. b._force = new Vector2(0.0f, 0.0f); b._torque = 0.0f; // Apply damping. // ODE: dv/dt + c * v = 0 // Solution: v(t) = v0 * exp(-c * t) // Time step: v(t + dt) = v0 * exp(-c * (t + dt)) = v0 * exp(-c * t) * exp(-c * dt) = v * exp(-c * dt) // v2 = exp(-c * dt) * v1 // Taylor expansion: // v2 = (1.0f - c * dt) * v1 b._linearVelocity *= MathUtils.Clamp(1.0f - step.dt * b._linearDamping, 0.0f, 1.0f); b._angularVelocity *= MathUtils.Clamp(1.0f - step.dt * b._angularDamping, 0.0f, 1.0f); } _contactSolver.Reset(ref step, _contacts); // Initialize velocity raints. _contactSolver.InitVelocityConstraints(ref step); for (int i = 0; i < _jointCount; ++i) { _joints[i].InitVelocityConstraints(ref step); } // Solve velocity raints. for (int i = 0; i < step.velocityIterations; ++i) { for (int j = 0; j < _jointCount; ++j) { _joints[j].SolveVelocityConstraints(ref step); } _contactSolver.SolveVelocityConstraints(); } // Post-solve (store impulses for warm starting). _contactSolver.FinalizeVelocityConstraints(); // Integrate positions. for (int i = 0; i < _bodyCount; ++i) { Body b = _bodies[i]; if (b.IsStatic) { continue; } // Check for large velocities. Vector2 translation = step.dt * b._linearVelocity; if (Vector2.Dot(translation, translation) > Settings.b2_maxTranslationSquared) { translation.Normalize(); b._linearVelocity = (Settings.b2_maxTranslation * step.inv_dt) * translation; } float rotation = step.dt * b._angularVelocity; if (rotation * rotation > Settings.b2_maxRotationSquared) { if (rotation < 0.0) { b._angularVelocity = -step.inv_dt * Settings.b2_maxRotation; } else { b._angularVelocity = step.inv_dt * Settings.b2_maxRotation; } } // Store positions for continuous collision. b._sweep.c0 = b._sweep.c; b._sweep.a0 = b._sweep.a; // Integrate b._sweep.c += step.dt * b._linearVelocity; b._sweep.a += step.dt * b._angularVelocity; // Compute new transform b.SynchronizeTransform(); // Note: shapes are synchronized later. } // Iterate over raints. for (int i = 0; i < step.positionIterations; ++i) { bool contactsOkay = _contactSolver.SolvePositionConstraints(Settings.b2_contactBaumgarte); bool jointsOkay = true; for (int j = 0; j < _jointCount; ++j) { bool jointOkay = _joints[j].SolvePositionConstraints(Settings.b2_contactBaumgarte); jointsOkay = jointsOkay && jointOkay; } if (contactsOkay && jointsOkay) { // Exit early if the position errors are small. break; } } Report(_contactSolver._constraints); if (allowSleep) { float minSleepTime = Settings.b2_FLT_MAX; #if !TARGET_float_IS_FIXED float linTolSqr = Settings.b2_linearSleepTolerance * Settings.b2_linearSleepTolerance; float angTolSqr = Settings.b2_angularSleepTolerance * Settings.b2_angularSleepTolerance; #endif for (int i = 0; i < _bodyCount; ++i) { Body b = _bodies[i]; if (b._invMass == 0.0f) { continue; } if ((b._flags & BodyFlags.AllowSleep) == 0) { b._sleepTime = 0.0f; minSleepTime = 0.0f; } if ((b._flags & BodyFlags.AllowSleep) == 0 || #if TARGET_float_IS_FIXED MathUtils.Abs(b._angularVelocity) > Settings.b2_angularSleepTolerance || MathUtils.Abs(b._linearVelocity.X) > Settings.b2_linearSleepTolerance || MathUtils.Abs(b._linearVelocity.Y) > Settings.b2_linearSleepTolerance) #else b._angularVelocity *b._angularVelocity > angTolSqr || Vector2.Dot(b._linearVelocity, b._linearVelocity) > linTolSqr) #endif { b._sleepTime = 0.0f; minSleepTime = 0.0f; } else { b._sleepTime += step.dt; minSleepTime = Math.Min(minSleepTime, b._sleepTime); } }
internal override bool SolvePositionConstraints(float baumgarte) { // TODO_ERIN block solve with limit. COME ON ERIN Body b1 = _bodyA; Body b2 = _bodyB; float angularError = 0.0f; float positionError = 0.0f; // Solve angular limit raint. if (_enableLimit && _limitState != LimitState.Inactive) { float angle = b2._sweep.a - b1._sweep.a - _referenceAngle; float limitImpulse = 0.0f; if (_limitState == LimitState.Equal) { // Prevent large angular corrections float C = MathUtils.Clamp(angle - _lowerAngle, -Settings.b2_maxAngularCorrection, Settings.b2_maxAngularCorrection); limitImpulse = -_motorMass * C; angularError = Math.Abs(C); } else if (_limitState == LimitState.AtLower) { float C = angle - _lowerAngle; angularError = -C; // Prevent large angular corrections and allow some slop. C = MathUtils.Clamp(C + Settings.b2_angularSlop, -Settings.b2_maxAngularCorrection, 0.0f); limitImpulse = -_motorMass * C; } else if (_limitState == LimitState.AtUpper) { float C = angle - _upperAngle; angularError = C; // Prevent large angular corrections and allow some slop. C = MathUtils.Clamp(C - Settings.b2_angularSlop, 0.0f, Settings.b2_maxAngularCorrection); limitImpulse = -_motorMass * C; } b1._sweep.a -= b1._invI * limitImpulse; b2._sweep.a += b2._invI * limitImpulse; b1.SynchronizeTransform(); b2.SynchronizeTransform(); } // Solve point-to-point raint. { XForm xf1, xf2; b1.GetXForm(out xf1); b2.GetXForm(out xf2); Vector2 r1 = MathUtils.Multiply(ref xf1.R, _localAnchor1 - b1.GetLocalCenter()); Vector2 r2 = MathUtils.Multiply(ref xf2.R, _localAnchor2 - b2.GetLocalCenter()); Vector2 C = b2._sweep.c + r2 - b1._sweep.c - r1; positionError = C.Length(); float invMass1 = b1._invMass, invMass2 = b2._invMass; float invI1 = b1._invI, invI2 = b2._invI; // Handle large detachment. float k_allowedStretch = 10.0f * Settings.b2_linearSlop; if (C.LengthSquared() > k_allowedStretch * k_allowedStretch) { // Use a particle solution (no rotation). Vector2 u = C; u.Normalize(); float k = invMass1 + invMass2; Debug.Assert(k > Settings.b2_FLT_EPSILON); float m = 1.0f / k; Vector2 impulse2 = m * (-C); float k_beta = 0.5f; b1._sweep.c -= k_beta * invMass1 * impulse2; b2._sweep.c += k_beta * invMass2 * impulse2; C = b2._sweep.c + r2 - b1._sweep.c - r1; } Mat22 K1 = new Mat22(new Vector2(invMass1 + invMass2, 0.0f), new Vector2(0.0f, invMass1 + invMass2)); Mat22 K2 = new Mat22(new Vector2(invI1 * r1.Y * r1.Y, -invI1 * r1.X * r1.Y), new Vector2(-invI1 * r1.X * r1.Y, invI1 * r1.X * r1.X)); Mat22 K3 = new Mat22(new Vector2(invI2 * r2.Y * r2.Y, -invI2 * r2.X * r2.Y), new Vector2(-invI2 * r2.X * r2.Y, invI2 * r2.X * r2.X)); Mat22 Ka; Mat22 K; Mat22.Add(ref K1, ref K2, out Ka); Mat22.Add(ref Ka, ref K3, out K); Vector2 impulse = K.Solve(-C); b1._sweep.c -= b1._invMass * impulse; b1._sweep.a -= b1._invI * MathUtils.Cross(r1, impulse); b2._sweep.c += b2._invMass * impulse; b2._sweep.a += b2._invI * MathUtils.Cross(r2, impulse); b1.SynchronizeTransform(); b2.SynchronizeTransform(); } return(positionError <= Settings.b2_linearSlop && angularError <= Settings.b2_angularSlop); }