| 1 | /* | 
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| 2 | Bullet Continuous Collision Detection and Physics Library | 
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| 3 | Copyright (c) 2003-2006 Erwin Coumans  http://continuousphysics.com/Bullet/ | 
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| 4 |  | 
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| 5 | This software is provided 'as-is', without any express or implied warranty. | 
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| 6 | In no event will the authors be held liable for any damages arising from the use of this software. | 
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| 7 | Permission is granted to anyone to use this software for any purpose, | 
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| 8 | including commercial applications, and to alter it and redistribute it freely, | 
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| 9 | subject to the following restrictions: | 
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| 10 |  | 
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| 11 | 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required. | 
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| 12 | 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software. | 
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| 13 | 3. This notice may not be removed or altered from any source distribution. | 
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| 14 | */ | 
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| 15 |  | 
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| 16 |  | 
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| 17 | #include "btHingeConstraint.h" | 
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| 18 | #include "BulletDynamics/Dynamics/btRigidBody.h" | 
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| 19 | #include "LinearMath/btTransformUtil.h" | 
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| 20 | #include "LinearMath/btMinMax.h" | 
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| 21 | #include <new> | 
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| 22 |  | 
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| 23 |  | 
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| 24 | btHingeConstraint::btHingeConstraint() | 
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| 25 | : btTypedConstraint (HINGE_CONSTRAINT_TYPE), | 
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| 26 | m_enableAngularMotor(false) | 
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| 27 | { | 
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| 28 | } | 
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| 29 |  | 
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| 30 | btHingeConstraint::btHingeConstraint(btRigidBody& rbA,btRigidBody& rbB, const btVector3& pivotInA,const btVector3& pivotInB, | 
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| 31 | btVector3& axisInA,btVector3& axisInB) | 
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| 32 | :btTypedConstraint(HINGE_CONSTRAINT_TYPE, rbA,rbB), | 
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| 33 | m_angularOnly(false), | 
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| 34 | m_enableAngularMotor(false) | 
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| 35 | { | 
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| 36 | m_rbAFrame.getOrigin() = pivotInA; | 
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| 37 |  | 
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| 38 | // since no frame is given, assume this to be zero angle and just pick rb transform axis | 
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| 39 | btVector3 rbAxisA1 = rbA.getCenterOfMassTransform().getBasis().getColumn(0); | 
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| 40 |  | 
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| 41 | btVector3 rbAxisA2; | 
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| 42 | btScalar projection = axisInA.dot(rbAxisA1); | 
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| 43 | if (projection >= 1.0f - SIMD_EPSILON) { | 
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| 44 | rbAxisA1 = -rbA.getCenterOfMassTransform().getBasis().getColumn(2); | 
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| 45 | rbAxisA2 = rbA.getCenterOfMassTransform().getBasis().getColumn(1); | 
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| 46 | } else if (projection <= -1.0f + SIMD_EPSILON) { | 
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| 47 | rbAxisA1 = rbA.getCenterOfMassTransform().getBasis().getColumn(2); | 
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| 48 | rbAxisA2 = rbA.getCenterOfMassTransform().getBasis().getColumn(1); | 
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| 49 | } else { | 
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| 50 | rbAxisA2 = axisInA.cross(rbAxisA1); | 
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| 51 | rbAxisA1 = rbAxisA2.cross(axisInA); | 
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| 52 | } | 
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| 53 |  | 
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| 54 | m_rbAFrame.getBasis().setValue( rbAxisA1.getX(),rbAxisA2.getX(),axisInA.getX(), | 
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| 55 | rbAxisA1.getY(),rbAxisA2.getY(),axisInA.getY(), | 
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| 56 | rbAxisA1.getZ(),rbAxisA2.getZ(),axisInA.getZ() ); | 
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| 57 |  | 
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| 58 | btQuaternion rotationArc = shortestArcQuat(axisInA,axisInB); | 
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| 59 | btVector3 rbAxisB1 =  quatRotate(rotationArc,rbAxisA1); | 
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| 60 | btVector3 rbAxisB2 =  axisInB.cross(rbAxisB1); | 
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| 61 |  | 
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| 62 | m_rbBFrame.getOrigin() = pivotInB; | 
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| 63 | m_rbBFrame.getBasis().setValue( rbAxisB1.getX(),rbAxisB2.getX(),-axisInB.getX(), | 
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| 64 | rbAxisB1.getY(),rbAxisB2.getY(),-axisInB.getY(), | 
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| 65 | rbAxisB1.getZ(),rbAxisB2.getZ(),-axisInB.getZ() ); | 
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| 66 |  | 
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| 67 | //start with free | 
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| 68 | m_lowerLimit = btScalar(1e30); | 
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| 69 | m_upperLimit = btScalar(-1e30); | 
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| 70 | m_biasFactor = 0.3f; | 
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| 71 | m_relaxationFactor = 1.0f; | 
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| 72 | m_limitSoftness = 0.9f; | 
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| 73 | m_solveLimit = false; | 
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| 74 |  | 
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| 75 | } | 
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| 76 |  | 
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| 77 |  | 
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| 78 |  | 
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| 79 | btHingeConstraint::btHingeConstraint(btRigidBody& rbA,const btVector3& pivotInA,btVector3& axisInA) | 
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| 80 | :btTypedConstraint(HINGE_CONSTRAINT_TYPE, rbA), m_angularOnly(false), m_enableAngularMotor(false) | 
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| 81 | { | 
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| 82 |  | 
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| 83 | // since no frame is given, assume this to be zero angle and just pick rb transform axis | 
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| 84 | // fixed axis in worldspace | 
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| 85 | btVector3 rbAxisA1, rbAxisA2; | 
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| 86 | btPlaneSpace1(axisInA, rbAxisA1, rbAxisA2); | 
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| 87 |  | 
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| 88 | m_rbAFrame.getOrigin() = pivotInA; | 
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| 89 | m_rbAFrame.getBasis().setValue( rbAxisA1.getX(),rbAxisA2.getX(),axisInA.getX(), | 
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| 90 | rbAxisA1.getY(),rbAxisA2.getY(),axisInA.getY(), | 
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| 91 | rbAxisA1.getZ(),rbAxisA2.getZ(),axisInA.getZ() ); | 
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| 92 |  | 
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| 93 | btVector3 axisInB = rbA.getCenterOfMassTransform().getBasis() * -axisInA; | 
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| 94 |  | 
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| 95 | btQuaternion rotationArc = shortestArcQuat(axisInA,axisInB); | 
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| 96 | btVector3 rbAxisB1 =  quatRotate(rotationArc,rbAxisA1); | 
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| 97 | btVector3 rbAxisB2 = axisInB.cross(rbAxisB1); | 
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| 98 |  | 
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| 99 |  | 
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| 100 | m_rbBFrame.getOrigin() = rbA.getCenterOfMassTransform()(pivotInA); | 
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| 101 | m_rbBFrame.getBasis().setValue( rbAxisB1.getX(),rbAxisB2.getX(),axisInB.getX(), | 
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| 102 | rbAxisB1.getY(),rbAxisB2.getY(),axisInB.getY(), | 
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| 103 | rbAxisB1.getZ(),rbAxisB2.getZ(),axisInB.getZ() ); | 
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| 104 |  | 
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| 105 | //start with free | 
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| 106 | m_lowerLimit = btScalar(1e30); | 
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| 107 | m_upperLimit = btScalar(-1e30); | 
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| 108 | m_biasFactor = 0.3f; | 
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| 109 | m_relaxationFactor = 1.0f; | 
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| 110 | m_limitSoftness = 0.9f; | 
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| 111 | m_solveLimit = false; | 
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| 112 | } | 
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| 113 |  | 
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| 114 | btHingeConstraint::btHingeConstraint(btRigidBody& rbA,btRigidBody& rbB, | 
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| 115 | const btTransform& rbAFrame, const btTransform& rbBFrame) | 
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| 116 | :btTypedConstraint(HINGE_CONSTRAINT_TYPE, rbA,rbB),m_rbAFrame(rbAFrame),m_rbBFrame(rbBFrame), | 
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| 117 | m_angularOnly(false), | 
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| 118 | m_enableAngularMotor(false) | 
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| 119 | { | 
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| 120 | // flip axis | 
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| 121 | m_rbBFrame.getBasis()[0][2] *= btScalar(-1.); | 
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| 122 | m_rbBFrame.getBasis()[1][2] *= btScalar(-1.); | 
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| 123 | m_rbBFrame.getBasis()[2][2] *= btScalar(-1.); | 
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| 124 |  | 
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| 125 | //start with free | 
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| 126 | m_lowerLimit = btScalar(1e30); | 
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| 127 | m_upperLimit = btScalar(-1e30); | 
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| 128 | m_biasFactor = 0.3f; | 
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| 129 | m_relaxationFactor = 1.0f; | 
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| 130 | m_limitSoftness = 0.9f; | 
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| 131 | m_solveLimit = false; | 
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| 132 | } | 
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| 133 |  | 
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| 134 |  | 
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| 135 |  | 
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| 136 | btHingeConstraint::btHingeConstraint(btRigidBody& rbA, const btTransform& rbAFrame) | 
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| 137 | :btTypedConstraint(HINGE_CONSTRAINT_TYPE, rbA),m_rbAFrame(rbAFrame),m_rbBFrame(rbAFrame), | 
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| 138 | m_angularOnly(false), | 
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| 139 | m_enableAngularMotor(false) | 
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| 140 | { | 
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| 141 | ///not providing rigidbody B means implicitly using worldspace for body B | 
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| 142 |  | 
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| 143 | // flip axis | 
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| 144 | m_rbBFrame.getBasis()[0][2] *= btScalar(-1.); | 
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| 145 | m_rbBFrame.getBasis()[1][2] *= btScalar(-1.); | 
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| 146 | m_rbBFrame.getBasis()[2][2] *= btScalar(-1.); | 
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| 147 |  | 
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| 148 | m_rbBFrame.getOrigin() = m_rbA.getCenterOfMassTransform()(m_rbAFrame.getOrigin()); | 
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| 149 |  | 
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| 150 | //start with free | 
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| 151 | m_lowerLimit = btScalar(1e30); | 
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| 152 | m_upperLimit = btScalar(-1e30); | 
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| 153 | m_biasFactor = 0.3f; | 
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| 154 | m_relaxationFactor = 1.0f; | 
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| 155 | m_limitSoftness = 0.9f; | 
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| 156 | m_solveLimit = false; | 
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| 157 | } | 
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| 158 |  | 
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| 159 | void    btHingeConstraint::buildJacobian() | 
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| 160 | { | 
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| 161 | m_appliedImpulse = btScalar(0.); | 
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| 162 |  | 
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| 163 | if (!m_angularOnly) | 
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| 164 | { | 
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| 165 | btVector3 pivotAInW = m_rbA.getCenterOfMassTransform()*m_rbAFrame.getOrigin(); | 
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| 166 | btVector3 pivotBInW = m_rbB.getCenterOfMassTransform()*m_rbBFrame.getOrigin(); | 
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| 167 | btVector3 relPos = pivotBInW - pivotAInW; | 
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| 168 |  | 
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| 169 | btVector3 normal[3]; | 
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| 170 | if (relPos.length2() > SIMD_EPSILON) | 
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| 171 | { | 
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| 172 | normal[0] = relPos.normalized(); | 
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| 173 | } | 
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| 174 | else | 
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| 175 | { | 
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| 176 | normal[0].setValue(btScalar(1.0),0,0); | 
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| 177 | } | 
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| 178 |  | 
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| 179 | btPlaneSpace1(normal[0], normal[1], normal[2]); | 
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| 180 |  | 
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| 181 | for (int i=0;i<3;i++) | 
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| 182 | { | 
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| 183 | new (&m_jac[i]) btJacobianEntry( | 
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| 184 | m_rbA.getCenterOfMassTransform().getBasis().transpose(), | 
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| 185 | m_rbB.getCenterOfMassTransform().getBasis().transpose(), | 
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| 186 | pivotAInW - m_rbA.getCenterOfMassPosition(), | 
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| 187 | pivotBInW - m_rbB.getCenterOfMassPosition(), | 
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| 188 | normal[i], | 
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| 189 | m_rbA.getInvInertiaDiagLocal(), | 
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| 190 | m_rbA.getInvMass(), | 
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| 191 | m_rbB.getInvInertiaDiagLocal(), | 
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| 192 | m_rbB.getInvMass()); | 
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| 193 | } | 
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| 194 | } | 
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| 195 |  | 
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| 196 | //calculate two perpendicular jointAxis, orthogonal to hingeAxis | 
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| 197 | //these two jointAxis require equal angular velocities for both bodies | 
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| 198 |  | 
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| 199 | //this is unused for now, it's a todo | 
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| 200 | btVector3 jointAxis0local; | 
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| 201 | btVector3 jointAxis1local; | 
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| 202 |  | 
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| 203 | btPlaneSpace1(m_rbAFrame.getBasis().getColumn(2),jointAxis0local,jointAxis1local); | 
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| 204 |  | 
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| 205 | getRigidBodyA().getCenterOfMassTransform().getBasis() * m_rbAFrame.getBasis().getColumn(2); | 
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| 206 | btVector3 jointAxis0 = getRigidBodyA().getCenterOfMassTransform().getBasis() * jointAxis0local; | 
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| 207 | btVector3 jointAxis1 = getRigidBodyA().getCenterOfMassTransform().getBasis() * jointAxis1local; | 
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| 208 | btVector3 hingeAxisWorld = getRigidBodyA().getCenterOfMassTransform().getBasis() * m_rbAFrame.getBasis().getColumn(2); | 
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| 209 |  | 
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| 210 | new (&m_jacAng[0])      btJacobianEntry(jointAxis0, | 
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| 211 | m_rbA.getCenterOfMassTransform().getBasis().transpose(), | 
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| 212 | m_rbB.getCenterOfMassTransform().getBasis().transpose(), | 
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| 213 | m_rbA.getInvInertiaDiagLocal(), | 
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| 214 | m_rbB.getInvInertiaDiagLocal()); | 
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| 215 |  | 
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| 216 | new (&m_jacAng[1])      btJacobianEntry(jointAxis1, | 
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| 217 | m_rbA.getCenterOfMassTransform().getBasis().transpose(), | 
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| 218 | m_rbB.getCenterOfMassTransform().getBasis().transpose(), | 
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| 219 | m_rbA.getInvInertiaDiagLocal(), | 
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| 220 | m_rbB.getInvInertiaDiagLocal()); | 
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| 221 |  | 
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| 222 | new (&m_jacAng[2])      btJacobianEntry(hingeAxisWorld, | 
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| 223 | m_rbA.getCenterOfMassTransform().getBasis().transpose(), | 
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| 224 | m_rbB.getCenterOfMassTransform().getBasis().transpose(), | 
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| 225 | m_rbA.getInvInertiaDiagLocal(), | 
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| 226 | m_rbB.getInvInertiaDiagLocal()); | 
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| 227 |  | 
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| 228 |  | 
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| 229 | // Compute limit information | 
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| 230 | btScalar hingeAngle = getHingeAngle(); | 
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| 231 |  | 
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| 232 | //set bias, sign, clear accumulator | 
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| 233 | m_correction = btScalar(0.); | 
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| 234 | m_limitSign = btScalar(0.); | 
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| 235 | m_solveLimit = false; | 
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| 236 | m_accLimitImpulse = btScalar(0.); | 
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| 237 |  | 
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| 238 | //      if (m_lowerLimit < m_upperLimit) | 
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| 239 | if (m_lowerLimit <= m_upperLimit) | 
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| 240 | { | 
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| 241 | //              if (hingeAngle <= m_lowerLimit*m_limitSoftness) | 
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| 242 | if (hingeAngle <= m_lowerLimit) | 
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| 243 | { | 
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| 244 | m_correction = (m_lowerLimit - hingeAngle); | 
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| 245 | m_limitSign = 1.0f; | 
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| 246 | m_solveLimit = true; | 
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| 247 | } | 
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| 248 | //              else if (hingeAngle >= m_upperLimit*m_limitSoftness) | 
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| 249 | else if (hingeAngle >= m_upperLimit) | 
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| 250 | { | 
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| 251 | m_correction = m_upperLimit - hingeAngle; | 
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| 252 | m_limitSign = -1.0f; | 
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| 253 | m_solveLimit = true; | 
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| 254 | } | 
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| 255 | } | 
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| 256 |  | 
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| 257 | //Compute K = J*W*J' for hinge axis | 
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| 258 | btVector3 axisA =  getRigidBodyA().getCenterOfMassTransform().getBasis() *  m_rbAFrame.getBasis().getColumn(2); | 
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| 259 | m_kHinge =   1.0f / (getRigidBodyA().computeAngularImpulseDenominator(axisA) + | 
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| 260 | getRigidBodyB().computeAngularImpulseDenominator(axisA)); | 
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| 261 |  | 
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| 262 | } | 
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| 263 |  | 
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| 264 | void    btHingeConstraint::solveConstraint(btScalar     timeStep) | 
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| 265 | { | 
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| 266 |  | 
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| 267 | btVector3 pivotAInW = m_rbA.getCenterOfMassTransform()*m_rbAFrame.getOrigin(); | 
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| 268 | btVector3 pivotBInW = m_rbB.getCenterOfMassTransform()*m_rbBFrame.getOrigin(); | 
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| 269 |  | 
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| 270 | btScalar tau = btScalar(0.3); | 
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| 271 |  | 
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| 272 | //linear part | 
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| 273 | if (!m_angularOnly) | 
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| 274 | { | 
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| 275 | btVector3 rel_pos1 = pivotAInW - m_rbA.getCenterOfMassPosition(); | 
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| 276 | btVector3 rel_pos2 = pivotBInW - m_rbB.getCenterOfMassPosition(); | 
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| 277 |  | 
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| 278 | btVector3 vel1 = m_rbA.getVelocityInLocalPoint(rel_pos1); | 
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| 279 | btVector3 vel2 = m_rbB.getVelocityInLocalPoint(rel_pos2); | 
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| 280 | btVector3 vel = vel1 - vel2; | 
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| 281 |  | 
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| 282 | for (int i=0;i<3;i++) | 
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| 283 | { | 
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| 284 | const btVector3& normal = m_jac[i].m_linearJointAxis; | 
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| 285 | btScalar jacDiagABInv = btScalar(1.) / m_jac[i].getDiagonal(); | 
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| 286 |  | 
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| 287 | btScalar rel_vel; | 
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| 288 | rel_vel = normal.dot(vel); | 
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| 289 | //positional error (zeroth order error) | 
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| 290 | btScalar depth = -(pivotAInW - pivotBInW).dot(normal); //this is the error projected on the normal | 
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| 291 | btScalar impulse = depth*tau/timeStep  * jacDiagABInv -  rel_vel * jacDiagABInv; | 
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| 292 | m_appliedImpulse += impulse; | 
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| 293 | btVector3 impulse_vector = normal * impulse; | 
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| 294 | m_rbA.applyImpulse(impulse_vector, pivotAInW - m_rbA.getCenterOfMassPosition()); | 
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| 295 | m_rbB.applyImpulse(-impulse_vector, pivotBInW - m_rbB.getCenterOfMassPosition()); | 
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| 296 | } | 
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| 297 | } | 
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| 298 |  | 
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| 299 |  | 
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| 300 | { | 
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| 301 | ///solve angular part | 
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| 302 |  | 
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| 303 | // get axes in world space | 
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| 304 | btVector3 axisA =  getRigidBodyA().getCenterOfMassTransform().getBasis() *  m_rbAFrame.getBasis().getColumn(2); | 
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| 305 | btVector3 axisB =  getRigidBodyB().getCenterOfMassTransform().getBasis() *  m_rbBFrame.getBasis().getColumn(2); | 
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| 306 |  | 
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| 307 | const btVector3& angVelA = getRigidBodyA().getAngularVelocity(); | 
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| 308 | const btVector3& angVelB = getRigidBodyB().getAngularVelocity(); | 
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| 309 |  | 
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| 310 | btVector3 angVelAroundHingeAxisA = axisA * axisA.dot(angVelA); | 
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| 311 | btVector3 angVelAroundHingeAxisB = axisB * axisB.dot(angVelB); | 
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| 312 |  | 
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| 313 | btVector3 angAorthog = angVelA - angVelAroundHingeAxisA; | 
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| 314 | btVector3 angBorthog = angVelB - angVelAroundHingeAxisB; | 
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| 315 | btVector3 velrelOrthog = angAorthog-angBorthog; | 
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| 316 | { | 
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| 317 | //solve orthogonal angular velocity correction | 
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| 318 | btScalar relaxation = btScalar(1.); | 
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| 319 | btScalar len = velrelOrthog.length(); | 
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| 320 | if (len > btScalar(0.00001)) | 
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| 321 | { | 
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| 322 | btVector3 normal = velrelOrthog.normalized(); | 
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| 323 | btScalar denom = getRigidBodyA().computeAngularImpulseDenominator(normal) + | 
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| 324 | getRigidBodyB().computeAngularImpulseDenominator(normal); | 
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| 325 | // scale for mass and relaxation | 
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| 326 | velrelOrthog *= (btScalar(1.)/denom) * m_relaxationFactor; | 
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| 327 | } | 
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| 328 |  | 
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| 329 | //solve angular positional correction | 
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| 330 | btVector3 angularError = -axisA.cross(axisB) *(btScalar(1.)/timeStep); | 
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| 331 | btScalar len2 = angularError.length(); | 
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| 332 | if (len2>btScalar(0.00001)) | 
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| 333 | { | 
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| 334 | btVector3 normal2 = angularError.normalized(); | 
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| 335 | btScalar denom2 = getRigidBodyA().computeAngularImpulseDenominator(normal2) + | 
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| 336 | getRigidBodyB().computeAngularImpulseDenominator(normal2); | 
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| 337 | angularError *= (btScalar(1.)/denom2) * relaxation; | 
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| 338 | } | 
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| 339 |  | 
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| 340 | m_rbA.applyTorqueImpulse(-velrelOrthog+angularError); | 
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| 341 | m_rbB.applyTorqueImpulse(velrelOrthog-angularError); | 
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| 342 |  | 
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| 343 | // solve limit | 
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| 344 | if (m_solveLimit) | 
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| 345 | { | 
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| 346 | btScalar amplitude = ( (angVelB - angVelA).dot( axisA )*m_relaxationFactor + m_correction* (btScalar(1.)/timeStep)*m_biasFactor  ) * m_limitSign; | 
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| 347 |  | 
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| 348 | btScalar impulseMag = amplitude * m_kHinge; | 
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| 349 |  | 
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| 350 | // Clamp the accumulated impulse | 
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| 351 | btScalar temp = m_accLimitImpulse; | 
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| 352 | m_accLimitImpulse = btMax(m_accLimitImpulse + impulseMag, btScalar(0) ); | 
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| 353 | impulseMag = m_accLimitImpulse - temp; | 
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| 354 |  | 
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| 355 |  | 
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| 356 | btVector3 impulse = axisA * impulseMag * m_limitSign; | 
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| 357 | m_rbA.applyTorqueImpulse(impulse); | 
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| 358 | m_rbB.applyTorqueImpulse(-impulse); | 
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| 359 | } | 
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| 360 | } | 
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| 361 |  | 
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| 362 | //apply motor | 
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| 363 | if (m_enableAngularMotor) | 
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| 364 | { | 
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| 365 | //todo: add limits too | 
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| 366 | btVector3 angularLimit(0,0,0); | 
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| 367 |  | 
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| 368 | btVector3 velrel = angVelAroundHingeAxisA - angVelAroundHingeAxisB; | 
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| 369 | btScalar projRelVel = velrel.dot(axisA); | 
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| 370 |  | 
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| 371 | btScalar desiredMotorVel = m_motorTargetVelocity; | 
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| 372 | btScalar motor_relvel = desiredMotorVel - projRelVel; | 
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| 373 |  | 
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| 374 | btScalar unclippedMotorImpulse = m_kHinge * motor_relvel;; | 
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| 375 | //todo: should clip against accumulated impulse | 
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| 376 | btScalar clippedMotorImpulse = unclippedMotorImpulse > m_maxMotorImpulse ? m_maxMotorImpulse : unclippedMotorImpulse; | 
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| 377 | clippedMotorImpulse = clippedMotorImpulse < -m_maxMotorImpulse ? -m_maxMotorImpulse : clippedMotorImpulse; | 
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| 378 | btVector3 motorImp = clippedMotorImpulse * axisA; | 
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| 379 |  | 
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| 380 | m_rbA.applyTorqueImpulse(motorImp+angularLimit); | 
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| 381 | m_rbB.applyTorqueImpulse(-motorImp-angularLimit); | 
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| 382 |  | 
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| 383 | } | 
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| 384 | } | 
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| 385 |  | 
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| 386 | } | 
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| 387 |  | 
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| 388 | void    btHingeConstraint::updateRHS(btScalar   timeStep) | 
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| 389 | { | 
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| 390 | (void)timeStep; | 
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| 391 |  | 
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| 392 | } | 
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| 393 |  | 
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| 394 | btScalar btHingeConstraint::getHingeAngle() | 
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| 395 | { | 
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| 396 | const btVector3 refAxis0  = getRigidBodyA().getCenterOfMassTransform().getBasis() * m_rbAFrame.getBasis().getColumn(0); | 
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| 397 | const btVector3 refAxis1  = getRigidBodyA().getCenterOfMassTransform().getBasis() * m_rbAFrame.getBasis().getColumn(1); | 
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| 398 | const btVector3 swingAxis = getRigidBodyB().getCenterOfMassTransform().getBasis() * m_rbBFrame.getBasis().getColumn(1); | 
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| 399 |  | 
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| 400 | return btAtan2Fast( swingAxis.dot(refAxis0), swingAxis.dot(refAxis1)  ); | 
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| 401 | } | 
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| 402 |  | 
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