241 lines
14 KiB
C++
241 lines
14 KiB
C++
/** @file
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* @author Daniel Chappuis
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* @copyright 2010-2016 Daniel Chappuis
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* @license BSD 3 clauses (see license file)
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*/
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#pragma once
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#include <ephysics/constraint/ContactPoint.hpp>
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#include <ephysics/configuration.hpp>
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#include <ephysics/constraint/Joint.hpp>
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#include <ephysics/collision/ContactManifold.hpp>
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#include <ephysics/engine/Island.hpp>
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#include <ephysics/engine/Impulse.hpp>
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#include <etk/Map.hpp>
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#include <set>
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namespace ephysics {
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/**
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* @brief This class represents the contact solver that is used to solve rigid bodies contacts.
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* The constraint solver is based on the "Sequential Impulse" technique described by
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* Erin Catto in his GDC slides (http://code.google.com/p/box2d/downloads/list).
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*
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* A constraint between two bodies is represented by a function C(x) which is equal to zero
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* when the constraint is satisfied. The condition C(x)=0 describes a valid position and the
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* condition dC(x)/dt=0 describes a valid velocity. We have dC(x)/dt = Jv + b = 0 where J is
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* the Jacobian matrix of the constraint, v is a vector that contains the velocity of both
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* bodies and b is the constraint bias. We are looking for a force F_c that will act on the
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* bodies to keep the constraint satisfied. Note that from the virtual work principle, we have
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* F_c = J^t * lambda where J^t is the transpose of the Jacobian matrix and lambda is a
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* Lagrange multiplier. Therefore, finding the force F_c is equivalent to finding the Lagrange
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* multiplier lambda.
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*
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* An impulse P = F * dt where F is a force and dt is the timestep. We can apply impulses a
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* body to change its velocity. The idea of the Sequential Impulse technique is to apply
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* impulses to bodies of each constraints in order to keep the constraint satisfied.
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*
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* --- Step 1 ---
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*
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* First, we int32_tegrate the applied force F_a acting of each rigid body (like gravity, ...) and
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* we obtain some new velocities v2' that tends to violate the constraints.
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*
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* v2' = v1 + dt * M^-1 * F_a
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*
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* where M is a matrix that contains mass and inertia tensor information.
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*
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* --- Step 2 ---
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*
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* During the second step, we iterate over all the constraints for a certain number of
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* iterations and for each constraint we compute the impulse to apply to the bodies needed
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* so that the new velocity of the bodies satisfy Jv + b = 0. From the Newton law, we know that
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* M * deltaV = P_c where M is the mass of the body, deltaV is the difference of velocity and
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* P_c is the constraint impulse to apply to the body. Therefore, we have
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* v2 = v2' + M^-1 * P_c. For each constraint, we can compute the Lagrange multiplier lambda
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* using : lambda = -m_c (Jv2' + b) where m_c = 1 / (J * M^-1 * J^t). Now that we have the
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* Lagrange multiplier lambda, we can compute the impulse P_c = J^t * lambda * dt to apply to
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* the bodies to satisfy the constraint.
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*
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* --- Step 3 ---
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*
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* In the third step, we int32_tegrate the new position x2 of the bodies using the new velocities
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* v2 computed in the second step with : x2 = x1 + dt * v2.
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*
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* Note that in the following code (as it is also explained in the slides from Erin Catto),
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* the value lambda is not only the lagrange multiplier but is the multiplication of the
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* Lagrange multiplier with the timestep dt. Therefore, in the following code, when we use
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* lambda, we mean (lambda * dt).
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*
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* We are using the accumulated impulse technique that is also described in the slides from
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* Erin Catto.
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*
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* We are also using warm starting. The idea is to warm start the solver at the beginning of
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* each step by applying the last impulstes for the constraints that we already existing at the
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* previous step. This allows the iterative solver to converge faster towards the solution.
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*
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* For contact constraints, we are also using split impulses so that the position correction
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* that uses Baumgarte stabilization does not change the momentum of the bodies.
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*
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* There are two ways to apply the friction constraints. Either the friction constraints are
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* applied at each contact point or they are applied only at the center of the contact manifold
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* between two bodies. If we solve the friction constraints at each contact point, we need
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* two constraints (two tangential friction directions) and if we solve the friction
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* constraints at the center of the contact manifold, we need two constraints for tangential
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* friction but also another twist friction constraint to prevent spin of the body around the
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* contact manifold center.
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*/
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class ContactSolver {
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private:
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/**
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* Contact solver int32_ternal data structure that to store all the
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* information relative to a contact point
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*/
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struct ContactPointSolver {
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float penetrationImpulse; //!< Accumulated normal impulse
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float friction1Impulse; //!< Accumulated impulse in the 1st friction direction
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float friction2Impulse; //!< Accumulated impulse in the 2nd friction direction
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float penetrationSplitImpulse; //!< Accumulated split impulse for penetration correction
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vec3 rollingResistanceImpulse; //!< Accumulated rolling resistance impulse
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vec3 normal; //!< Normal vector of the contact
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vec3 frictionVector1; //!< First friction vector in the tangent plane
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vec3 frictionvec2; //!< Second friction vector in the tangent plane
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vec3 oldFrictionVector1; //!< Old first friction vector in the tangent plane
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vec3 oldFrictionvec2; //!< Old second friction vector in the tangent plane
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vec3 r1; //!< Vector from the body 1 center to the contact point
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vec3 r2; //!< Vector from the body 2 center to the contact point
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vec3 r1CrossT1; //!< Cross product of r1 with 1st friction vector
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vec3 r1CrossT2; //!< Cross product of r1 with 2nd friction vector
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vec3 r2CrossT1; //!< Cross product of r2 with 1st friction vector
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vec3 r2CrossT2; //!< Cross product of r2 with 2nd friction vector
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vec3 r1CrossN; //!< Cross product of r1 with the contact normal
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vec3 r2CrossN; //!< Cross product of r2 with the contact normal
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float penetrationDepth; //!< Penetration depth
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float restitutionBias; //!< Velocity restitution bias
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float inversePenetrationMass; //!< Inverse of the matrix K for the penenetration
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float inverseFriction1Mass; //!< Inverse of the matrix K for the 1st friction
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float inverseFriction2Mass; //!< Inverse of the matrix K for the 2nd friction
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bool isRestingContact; //!< True if the contact was existing last time step
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ContactPoint* externalContact; //!< Pointer to the external contact
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};
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/**
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* @brief Contact solver int32_ternal data structure to store all the information relative to a contact manifold.
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*/
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struct ContactManifoldSolver {
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uint32_t indexBody1; //!< Index of body 1 in the constraint solver
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uint32_t indexBody2; //!< Index of body 2 in the constraint solver
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float massInverseBody1; //!< Inverse of the mass of body 1
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float massInverseBody2; //!< Inverse of the mass of body 2
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etk::Matrix3x3 inverseInertiaTensorBody1; //!< Inverse inertia tensor of body 1
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etk::Matrix3x3 inverseInertiaTensorBody2; //!< Inverse inertia tensor of body 2
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ContactPointSolver contacts[MAX_CONTACT_POINTS_IN_MANIFOLD]; //!< Contact point constraints
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uint32_t nbContacts; //!< Number of contact points
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bool isBody1DynamicType; //!< True if the body 1 is of type dynamic
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bool isBody2DynamicType; //!< True if the body 2 is of type dynamic
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float restitutionFactor; //!< Mix of the restitution factor for two bodies
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float frictionCoefficient; //!< Mix friction coefficient for the two bodies
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float rollingResistanceFactor; //!< Rolling resistance factor between the two bodies
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ContactManifold* externalContactManifold; //!< Pointer to the external contact manifold
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// - Variables used when friction constraints are apply at the center of the manifold-//
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vec3 normal; //!< Average normal vector of the contact manifold
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vec3 frictionPointBody1; //!< Point on body 1 where to apply the friction constraints
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vec3 frictionPointBody2; //!< Point on body 2 where to apply the friction constraints
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vec3 r1Friction; //!< R1 vector for the friction constraints
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vec3 r2Friction; //!< R2 vector for the friction constraints
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vec3 r1CrossT1; //!< Cross product of r1 with 1st friction vector
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vec3 r1CrossT2; //!< Cross product of r1 with 2nd friction vector
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vec3 r2CrossT1; //!< Cross product of r2 with 1st friction vector
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vec3 r2CrossT2; //!< Cross product of r2 with 2nd friction vector
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float inverseFriction1Mass; //!< Matrix K for the first friction constraint
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float inverseFriction2Mass; //!< Matrix K for the second friction constraint
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float inverseTwistFrictionMass; //!< Matrix K for the twist friction constraint
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etk::Matrix3x3 inverseRollingResistance; //!< Matrix K for the rolling resistance constraint
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vec3 frictionVector1; //!< First friction direction at contact manifold center
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vec3 frictionvec2; //!< Second friction direction at contact manifold center
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vec3 oldFrictionVector1; //!< Old 1st friction direction at contact manifold center
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vec3 oldFrictionvec2; //!< Old 2nd friction direction at contact manifold center
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float friction1Impulse; //!< First friction direction impulse at manifold center
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float friction2Impulse; //!< Second friction direction impulse at manifold center
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float frictionTwistImpulse; //!< Twist friction impulse at contact manifold center
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vec3 rollingResistanceImpulse; //!< Rolling resistance impulse
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};
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static const float BETA; //!< Beta value for the penetration depth position correction without split impulses
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static const float BETA_SPLIT_IMPULSE; //!< Beta value for the penetration depth position correction with split impulses
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static const float SLOP; //!< Slop distance (allowed penetration distance between bodies)
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vec3* m_splitLinearVelocities; //!< Split linear velocities for the position contact solver (split impulse)
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vec3* m_splitAngularVelocities; //!< Split angular velocities for the position contact solver (split impulse)
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float m_timeStep; //!< Current time step
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ContactManifoldSolver* m_contactConstraints; //!< Contact constraints
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uint32_t m_numberContactManifolds; //!< Number of contact constraints
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vec3* m_linearVelocities; //!< Array of linear velocities
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vec3* m_angularVelocities; //!< Array of angular velocities
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const etk::Map<RigidBody*, uint32_t>& m_mapBodyToConstrainedVelocityIndex; //!< Reference to the map of rigid body to their index in the constrained velocities array
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bool m_isWarmStartingActive; //!< True if the warm starting of the solver is active
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bool m_isSplitImpulseActive; //!< True if the split impulse position correction is active
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bool m_isSolveFrictionAtContactManifoldCenterActive; //!< True if we solve 3 friction constraints at the contact manifold center only instead of 2 friction constraints at each contact point
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/// Initialize the contact constraints before solving the system
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void initializeContactConstraints();
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/// Apply an impulse to the two bodies of a constraint
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void applyImpulse(const Impulse& impulse, const ContactManifoldSolver& manifold);
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/// Apply an impulse to the two bodies of a constraint
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void applySplitImpulse(const Impulse& impulse,
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const ContactManifoldSolver& manifold);
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/// Compute the collision restitution factor from the restitution factor of each body
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float computeMixedRestitutionFactor(RigidBody *body1,
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RigidBody *body2) const;
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/// Compute the mixed friction coefficient from the friction coefficient of each body
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float computeMixedFrictionCoefficient(RigidBody* body1,
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RigidBody* body2) const;
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/// Compute th mixed rolling resistance factor between two bodies
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float computeMixedRollingResistance(RigidBody* body1, RigidBody* body2) const;
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/// Compute the two unit orthogonal vectors "t1" and "t2" that span the tangential friction
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/// plane for a contact point. The two vectors have to be
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/// such that : t1 x t2 = contactNormal.
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void computeFrictionVectors(const vec3& deltaVelocity,
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ContactPointSolver &contactPoint) const;
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/// Compute the two unit orthogonal vectors "t1" and "t2" that span the tangential friction
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/// plane for a contact manifold. The two vectors have to be
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/// such that : t1 x t2 = contactNormal.
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void computeFrictionVectors(const vec3& deltaVelocity,
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ContactManifoldSolver& contactPoint) const;
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/// Compute a penetration constraint impulse
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const Impulse computePenetrationImpulse(float deltaLambda,
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const ContactPointSolver& contactPoint) const;
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/// Compute the first friction constraint impulse
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const Impulse computeFriction1Impulse(float deltaLambda,
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const ContactPointSolver& contactPoint) const;
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/// Compute the second friction constraint impulse
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const Impulse computeFriction2Impulse(float deltaLambda,
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const ContactPointSolver& contactPoint) const;
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public:
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/// Constructor
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ContactSolver(const etk::Map<RigidBody*, uint32_t>& mapBodyToVelocityIndex);
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/// Destructor
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virtual ~ContactSolver();
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/// Initialize the constraint solver for a given island
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void initializeForIsland(float dt, Island* island);
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/// Set the split velocities arrays
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void setSplitVelocitiesArrays(vec3* splitLinearVelocities,
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vec3* splitAngularVelocities);
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/// Set the constrained velocities arrays
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void setConstrainedVelocitiesArrays(vec3* constrainedLinearVelocities,
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vec3* constrainedAngularVelocities);
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/// Warm start the solver.
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void warmStart();
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/// Store the computed impulses to use them to
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/// warm start the solver at the next iteration
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void storeImpulses();
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/// Solve the contacts
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void solve();
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/// Return true if the split impulses position correction technique is used for contacts
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bool isSplitImpulseActive() const;
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/// Activate or Deactivate the split impulses for contacts
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void setIsSplitImpulseActive(bool isActive);
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/// Activate or deactivate the solving of friction constraints at the center of
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/// the contact manifold instead of solving them at each contact point
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void setIsSolveFrictionAtContactManifoldCenterActive(bool isActive);
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/// Clean up the constraint solver
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void cleanup();
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};
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}
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