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authorchai <chaifix@163.com>2019-03-19 23:06:27 +0800
committerchai <chaifix@163.com>2019-03-19 23:06:27 +0800
commit1497dccd63a84b7ee2b229b1ad9c5c02718f2a78 (patch)
treef8d1bff50da13e126d08c7345653e002e293202d /Source/3rdParty/Box2D/Dynamics/b2Island.cpp
parent5e2a973516e0729b225da9de0b03015dc5854ac4 (diff)
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-/*
-* Copyright (c) 2006-2011 Erin Catto http://www.box2d.org
-*
-* This software is provided 'as-is', without any express or implied
-* warranty. In no event will the authors be held liable for any damages
-* arising from the use of this software.
-* Permission is granted to anyone to use this software for any purpose,
-* including commercial applications, and to alter it and redistribute it
-* freely, subject to the following restrictions:
-* 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.
-* 2. Altered source versions must be plainly marked as such, and must not be
-* misrepresented as being the original software.
-* 3. This notice may not be removed or altered from any source distribution.
-*/
-
-#include "Box2D/Collision/b2Distance.h"
-#include "Box2D/Dynamics/b2Island.h"
-#include "Box2D/Dynamics/b2Body.h"
-#include "Box2D/Dynamics/b2Fixture.h"
-#include "Box2D/Dynamics/b2World.h"
-#include "Box2D/Dynamics/Contacts/b2Contact.h"
-#include "Box2D/Dynamics/Contacts/b2ContactSolver.h"
-#include "Box2D/Dynamics/Joints/b2Joint.h"
-#include "Box2D/Common/b2StackAllocator.h"
-#include "Box2D/Common/b2Timer.h"
-
-/*
-Position Correction Notes
-=========================
-I tried the several algorithms for position correction of the 2D revolute joint.
-I looked at these systems:
-- simple pendulum (1m diameter sphere on massless 5m stick) with initial angular velocity of 100 rad/s.
-- suspension bridge with 30 1m long planks of length 1m.
-- multi-link chain with 30 1m long links.
-
-Here are the algorithms:
-
-Baumgarte - A fraction of the position error is added to the velocity error. There is no
-separate position solver.
-
-Pseudo Velocities - After the velocity solver and position integration,
-the position error, Jacobian, and effective mass are recomputed. Then
-the velocity constraints are solved with pseudo velocities and a fraction
-of the position error is added to the pseudo velocity error. The pseudo
-velocities are initialized to zero and there is no warm-starting. After
-the position solver, the pseudo velocities are added to the positions.
-This is also called the First Order World method or the Position LCP method.
-
-Modified Nonlinear Gauss-Seidel (NGS) - Like Pseudo Velocities except the
-position error is re-computed for each constraint and the positions are updated
-after the constraint is solved. The radius vectors (aka Jacobians) are
-re-computed too (otherwise the algorithm has horrible instability). The pseudo
-velocity states are not needed because they are effectively zero at the beginning
-of each iteration. Since we have the current position error, we allow the
-iterations to terminate early if the error becomes smaller than b2_linearSlop.
-
-Full NGS or just NGS - Like Modified NGS except the effective mass are re-computed
-each time a constraint is solved.
-
-Here are the results:
-Baumgarte - this is the cheapest algorithm but it has some stability problems,
-especially with the bridge. The chain links separate easily close to the root
-and they jitter as they struggle to pull together. This is one of the most common
-methods in the field. The big drawback is that the position correction artificially
-affects the momentum, thus leading to instabilities and false bounce. I used a
-bias factor of 0.2. A larger bias factor makes the bridge less stable, a smaller
-factor makes joints and contacts more spongy.
-
-Pseudo Velocities - the is more stable than the Baumgarte method. The bridge is
-stable. However, joints still separate with large angular velocities. Drag the
-simple pendulum in a circle quickly and the joint will separate. The chain separates
-easily and does not recover. I used a bias factor of 0.2. A larger value lead to
-the bridge collapsing when a heavy cube drops on it.
-
-Modified NGS - this algorithm is better in some ways than Baumgarte and Pseudo
-Velocities, but in other ways it is worse. The bridge and chain are much more
-stable, but the simple pendulum goes unstable at high angular velocities.
-
-Full NGS - stable in all tests. The joints display good stiffness. The bridge
-still sags, but this is better than infinite forces.
-
-Recommendations
-Pseudo Velocities are not really worthwhile because the bridge and chain cannot
-recover from joint separation. In other cases the benefit over Baumgarte is small.
-
-Modified NGS is not a robust method for the revolute joint due to the violent
-instability seen in the simple pendulum. Perhaps it is viable with other constraint
-types, especially scalar constraints where the effective mass is a scalar.
-
-This leaves Baumgarte and Full NGS. Baumgarte has small, but manageable instabilities
-and is very fast. I don't think we can escape Baumgarte, especially in highly
-demanding cases where high constraint fidelity is not needed.
-
-Full NGS is robust and easy on the eyes. I recommend this as an option for
-higher fidelity simulation and certainly for suspension bridges and long chains.
-Full NGS might be a good choice for ragdolls, especially motorized ragdolls where
-joint separation can be problematic. The number of NGS iterations can be reduced
-for better performance without harming robustness much.
-
-Each joint in a can be handled differently in the position solver. So I recommend
-a system where the user can select the algorithm on a per joint basis. I would
-probably default to the slower Full NGS and let the user select the faster
-Baumgarte method in performance critical scenarios.
-*/
-
-/*
-Cache Performance
-
-The Box2D solvers are dominated by cache misses. Data structures are designed
-to increase the number of cache hits. Much of misses are due to random access
-to body data. The constraint structures are iterated over linearly, which leads
-to few cache misses.
-
-The bodies are not accessed during iteration. Instead read only data, such as
-the mass values are stored with the constraints. The mutable data are the constraint
-impulses and the bodies velocities/positions. The impulses are held inside the
-constraint structures. The body velocities/positions are held in compact, temporary
-arrays to increase the number of cache hits. Linear and angular velocity are
-stored in a single array since multiple arrays lead to multiple misses.
-*/
-
-/*
-2D Rotation
-
-R = [cos(theta) -sin(theta)]
- [sin(theta) cos(theta) ]
-
-thetaDot = omega
-
-Let q1 = cos(theta), q2 = sin(theta).
-R = [q1 -q2]
- [q2 q1]
-
-q1Dot = -thetaDot * q2
-q2Dot = thetaDot * q1
-
-q1_new = q1_old - dt * w * q2
-q2_new = q2_old + dt * w * q1
-then normalize.
-
-This might be faster than computing sin+cos.
-However, we can compute sin+cos of the same angle fast.
-*/
-
-b2Island::b2Island(
- int32 bodyCapacity,
- int32 contactCapacity,
- int32 jointCapacity,
- b2StackAllocator* allocator,
- b2ContactListener* listener)
-{
- m_bodyCapacity = bodyCapacity;
- m_contactCapacity = contactCapacity;
- m_jointCapacity = jointCapacity;
- m_bodyCount = 0;
- m_contactCount = 0;
- m_jointCount = 0;
-
- m_allocator = allocator;
- m_listener = listener;
-
- m_bodies = (b2Body**)m_allocator->Allocate(bodyCapacity * sizeof(b2Body*));
- m_contacts = (b2Contact**)m_allocator->Allocate(contactCapacity * sizeof(b2Contact*));
- m_joints = (b2Joint**)m_allocator->Allocate(jointCapacity * sizeof(b2Joint*));
-
- m_velocities = (b2Velocity*)m_allocator->Allocate(m_bodyCapacity * sizeof(b2Velocity));
- m_positions = (b2Position*)m_allocator->Allocate(m_bodyCapacity * sizeof(b2Position));
-}
-
-b2Island::~b2Island()
-{
- // Warning: the order should reverse the constructor order.
- m_allocator->Free(m_positions);
- m_allocator->Free(m_velocities);
- m_allocator->Free(m_joints);
- m_allocator->Free(m_contacts);
- m_allocator->Free(m_bodies);
-}
-
-void b2Island::Solve(b2Profile* profile, const b2TimeStep& step, const b2Vec2& gravity, bool allowSleep)
-{
- b2Timer timer;
-
- float32 h = step.dt;
-
- // Integrate velocities and apply damping. Initialize the body state.
- for (int32 i = 0; i < m_bodyCount; ++i)
- {
- b2Body* b = m_bodies[i];
-
- b2Vec2 c = b->m_sweep.c;
- float32 a = b->m_sweep.a;
- b2Vec2 v = b->m_linearVelocity;
- float32 w = b->m_angularVelocity;
-
- // Store positions for continuous collision.
- b->m_sweep.c0 = b->m_sweep.c;
- b->m_sweep.a0 = b->m_sweep.a;
-
- if (b->m_type == b2_dynamicBody)
- {
- // Integrate velocities.
- v += h * (b->m_gravityScale * gravity + b->m_invMass * b->m_force);
- w += h * b->m_invI * b->m_torque;
-
- // 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
- // Pade approximation:
- // v2 = v1 * 1 / (1 + c * dt)
- v *= 1.0f / (1.0f + h * b->m_linearDamping);
- w *= 1.0f / (1.0f + h * b->m_angularDamping);
- }
-
- m_positions[i].c = c;
- m_positions[i].a = a;
- m_velocities[i].v = v;
- m_velocities[i].w = w;
- }
-
- timer.Reset();
-
- // Solver data
- b2SolverData solverData;
- solverData.step = step;
- solverData.positions = m_positions;
- solverData.velocities = m_velocities;
-
- // Initialize velocity constraints.
- b2ContactSolverDef contactSolverDef;
- contactSolverDef.step = step;
- contactSolverDef.contacts = m_contacts;
- contactSolverDef.count = m_contactCount;
- contactSolverDef.positions = m_positions;
- contactSolverDef.velocities = m_velocities;
- contactSolverDef.allocator = m_allocator;
-
- b2ContactSolver contactSolver(&contactSolverDef);
- contactSolver.InitializeVelocityConstraints();
-
- if (step.warmStarting)
- {
- contactSolver.WarmStart();
- }
-
- for (int32 i = 0; i < m_jointCount; ++i)
- {
- m_joints[i]->InitVelocityConstraints(solverData);
- }
-
- profile->solveInit = timer.GetMilliseconds();
-
- // Solve velocity constraints
- timer.Reset();
- for (int32 i = 0; i < step.velocityIterations; ++i)
- {
- for (int32 j = 0; j < m_jointCount; ++j)
- {
- m_joints[j]->SolveVelocityConstraints(solverData);
- }
-
- contactSolver.SolveVelocityConstraints();
- }
-
- // Store impulses for warm starting
- contactSolver.StoreImpulses();
- profile->solveVelocity = timer.GetMilliseconds();
-
- // Integrate positions
- for (int32 i = 0; i < m_bodyCount; ++i)
- {
- b2Vec2 c = m_positions[i].c;
- float32 a = m_positions[i].a;
- b2Vec2 v = m_velocities[i].v;
- float32 w = m_velocities[i].w;
-
- // Check for large velocities
- b2Vec2 translation = h * v;
- if (b2Dot(translation, translation) > b2_maxTranslationSquared)
- {
- float32 ratio = b2_maxTranslation / translation.Length();
- v *= ratio;
- }
-
- float32 rotation = h * w;
- if (rotation * rotation > b2_maxRotationSquared)
- {
- float32 ratio = b2_maxRotation / b2Abs(rotation);
- w *= ratio;
- }
-
- // Integrate
- c += h * v;
- a += h * w;
-
- m_positions[i].c = c;
- m_positions[i].a = a;
- m_velocities[i].v = v;
- m_velocities[i].w = w;
- }
-
- // Solve position constraints
- timer.Reset();
- bool positionSolved = false;
- for (int32 i = 0; i < step.positionIterations; ++i)
- {
- bool contactsOkay = contactSolver.SolvePositionConstraints();
-
- bool jointsOkay = true;
- for (int32 j = 0; j < m_jointCount; ++j)
- {
- bool jointOkay = m_joints[j]->SolvePositionConstraints(solverData);
- jointsOkay = jointsOkay && jointOkay;
- }
-
- if (contactsOkay && jointsOkay)
- {
- // Exit early if the position errors are small.
- positionSolved = true;
- break;
- }
- }
-
- // Copy state buffers back to the bodies
- for (int32 i = 0; i < m_bodyCount; ++i)
- {
- b2Body* body = m_bodies[i];
- body->m_sweep.c = m_positions[i].c;
- body->m_sweep.a = m_positions[i].a;
- body->m_linearVelocity = m_velocities[i].v;
- body->m_angularVelocity = m_velocities[i].w;
- body->SynchronizeTransform();
- }
-
- profile->solvePosition = timer.GetMilliseconds();
-
- Report(contactSolver.m_velocityConstraints);
-
- if (allowSleep)
- {
- float32 minSleepTime = b2_maxFloat;
-
- const float32 linTolSqr = b2_linearSleepTolerance * b2_linearSleepTolerance;
- const float32 angTolSqr = b2_angularSleepTolerance * b2_angularSleepTolerance;
-
- for (int32 i = 0; i < m_bodyCount; ++i)
- {
- b2Body* b = m_bodies[i];
- if (b->GetType() == b2_staticBody)
- {
- continue;
- }
-
- if ((b->m_flags & b2Body::e_autoSleepFlag) == 0 ||
- b->m_angularVelocity * b->m_angularVelocity > angTolSqr ||
- b2Dot(b->m_linearVelocity, b->m_linearVelocity) > linTolSqr)
- {
- b->m_sleepTime = 0.0f;
- minSleepTime = 0.0f;
- }
- else
- {
- b->m_sleepTime += h;
- minSleepTime = b2Min(minSleepTime, b->m_sleepTime);
- }
- }
-
- if (minSleepTime >= b2_timeToSleep && positionSolved)
- {
- for (int32 i = 0; i < m_bodyCount; ++i)
- {
- b2Body* b = m_bodies[i];
- b->SetAwake(false);
- }
- }
- }
-}
-
-void b2Island::SolveTOI(const b2TimeStep& subStep, int32 toiIndexA, int32 toiIndexB)
-{
- b2Assert(toiIndexA < m_bodyCount);
- b2Assert(toiIndexB < m_bodyCount);
-
- // Initialize the body state.
- for (int32 i = 0; i < m_bodyCount; ++i)
- {
- b2Body* b = m_bodies[i];
- m_positions[i].c = b->m_sweep.c;
- m_positions[i].a = b->m_sweep.a;
- m_velocities[i].v = b->m_linearVelocity;
- m_velocities[i].w = b->m_angularVelocity;
- }
-
- b2ContactSolverDef contactSolverDef;
- contactSolverDef.contacts = m_contacts;
- contactSolverDef.count = m_contactCount;
- contactSolverDef.allocator = m_allocator;
- contactSolverDef.step = subStep;
- contactSolverDef.positions = m_positions;
- contactSolverDef.velocities = m_velocities;
- b2ContactSolver contactSolver(&contactSolverDef);
-
- // Solve position constraints.
- for (int32 i = 0; i < subStep.positionIterations; ++i)
- {
- bool contactsOkay = contactSolver.SolveTOIPositionConstraints(toiIndexA, toiIndexB);
- if (contactsOkay)
- {
- break;
- }
- }
-
-#if 0
- // Is the new position really safe?
- for (int32 i = 0; i < m_contactCount; ++i)
- {
- b2Contact* c = m_contacts[i];
- b2Fixture* fA = c->GetFixtureA();
- b2Fixture* fB = c->GetFixtureB();
-
- b2Body* bA = fA->GetBody();
- b2Body* bB = fB->GetBody();
-
- int32 indexA = c->GetChildIndexA();
- int32 indexB = c->GetChildIndexB();
-
- b2DistanceInput input;
- input.proxyA.Set(fA->GetShape(), indexA);
- input.proxyB.Set(fB->GetShape(), indexB);
- input.transformA = bA->GetTransform();
- input.transformB = bB->GetTransform();
- input.useRadii = false;
-
- b2DistanceOutput output;
- b2SimplexCache cache;
- cache.count = 0;
- b2Distance(&output, &cache, &input);
-
- if (output.distance == 0 || cache.count == 3)
- {
- cache.count += 0;
- }
- }
-#endif
-
- // Leap of faith to new safe state.
- m_bodies[toiIndexA]->m_sweep.c0 = m_positions[toiIndexA].c;
- m_bodies[toiIndexA]->m_sweep.a0 = m_positions[toiIndexA].a;
- m_bodies[toiIndexB]->m_sweep.c0 = m_positions[toiIndexB].c;
- m_bodies[toiIndexB]->m_sweep.a0 = m_positions[toiIndexB].a;
-
- // No warm starting is needed for TOI events because warm
- // starting impulses were applied in the discrete solver.
- contactSolver.InitializeVelocityConstraints();
-
- // Solve velocity constraints.
- for (int32 i = 0; i < subStep.velocityIterations; ++i)
- {
- contactSolver.SolveVelocityConstraints();
- }
-
- // Don't store the TOI contact forces for warm starting
- // because they can be quite large.
-
- float32 h = subStep.dt;
-
- // Integrate positions
- for (int32 i = 0; i < m_bodyCount; ++i)
- {
- b2Vec2 c = m_positions[i].c;
- float32 a = m_positions[i].a;
- b2Vec2 v = m_velocities[i].v;
- float32 w = m_velocities[i].w;
-
- // Check for large velocities
- b2Vec2 translation = h * v;
- if (b2Dot(translation, translation) > b2_maxTranslationSquared)
- {
- float32 ratio = b2_maxTranslation / translation.Length();
- v *= ratio;
- }
-
- float32 rotation = h * w;
- if (rotation * rotation > b2_maxRotationSquared)
- {
- float32 ratio = b2_maxRotation / b2Abs(rotation);
- w *= ratio;
- }
-
- // Integrate
- c += h * v;
- a += h * w;
-
- m_positions[i].c = c;
- m_positions[i].a = a;
- m_velocities[i].v = v;
- m_velocities[i].w = w;
-
- // Sync bodies
- b2Body* body = m_bodies[i];
- body->m_sweep.c = c;
- body->m_sweep.a = a;
- body->m_linearVelocity = v;
- body->m_angularVelocity = w;
- body->SynchronizeTransform();
- }
-
- Report(contactSolver.m_velocityConstraints);
-}
-
-void b2Island::Report(const b2ContactVelocityConstraint* constraints)
-{
- if (m_listener == nullptr)
- {
- return;
- }
-
- for (int32 i = 0; i < m_contactCount; ++i)
- {
- b2Contact* c = m_contacts[i];
-
- const b2ContactVelocityConstraint* vc = constraints + i;
-
- b2ContactImpulse impulse;
- impulse.count = vc->pointCount;
- for (int32 j = 0; j < vc->pointCount; ++j)
- {
- impulse.normalImpulses[j] = vc->points[j].normalImpulse;
- impulse.tangentImpulses[j] = vc->points[j].tangentImpulse;
- }
-
- m_listener->PostSolve(c, &impulse);
- }
-}