axmol/Box2D/Dynamics/b2World.cpp

/*
* 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/Dynamics/b2World.h>
#include <Box2D/Dynamics/b2Body.h>
#include <Box2D/Dynamics/b2Fixture.h>
#include <Box2D/Dynamics/b2Island.h>
#include <Box2D/Dynamics/Joints/b2PulleyJoint.h>
#include <Box2D/Dynamics/Contacts/b2Contact.h>
#include <Box2D/Dynamics/Contacts/b2ContactSolver.h>
#include <Box2D/Collision/b2Collision.h>
#include <Box2D/Collision/b2BroadPhase.h>
#include <Box2D/Collision/Shapes/b2CircleShape.h>
#include <Box2D/Collision/Shapes/b2EdgeShape.h>
#include <Box2D/Collision/Shapes/b2ChainShape.h>
#include <Box2D/Collision/Shapes/b2PolygonShape.h>
#include <Box2D/Collision/b2TimeOfImpact.h>
#include <Box2D/Common/b2Draw.h>
#include <Box2D/Common/b2Timer.h>
#include <new>

b2World::b2World(const b2Vec2& gravity)
{
    m_destructionListener = NULL;
    m_debugDraw = NULL;

    m_bodyList = NULL;
    m_jointList = NULL;

    m_bodyCount = 0;
    m_jointCount = 0;

    m_warmStarting = true;
    m_continuousPhysics = true;
    m_subStepping = false;

    m_stepComplete = true;

    m_allowSleep = true;
    m_gravity = gravity;

    m_flags = e_clearForces;

    m_inv_dt0 = 0.0f;

    m_contactManager.m_allocator = &m_blockAllocator;

    memset(&m_profile, 0, sizeof(b2Profile));
}

b2World::~b2World()
{
    // Some shapes allocate using b2Alloc.
    b2Body* b = m_bodyList;
    while (b)
    {
        b2Body* bNext = b->m_next;

        b2Fixture* f = b->m_fixtureList;
        while (f)
        {
            b2Fixture* fNext = f->m_next;
            f->m_proxyCount = 0;
            f->Destroy(&m_blockAllocator);
            f = fNext;
        }

        b = bNext;
    }
}

void b2World::SetDestructionListener(b2DestructionListener* listener)
{
    m_destructionListener = listener;
}

void b2World::SetContactFilter(b2ContactFilter* filter)
{
    m_contactManager.m_contactFilter = filter;
}

void b2World::SetContactListener(b2ContactListener* listener)
{
    m_contactManager.m_contactListener = listener;
}

void b2World::SetDebugDraw(b2Draw* debugDraw)
{
    m_debugDraw = debugDraw;
}

b2Body* b2World::CreateBody(const b2BodyDef* def)
{
    b2Assert(IsLocked() == false);
    if (IsLocked())
    {
        return NULL;
    }

    void* mem = m_blockAllocator.Allocate(sizeof(b2Body));
    b2Body* b = new (mem) b2Body(def, this);

    // Add to world doubly linked list.
    b->m_prev = NULL;
    b->m_next = m_bodyList;
    if (m_bodyList)
    {
        m_bodyList->m_prev = b;
    }
    m_bodyList = b;
    ++m_bodyCount;

    return b;
}

void b2World::DestroyBody(b2Body* b)
{
    b2Assert(m_bodyCount > 0);
    b2Assert(IsLocked() == false);
    if (IsLocked())
    {
        return;
    }

    // Delete the attached joints.
    b2JointEdge* je = b->m_jointList;
    while (je)
    {
        b2JointEdge* je0 = je;
        je = je->next;

        if (m_destructionListener)
        {
            m_destructionListener->SayGoodbye(je0->joint);
        }

        DestroyJoint(je0->joint);

        b->m_jointList = je;
    }
    b->m_jointList = NULL;

    // Delete the attached contacts.
    b2ContactEdge* ce = b->m_contactList;
    while (ce)
    {
        b2ContactEdge* ce0 = ce;
        ce = ce->next;
        m_contactManager.Destroy(ce0->contact);
    }
    b->m_contactList = NULL;

    // Delete the attached fixtures. This destroys broad-phase proxies.
    b2Fixture* f = b->m_fixtureList;
    while (f)
    {
        b2Fixture* f0 = f;
        f = f->m_next;

        if (m_destructionListener)
        {
            m_destructionListener->SayGoodbye(f0);
        }

        f0->DestroyProxies(&m_contactManager.m_broadPhase);
        f0->Destroy(&m_blockAllocator);
        f0->~b2Fixture();
        m_blockAllocator.Free(f0, sizeof(b2Fixture));

        b->m_fixtureList = f;
        b->m_fixtureCount -= 1;
    }
    b->m_fixtureList = NULL;
    b->m_fixtureCount = 0;

    // Remove world body list.
    if (b->m_prev)
    {
        b->m_prev->m_next = b->m_next;
    }

    if (b->m_next)
    {
        b->m_next->m_prev = b->m_prev;
    }

    if (b == m_bodyList)
    {
        m_bodyList = b->m_next;
    }

    --m_bodyCount;
    b->~b2Body();
    m_blockAllocator.Free(b, sizeof(b2Body));
}

b2Joint* b2World::CreateJoint(const b2JointDef* def)
{
    b2Assert(IsLocked() == false);
    if (IsLocked())
    {
        return NULL;
    }

    b2Joint* j = b2Joint::Create(def, &m_blockAllocator);

    // Connect to the world list.
    j->m_prev = NULL;
    j->m_next = m_jointList;
    if (m_jointList)
    {
        m_jointList->m_prev = j;
    }
    m_jointList = j;
    ++m_jointCount;

    // Connect to the bodies' doubly linked lists.
    j->m_edgeA.joint = j;
    j->m_edgeA.other = j->m_bodyB;
    j->m_edgeA.prev = NULL;
    j->m_edgeA.next = j->m_bodyA->m_jointList;
    if (j->m_bodyA->m_jointList) j->m_bodyA->m_jointList->prev = &j->m_edgeA;
    j->m_bodyA->m_jointList = &j->m_edgeA;

    j->m_edgeB.joint = j;
    j->m_edgeB.other = j->m_bodyA;
    j->m_edgeB.prev = NULL;
    j->m_edgeB.next = j->m_bodyB->m_jointList;
    if (j->m_bodyB->m_jointList) j->m_bodyB->m_jointList->prev = &j->m_edgeB;
    j->m_bodyB->m_jointList = &j->m_edgeB;

    b2Body* bodyA = def->bodyA;
    b2Body* bodyB = def->bodyB;

    // If the joint prevents collisions, then flag any contacts for filtering.
    if (def->collideConnected == false)
    {
        b2ContactEdge* edge = bodyB->GetContactList();
        while (edge)
        {
            if (edge->other == bodyA)
            {
                // Flag the contact for filtering at the next time step (where either
                // body is awake).
                edge->contact->FlagForFiltering();
            }

            edge = edge->next;
        }
    }

    // Note: creating a joint doesn't wake the bodies.

    return j;
}

void b2World::DestroyJoint(b2Joint* j)
{
    b2Assert(IsLocked() == false);
    if (IsLocked())
    {
        return;
    }

    bool collideConnected = j->m_collideConnected;

    // Remove from the doubly linked list.
    if (j->m_prev)
    {
        j->m_prev->m_next = j->m_next;
    }

    if (j->m_next)
    {
        j->m_next->m_prev = j->m_prev;
    }

    if (j == m_jointList)
    {
        m_jointList = j->m_next;
    }

    // Disconnect from island graph.
    b2Body* bodyA = j->m_bodyA;
    b2Body* bodyB = j->m_bodyB;

    // Wake up connected bodies.
    bodyA->SetAwake(true);
    bodyB->SetAwake(true);

    // Remove from body 1.
    if (j->m_edgeA.prev)
    {
        j->m_edgeA.prev->next = j->m_edgeA.next;
    }

    if (j->m_edgeA.next)
    {
        j->m_edgeA.next->prev = j->m_edgeA.prev;
    }

    if (&j->m_edgeA == bodyA->m_jointList)
    {
        bodyA->m_jointList = j->m_edgeA.next;
    }

    j->m_edgeA.prev = NULL;
    j->m_edgeA.next = NULL;

    // Remove from body 2
    if (j->m_edgeB.prev)
    {
        j->m_edgeB.prev->next = j->m_edgeB.next;
    }

    if (j->m_edgeB.next)
    {
        j->m_edgeB.next->prev = j->m_edgeB.prev;
    }

    if (&j->m_edgeB == bodyB->m_jointList)
    {
        bodyB->m_jointList = j->m_edgeB.next;
    }

    j->m_edgeB.prev = NULL;
    j->m_edgeB.next = NULL;

    b2Joint::Destroy(j, &m_blockAllocator);

    b2Assert(m_jointCount > 0);
    --m_jointCount;

    // If the joint prevents collisions, then flag any contacts for filtering.
    if (collideConnected == false)
    {
        b2ContactEdge* edge = bodyB->GetContactList();
        while (edge)
        {
            if (edge->other == bodyA)
            {
                // Flag the contact for filtering at the next time step (where either
                // body is awake).
                edge->contact->FlagForFiltering();
            }

            edge = edge->next;
        }
    }
}

//
void b2World::SetAllowSleeping(bool flag)
{
    if (flag == m_allowSleep)
    {
        return;
    }

    m_allowSleep = flag;
    if (m_allowSleep == false)
    {
        for (b2Body* b = m_bodyList; b; b = b->m_next)
        {
            b->SetAwake(true);
        }
    }
}

// Find islands, integrate and solve constraints, solve position constraints
void b2World::Solve(const b2TimeStep& step)
{
    m_profile.solveInit = 0.0f;
    m_profile.solveVelocity = 0.0f;
    m_profile.solvePosition = 0.0f;

    // Size the island for the worst case.
    b2Island island(m_bodyCount,
                    m_contactManager.m_contactCount,
                    m_jointCount,
                    &m_stackAllocator,
                    m_contactManager.m_contactListener);

    // Clear all the island flags.
    for (b2Body* b = m_bodyList; b; b = b->m_next)
    {
        b->m_flags &= ~b2Body::e_islandFlag;
    }
    for (b2Contact* c = m_contactManager.m_contactList; c; c = c->m_next)
    {
        c->m_flags &= ~b2Contact::e_islandFlag;
    }
    for (b2Joint* j = m_jointList; j; j = j->m_next)
    {
        j->m_islandFlag = false;
    }

    // Build and simulate all awake islands.
    int32 stackSize = m_bodyCount;
    b2Body** stack = (b2Body**)m_stackAllocator.Allocate(stackSize * sizeof(b2Body*));
    for (b2Body* seed = m_bodyList; seed; seed = seed->m_next)
    {
        if (seed->m_flags & b2Body::e_islandFlag)
        {
            continue;
        }

        if (seed->IsAwake() == false || seed->IsActive() == false)
        {
            continue;
        }

        // The seed can be dynamic or kinematic.
        if (seed->GetType() == b2_staticBody)
        {
            continue;
        }

        // Reset island and stack.
        island.Clear();
        int32 stackCount = 0;
        stack[stackCount++] = seed;
        seed->m_flags |= b2Body::e_islandFlag;

        // Perform a depth first search (DFS) on the constraint graph.
        while (stackCount > 0)
        {
            // Grab the next body off the stack and add it to the island.
            b2Body* b = stack[--stackCount];
            b2Assert(b->IsActive() == true);
            island.Add(b);

            // Make sure the body is awake.
            b->SetAwake(true);

            // To keep islands as small as possible, we don't
            // propagate islands across static bodies.
            if (b->GetType() == b2_staticBody)
            {
                continue;
            }

            // Search all contacts connected to this body.
            for (b2ContactEdge* ce = b->m_contactList; ce; ce = ce->next)
            {
                b2Contact* contact = ce->contact;

                // Has this contact already been added to an island?
                if (contact->m_flags & b2Contact::e_islandFlag)
                {
                    continue;
                }

                // Is this contact solid and touching?
                if (contact->IsEnabled() == false ||
                    contact->IsTouching() == false)
                {
                    continue;
                }

                // Skip sensors.
                bool sensorA = contact->m_fixtureA->m_isSensor;
                bool sensorB = contact->m_fixtureB->m_isSensor;
                if (sensorA || sensorB)
                {
                    continue;
                }

                island.Add(contact);
                contact->m_flags |= b2Contact::e_islandFlag;

                b2Body* other = ce->other;

                // Was the other body already added to this island?
                if (other->m_flags & b2Body::e_islandFlag)
                {
                    continue;
                }

                b2Assert(stackCount < stackSize);
                stack[stackCount++] = other;
                other->m_flags |= b2Body::e_islandFlag;
            }

            // Search all joints connect to this body.
            for (b2JointEdge* je = b->m_jointList; je; je = je->next)
            {
                if (je->joint->m_islandFlag == true)
                {
                    continue;
                }

                b2Body* other = je->other;

                // Don't simulate joints connected to inactive bodies.
                if (other->IsActive() == false)
                {
                    continue;
                }

                island.Add(je->joint);
                je->joint->m_islandFlag = true;

                if (other->m_flags & b2Body::e_islandFlag)
                {
                    continue;
                }

                b2Assert(stackCount < stackSize);
                stack[stackCount++] = other;
                other->m_flags |= b2Body::e_islandFlag;
            }
        }

        b2Profile profile;
        island.Solve(&profile, step, m_gravity, m_allowSleep);
        m_profile.solveInit += profile.solveInit;
        m_profile.solveVelocity += profile.solveVelocity;
        m_profile.solvePosition += profile.solvePosition;

        // Post solve cleanup.
        for (int32 i = 0; i < island.m_bodyCount; ++i)
        {
            // Allow static bodies to participate in other islands.
            b2Body* b = island.m_bodies[i];
            if (b->GetType() == b2_staticBody)
            {
                b->m_flags &= ~b2Body::e_islandFlag;
            }
        }
    }

    m_stackAllocator.Free(stack);

    {
        b2Timer timer;
        // Synchronize fixtures, check for out of range bodies.
        for (b2Body* b = m_bodyList; b; b = b->GetNext())
        {
            // If a body was not in an island then it did not move.
            if ((b->m_flags & b2Body::e_islandFlag) == 0)
            {
                continue;
            }

            if (b->GetType() == b2_staticBody)
            {
                continue;
            }

            // Update fixtures (for broad-phase).
            b->SynchronizeFixtures();
        }

        // Look for new contacts.
        m_contactManager.FindNewContacts();
        m_profile.broadphase = timer.GetMilliseconds();
    }
}

// Find TOI contacts and solve them.
void b2World::SolveTOI(const b2TimeStep& step)
{
    b2Island island(2 * b2_maxTOIContacts, b2_maxTOIContacts, 0, &m_stackAllocator, m_contactManager.m_contactListener);

    if (m_stepComplete)
    {
        for (b2Body* b = m_bodyList; b; b = b->m_next)
        {
            b->m_flags &= ~b2Body::e_islandFlag;
            b->m_sweep.alpha0 = 0.0f;
        }

        for (b2Contact* c = m_contactManager.m_contactList; c; c = c->m_next)
        {
            // Invalidate TOI
            c->m_flags &= ~(b2Contact::e_toiFlag | b2Contact::e_islandFlag);
            c->m_toiCount = 0;
            c->m_toi = 1.0f;
        }
    }

    // Find TOI events and solve them.
    for (;;)
    {
        // Find the first TOI.
        b2Contact* minContact = NULL;
        float32 minAlpha = 1.0f;

        for (b2Contact* c = m_contactManager.m_contactList; c; c = c->m_next)
        {
            // Is this contact disabled?
            if (c->IsEnabled() == false)
            {
                continue;
            }

            // Prevent excessive sub-stepping.
            if (c->m_toiCount > b2_maxSubSteps)
            {
                continue;
            }

            float32 alpha = 1.0f;
            if (c->m_flags & b2Contact::e_toiFlag)
            {
                // This contact has a valid cached TOI.
                alpha = c->m_toi;
            }
            else
            {
                b2Fixture* fA = c->GetFixtureA();
                b2Fixture* fB = c->GetFixtureB();

                // Is there a sensor?
                if (fA->IsSensor() || fB->IsSensor())
                {
                    continue;
                }

                b2Body* bA = fA->GetBody();
                b2Body* bB = fB->GetBody();

                b2BodyType typeA = bA->m_type;
                b2BodyType typeB = bB->m_type;
                b2Assert(typeA == b2_dynamicBody || typeB == b2_dynamicBody);

                bool activeA = bA->IsAwake() && typeA != b2_staticBody;
                bool activeB = bB->IsAwake() && typeB != b2_staticBody;

                // Is at least one body active (awake and dynamic or kinematic)?
                if (activeA == false && activeB == false)
                {
                    continue;
                }

                bool collideA = bA->IsBullet() || typeA != b2_dynamicBody;
                bool collideB = bB->IsBullet() || typeB != b2_dynamicBody;

                // Are these two non-bullet dynamic bodies?
                if (collideA == false && collideB == false)
                {
                    continue;
                }

                // Compute the TOI for this contact.
                // Put the sweeps onto the same time interval.
                float32 alpha0 = bA->m_sweep.alpha0;

                if (bA->m_sweep.alpha0 < bB->m_sweep.alpha0)
                {
                    alpha0 = bB->m_sweep.alpha0;
                    bA->m_sweep.Advance(alpha0);
                }
                else if (bB->m_sweep.alpha0 < bA->m_sweep.alpha0)
                {
                    alpha0 = bA->m_sweep.alpha0;
                    bB->m_sweep.Advance(alpha0);
                }

                b2Assert(alpha0 < 1.0f);

                int32 indexA = c->GetChildIndexA();
                int32 indexB = c->GetChildIndexB();

                // Compute the time of impact in interval [0, minTOI]
                b2TOIInput input;
                input.proxyA.Set(fA->GetShape(), indexA);
                input.proxyB.Set(fB->GetShape(), indexB);
                input.sweepA = bA->m_sweep;
                input.sweepB = bB->m_sweep;
                input.tMax = 1.0f;

                b2TOIOutput output;
                b2TimeOfImpact(&output, &input);

                // Beta is the fraction of the remaining portion of the .
                float32 beta = output.t;
                if (output.state == b2TOIOutput::e_touching)
                {
                    alpha = b2Min(alpha0 + (1.0f - alpha0) * beta, 1.0f);
                }
                else
                {
                    alpha = 1.0f;
                }

                c->m_toi = alpha;
                c->m_flags |= b2Contact::e_toiFlag;
            }

            if (alpha < minAlpha)
            {
                // This is the minimum TOI found so far.
                minContact = c;
                minAlpha = alpha;
            }
        }

        if (minContact == NULL || 1.0f - 10.0f * b2_epsilon < minAlpha)
        {
            // No more TOI events. Done!
            m_stepComplete = true;
            break;
        }

        // Advance the bodies to the TOI.
        b2Fixture* fA = minContact->GetFixtureA();
        b2Fixture* fB = minContact->GetFixtureB();
        b2Body* bA = fA->GetBody();
        b2Body* bB = fB->GetBody();

        b2Sweep backup1 = bA->m_sweep;
        b2Sweep backup2 = bB->m_sweep;

        bA->Advance(minAlpha);
        bB->Advance(minAlpha);

        // The TOI contact likely has some new contact points.
        minContact->Update(m_contactManager.m_contactListener);
        minContact->m_flags &= ~b2Contact::e_toiFlag;
        ++minContact->m_toiCount;

        // Is the contact solid?
        if (minContact->IsEnabled() == false || minContact->IsTouching() == false)
        {
            // Restore the sweeps.
            minContact->SetEnabled(false);
            bA->m_sweep = backup1;
            bB->m_sweep = backup2;
            bA->SynchronizeTransform();
            bB->SynchronizeTransform();
            continue;
        }

        bA->SetAwake(true);
        bB->SetAwake(true);

        // Build the island
        island.Clear();
        island.Add(bA);
        island.Add(bB);
        island.Add(minContact);

        bA->m_flags |= b2Body::e_islandFlag;
        bB->m_flags |= b2Body::e_islandFlag;
        minContact->m_flags |= b2Contact::e_islandFlag;

        // Get contacts on bodyA and bodyB.
        b2Body* bodies[2] = {bA, bB};
        for (int32 i = 0; i < 2; ++i)
        {
            b2Body* body = bodies[i];
            if (body->m_type == b2_dynamicBody)
            {
                for (b2ContactEdge* ce = body->m_contactList; ce; ce = ce->next)
                {
                    if (island.m_bodyCount == island.m_bodyCapacity)
                    {
                        break;
                    }

                    if (island.m_contactCount == island.m_contactCapacity)
                    {
                        break;
                    }

                    b2Contact* contact = ce->contact;

                    // Has this contact already been added to the island?
                    if (contact->m_flags & b2Contact::e_islandFlag)
                    {
                        continue;
                    }

                    // Only add static, kinematic, or bullet bodies.
                    b2Body* other = ce->other;
                    if (other->m_type == b2_dynamicBody &&
                        body->IsBullet() == false && other->IsBullet() == false)
                    {
                        continue;
                    }

                    // Skip sensors.
                    bool sensorA = contact->m_fixtureA->m_isSensor;
                    bool sensorB = contact->m_fixtureB->m_isSensor;
                    if (sensorA || sensorB)
                    {
                        continue;
                    }

                    // Tentatively advance the body to the TOI.
                    b2Sweep backup = other->m_sweep;
                    if ((other->m_flags & b2Body::e_islandFlag) == 0)
                    {
                        other->Advance(minAlpha);
                    }

                    // Update the contact points
                    contact->Update(m_contactManager.m_contactListener);

                    // Was the contact disabled by the user?
                    if (contact->IsEnabled() == false)
                    {
                        other->m_sweep = backup;
                        other->SynchronizeTransform();
                        continue;
                    }

                    // Are there contact points?
                    if (contact->IsTouching() == false)
                    {
                        other->m_sweep = backup;
                        other->SynchronizeTransform();
                        continue;
                    }

                    // Add the contact to the island
                    contact->m_flags |= b2Contact::e_islandFlag;
                    island.Add(contact);

                    // Has the other body already been added to the island?
                    if (other->m_flags & b2Body::e_islandFlag)
                    {
                        continue;
                    }
                    
                    // Add the other body to the island.
                    other->m_flags |= b2Body::e_islandFlag;

                    if (other->m_type != b2_staticBody)
                    {
                        other->SetAwake(true);
                    }

                    island.Add(other);
                }
            }
        }

        b2TimeStep subStep;
        subStep.dt = (1.0f - minAlpha) * step.dt;
        subStep.inv_dt = 1.0f / subStep.dt;
        subStep.dtRatio = 1.0f;
        subStep.positionIterations = 20;
        subStep.velocityIterations = step.velocityIterations;
        subStep.warmStarting = false;
        island.SolveTOI(subStep, bA->m_islandIndex, bB->m_islandIndex);

        // Reset island flags and synchronize broad-phase proxies.
        for (int32 i = 0; i < island.m_bodyCount; ++i)
        {
            b2Body* body = island.m_bodies[i];
            body->m_flags &= ~b2Body::e_islandFlag;

            if (body->m_type != b2_dynamicBody)
            {
                continue;
            }

            body->SynchronizeFixtures();

            // Invalidate all contact TOIs on this displaced body.
            for (b2ContactEdge* ce = body->m_contactList; ce; ce = ce->next)
            {
                ce->contact->m_flags &= ~(b2Contact::e_toiFlag | b2Contact::e_islandFlag);
            }
        }

        // Commit fixture proxy movements to the broad-phase so that new contacts are created.
        // Also, some contacts can be destroyed.
        m_contactManager.FindNewContacts();

        if (m_subStepping)
        {
            m_stepComplete = false;
            break;
        }
    }
}

void b2World::Step(float32 dt, int32 velocityIterations, int32 positionIterations)
{
    b2Timer stepTimer;

    // If new fixtures were added, we need to find the new contacts.
    if (m_flags & e_newFixture)
    {
        m_contactManager.FindNewContacts();
        m_flags &= ~e_newFixture;
    }

    m_flags |= e_locked;

    b2TimeStep step;
    step.dt = dt;
    step.velocityIterations    = velocityIterations;
    step.positionIterations = positionIterations;
    if (dt > 0.0f)
    {
        step.inv_dt = 1.0f / dt;
    }
    else
    {
        step.inv_dt = 0.0f;
    }

    step.dtRatio = m_inv_dt0 * dt;

    step.warmStarting = m_warmStarting;
    
    // Update contacts. This is where some contacts are destroyed.
    {
        b2Timer timer;
        m_contactManager.Collide();
        m_profile.collide = timer.GetMilliseconds();
    }

    // Integrate velocities, solve velocity constraints, and integrate positions.
    if (m_stepComplete && step.dt > 0.0f)
    {
        b2Timer timer;
        Solve(step);
        m_profile.solve = timer.GetMilliseconds();
    }

    // Handle TOI events.
    if (m_continuousPhysics && step.dt > 0.0f)
    {
        b2Timer timer;
        SolveTOI(step);
        m_profile.solveTOI = timer.GetMilliseconds();
    }

    if (step.dt > 0.0f)
    {
        m_inv_dt0 = step.inv_dt;
    }

    if (m_flags & e_clearForces)
    {
        ClearForces();
    }

    m_flags &= ~e_locked;

    m_profile.step = stepTimer.GetMilliseconds();
}

void b2World::ClearForces()
{
    for (b2Body* body = m_bodyList; body; body = body->GetNext())
    {
        body->m_force.SetZero();
        body->m_torque = 0.0f;
    }
}

struct b2WorldQueryWrapper
{
    bool QueryCallback(int32 proxyId)
    {
        b2FixtureProxy* proxy = (b2FixtureProxy*)broadPhase->GetUserData(proxyId);
        return callback->ReportFixture(proxy->fixture);
    }

    const b2BroadPhase* broadPhase;
    b2QueryCallback* callback;
};

void b2World::QueryAABB(b2QueryCallback* callback, const b2AABB& aabb) const
{
    b2WorldQueryWrapper wrapper;
    wrapper.broadPhase = &m_contactManager.m_broadPhase;
    wrapper.callback = callback;
    m_contactManager.m_broadPhase.Query(&wrapper, aabb);
}

struct b2WorldRayCastWrapper
{
    float32 RayCastCallback(const b2RayCastInput& input, int32 proxyId)
    {
        void* userData = broadPhase->GetUserData(proxyId);
        b2FixtureProxy* proxy = (b2FixtureProxy*)userData;
        b2Fixture* fixture = proxy->fixture;
        int32 index = proxy->childIndex;
        b2RayCastOutput output;
        bool hit = fixture->RayCast(&output, input, index);

        if (hit)
        {
            float32 fraction = output.fraction;
            b2Vec2 point = (1.0f - fraction) * input.p1 + fraction * input.p2;
            return callback->ReportFixture(fixture, point, output.normal, fraction);
        }

        return input.maxFraction;
    }

    const b2BroadPhase* broadPhase;
    b2RayCastCallback* callback;
};

void b2World::RayCast(b2RayCastCallback* callback, const b2Vec2& point1, const b2Vec2& point2) const
{
    b2WorldRayCastWrapper wrapper;
    wrapper.broadPhase = &m_contactManager.m_broadPhase;
    wrapper.callback = callback;
    b2RayCastInput input;
    input.maxFraction = 1.0f;
    input.p1 = point1;
    input.p2 = point2;
    m_contactManager.m_broadPhase.RayCast(&wrapper, input);
}

void b2World::DrawShape(b2Fixture* fixture, const b2Transform& xf, const b2Color& color)
{
    switch (fixture->GetType())
    {
    case b2Shape::e_circle:
        {
            b2CircleShape* circle = (b2CircleShape*)fixture->GetShape();

            b2Vec2 center = b2Mul(xf, circle->m_p);
            float32 radius = circle->m_radius;
            b2Vec2 axis = b2Mul(xf.q, b2Vec2(1.0f, 0.0f));

            m_debugDraw->DrawSolidCircle(center, radius, axis, color);
        }
        break;

    case b2Shape::e_edge:
        {
            b2EdgeShape* edge = (b2EdgeShape*)fixture->GetShape();
            b2Vec2 v1 = b2Mul(xf, edge->m_vertex1);
            b2Vec2 v2 = b2Mul(xf, edge->m_vertex2);
            m_debugDraw->DrawSegment(v1, v2, color);
        }
        break;

    case b2Shape::e_chain:
        {
            b2ChainShape* chain = (b2ChainShape*)fixture->GetShape();
            int32 count = chain->m_count;
            const b2Vec2* vertices = chain->m_vertices;

            b2Vec2 v1 = b2Mul(xf, vertices[0]);
            for (int32 i = 1; i < count; ++i)
            {
                b2Vec2 v2 = b2Mul(xf, vertices[i]);
                m_debugDraw->DrawSegment(v1, v2, color);
                m_debugDraw->DrawCircle(v1, 0.05f, color);
                v1 = v2;
            }
        }
        break;

    case b2Shape::e_polygon:
        {
            b2PolygonShape* poly = (b2PolygonShape*)fixture->GetShape();
            int32 vertexCount = poly->m_vertexCount;
            b2Assert(vertexCount <= b2_maxPolygonVertices);
            b2Vec2 vertices[b2_maxPolygonVertices];

            for (int32 i = 0; i < vertexCount; ++i)
            {
                vertices[i] = b2Mul(xf, poly->m_vertices[i]);
            }

            m_debugDraw->DrawSolidPolygon(vertices, vertexCount, color);
        }
        break;
            
    default:
        break;
    }
}

void b2World::DrawJoint(b2Joint* joint)
{
    b2Body* bodyA = joint->GetBodyA();
    b2Body* bodyB = joint->GetBodyB();
    const b2Transform& xf1 = bodyA->GetTransform();
    const b2Transform& xf2 = bodyB->GetTransform();
    b2Vec2 x1 = xf1.p;
    b2Vec2 x2 = xf2.p;
    b2Vec2 p1 = joint->GetAnchorA();
    b2Vec2 p2 = joint->GetAnchorB();

    b2Color color(0.5f, 0.8f, 0.8f);

    switch (joint->GetType())
    {
    case e_distanceJoint:
        m_debugDraw->DrawSegment(p1, p2, color);
        break;

    case e_pulleyJoint:
        {
            b2PulleyJoint* pulley = (b2PulleyJoint*)joint;
            b2Vec2 s1 = pulley->GetGroundAnchorA();
            b2Vec2 s2 = pulley->GetGroundAnchorB();
            m_debugDraw->DrawSegment(s1, p1, color);
            m_debugDraw->DrawSegment(s2, p2, color);
            m_debugDraw->DrawSegment(s1, s2, color);
        }
        break;

    case e_mouseJoint:
        // don't draw this
        break;

    default:
        m_debugDraw->DrawSegment(x1, p1, color);
        m_debugDraw->DrawSegment(p1, p2, color);
        m_debugDraw->DrawSegment(x2, p2, color);
    }
}

void b2World::DrawDebugData()
{
    if (m_debugDraw == NULL)
    {
        return;
    }

    uint32 flags = m_debugDraw->GetFlags();

    if (flags & b2Draw::e_shapeBit)
    {
        for (b2Body* b = m_bodyList; b; b = b->GetNext())
        {
            const b2Transform& xf = b->GetTransform();
            for (b2Fixture* f = b->GetFixtureList(); f; f = f->GetNext())
            {
                if (b->IsActive() == false)
                {
                    DrawShape(f, xf, b2Color(0.5f, 0.5f, 0.3f));
                }
                else if (b->GetType() == b2_staticBody)
                {
                    DrawShape(f, xf, b2Color(0.5f, 0.9f, 0.5f));
                }
                else if (b->GetType() == b2_kinematicBody)
                {
                    DrawShape(f, xf, b2Color(0.5f, 0.5f, 0.9f));
                }
                else if (b->IsAwake() == false)
                {
                    DrawShape(f, xf, b2Color(0.6f, 0.6f, 0.6f));
                }
                else
                {
                    DrawShape(f, xf, b2Color(0.9f, 0.7f, 0.7f));
                }
            }
        }
    }

    if (flags & b2Draw::e_jointBit)
    {
        for (b2Joint* j = m_jointList; j; j = j->GetNext())
        {
            DrawJoint(j);
        }
    }

    if (flags & b2Draw::e_pairBit)
    {
        b2Color color(0.3f, 0.9f, 0.9f);
        for (b2Contact* c = m_contactManager.m_contactList; c; c = c->GetNext())
        {
            //b2Fixture* fixtureA = c->GetFixtureA();
            //b2Fixture* fixtureB = c->GetFixtureB();

            //b2Vec2 cA = fixtureA->GetAABB().GetCenter();
            //b2Vec2 cB = fixtureB->GetAABB().GetCenter();

            //m_debugDraw->DrawSegment(cA, cB, color);
        }
    }

    if (flags & b2Draw::e_aabbBit)
    {
        b2Color color(0.9f, 0.3f, 0.9f);
        b2BroadPhase* bp = &m_contactManager.m_broadPhase;

        for (b2Body* b = m_bodyList; b; b = b->GetNext())
        {
            if (b->IsActive() == false)
            {
                continue;
            }

            for (b2Fixture* f = b->GetFixtureList(); f; f = f->GetNext())
            {
                for (int32 i = 0; i < f->m_proxyCount; ++i)
                {
                    b2FixtureProxy* proxy = f->m_proxies + i;
                    b2AABB aabb = bp->GetFatAABB(proxy->proxyId);
                    b2Vec2 vs[4];
                    vs[0].Set(aabb.lowerBound.x, aabb.lowerBound.y);
                    vs[1].Set(aabb.upperBound.x, aabb.lowerBound.y);
                    vs[2].Set(aabb.upperBound.x, aabb.upperBound.y);
                    vs[3].Set(aabb.lowerBound.x, aabb.upperBound.y);

                    m_debugDraw->DrawPolygon(vs, 4, color);
                }
            }
        }
    }

    if (flags & b2Draw::e_centerOfMassBit)
    {
        for (b2Body* b = m_bodyList; b; b = b->GetNext())
        {
            b2Transform xf = b->GetTransform();
            xf.p = b->GetWorldCenter();
            m_debugDraw->DrawTransform(xf);
        }
    }
}

int32 b2World::GetProxyCount() const
{
    return m_contactManager.m_broadPhase.GetProxyCount();
}

int32 b2World::GetTreeHeight() const
{
    return m_contactManager.m_broadPhase.GetTreeHeight();
}

int32 b2World::GetTreeBalance() const
{
    return m_contactManager.m_broadPhase.GetTreeBalance();
}

float32 b2World::GetTreeQuality() const
{
    return m_contactManager.m_broadPhase.GetTreeQuality();
}

void b2World::Dump()
{
    if ((m_flags & e_locked) == e_locked)
    {
        return;
    }

    b2Log("b2Vec2 g(%.15lef, %.15lef);\n", m_gravity.x, m_gravity.y);
    b2Log("m_world->SetGravity(g);\n");

    b2Log("b2Body** bodies = (b2Body**)b2Alloc(%d * sizeof(b2Body*));\n", m_bodyCount);
    b2Log("b2Joint** joints = (b2Joint**)b2Alloc(%d * sizeof(b2Joint*));\n", m_jointCount);
    int32 i = 0;
    for (b2Body* b = m_bodyList; b; b = b->m_next)
    {
        b->m_islandIndex = i;
        b->Dump();
        ++i;
    }

    i = 0;
    for (b2Joint* j = m_jointList; j; j = j->m_next)
    {
        j->m_index = i;
        ++i;
    }

    // First pass on joints, skip gear joints.
    for (b2Joint* j = m_jointList; j; j = j->m_next)
    {
        if (j->m_type == e_gearJoint)
        {
            continue;
        }

        b2Log("{\n");
        j->Dump();
        b2Log("}\n");
    }

    // Second pass on joints, only gear joints.
    for (b2Joint* j = m_jointList; j; j = j->m_next)
    {
        if (j->m_type != e_gearJoint)
        {
            continue;
        }

        b2Log("{\n");
        j->Dump();
        b2Log("}\n");
    }

    b2Log("b2Free(joints);\n");
    b2Log("b2Free(bodies);\n");
    b2Log("joints = NULL;\n");
    b2Log("bodies = NULL;\n");
}