Warning, file /education/gcompris/external/qml-box2d/Box2D/Collision/b2TimeOfImpact.cpp was not indexed or was modified since last indexation (in which case cross-reference links may be missing, inaccurate or erroneous).

 /*
 * Copyright (c) 2007-2009 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/b2Collision.h>
 #include <Box2D/Collision/b2Distance.h>
 #include <Box2D/Collision/b2TimeOfImpact.h>
 #include <Box2D/Collision/Shapes/b2CircleShape.h>
 #include <Box2D/Collision/Shapes/b2PolygonShape.h>
 #include <Box2D/Common/b2Timer.h>
 
 #include <stdio.h>
 
 float32 b2_toiTime, b2_toiMaxTime;
 int32 b2_toiCalls, b2_toiIters, b2_toiMaxIters;
 int32 b2_toiRootIters, b2_toiMaxRootIters;
 
 //
 struct b2SeparationFunction
 {
     enum Type
     {
         e_points,
         e_faceA,
         e_faceB
     };
 
     // TODO_ERIN might not need to return the separation
 
     float32 Initialize(const b2SimplexCache* cache,
         const b2DistanceProxy* proxyA, const b2Sweep& sweepA,
         const b2DistanceProxy* proxyB, const b2Sweep& sweepB,
         float32 t1)
     {
         m_proxyA = proxyA;
         m_proxyB = proxyB;
         int32 count = cache->count;
         b2Assert(0 < count && count < 3);
 
         m_sweepA = sweepA;
         m_sweepB = sweepB;
 
         b2Transform xfA, xfB;
         m_sweepA.GetTransform(&xfA, t1);
         m_sweepB.GetTransform(&xfB, t1);
 
         if (count == 1)
         {
             m_type = e_points;
             b2Vec2 localPointA = m_proxyA->GetVertex(cache->indexA[0]);
             b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
             b2Vec2 pointA = b2Mul(xfA, localPointA);
             b2Vec2 pointB = b2Mul(xfB, localPointB);
             m_axis = pointB - pointA;
             float32 s = m_axis.Normalize();
             return s;
         }
         else if (cache->indexA[0] == cache->indexA[1])
         {
             // Two points on B and one on A.
             m_type = e_faceB;
             b2Vec2 localPointB1 = proxyB->GetVertex(cache->indexB[0]);
             b2Vec2 localPointB2 = proxyB->GetVertex(cache->indexB[1]);
 
             m_axis = b2Cross(localPointB2 - localPointB1, 1.0f);
             m_axis.Normalize();
             b2Vec2 normal = b2Mul(xfB.q, m_axis);
 
             m_localPoint = 0.5f * (localPointB1 + localPointB2);
             b2Vec2 pointB = b2Mul(xfB, m_localPoint);
 
             b2Vec2 localPointA = proxyA->GetVertex(cache->indexA[0]);
             b2Vec2 pointA = b2Mul(xfA, localPointA);
 
             float32 s = b2Dot(pointA - pointB, normal);
             if (s < 0.0f)
             {
                 m_axis = -m_axis;
                 s = -s;
             }
             return s;
         }
         else
         {
             // Two points on A and one or two points on B.
             m_type = e_faceA;
             b2Vec2 localPointA1 = m_proxyA->GetVertex(cache->indexA[0]);
             b2Vec2 localPointA2 = m_proxyA->GetVertex(cache->indexA[1]);
             
             m_axis = b2Cross(localPointA2 - localPointA1, 1.0f);
             m_axis.Normalize();
             b2Vec2 normal = b2Mul(xfA.q, m_axis);
 
             m_localPoint = 0.5f * (localPointA1 + localPointA2);
             b2Vec2 pointA = b2Mul(xfA, m_localPoint);
 
             b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
             b2Vec2 pointB = b2Mul(xfB, localPointB);
 
             float32 s = b2Dot(pointB - pointA, normal);
             if (s < 0.0f)
             {
                 m_axis = -m_axis;
                 s = -s;
             }
             return s;
         }
     }
 
     //
     float32 FindMinSeparation(int32* indexA, int32* indexB, float32 t) const
     {
         b2Transform xfA, xfB;
         m_sweepA.GetTransform(&xfA, t);
         m_sweepB.GetTransform(&xfB, t);
 
         switch (m_type)
         {
         case e_points:
             {
                 b2Vec2 axisA = b2MulT(xfA.q,  m_axis);
                 b2Vec2 axisB = b2MulT(xfB.q, -m_axis);
 
                 *indexA = m_proxyA->GetSupport(axisA);
                 *indexB = m_proxyB->GetSupport(axisB);
 
                 b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
                 b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
                 
                 b2Vec2 pointA = b2Mul(xfA, localPointA);
                 b2Vec2 pointB = b2Mul(xfB, localPointB);
 
                 float32 separation = b2Dot(pointB - pointA, m_axis);
                 return separation;
             }
 
         case e_faceA:
             {
                 b2Vec2 normal = b2Mul(xfA.q, m_axis);
                 b2Vec2 pointA = b2Mul(xfA, m_localPoint);
 
                 b2Vec2 axisB = b2MulT(xfB.q, -normal);
                 
                 *indexA = -1;
                 *indexB = m_proxyB->GetSupport(axisB);
 
                 b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
                 b2Vec2 pointB = b2Mul(xfB, localPointB);
 
                 float32 separation = b2Dot(pointB - pointA, normal);
                 return separation;
             }
 
         case e_faceB:
             {
                 b2Vec2 normal = b2Mul(xfB.q, m_axis);
                 b2Vec2 pointB = b2Mul(xfB, m_localPoint);
 
                 b2Vec2 axisA = b2MulT(xfA.q, -normal);
 
                 *indexB = -1;
                 *indexA = m_proxyA->GetSupport(axisA);
 
                 b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
                 b2Vec2 pointA = b2Mul(xfA, localPointA);
 
                 float32 separation = b2Dot(pointA - pointB, normal);
                 return separation;
             }
 
         default:
             b2Assert(false);
             *indexA = -1;
             *indexB = -1;
             return 0.0f;
         }
     }
 
     //
     float32 Evaluate(int32 indexA, int32 indexB, float32 t) const
     {
         b2Transform xfA, xfB;
         m_sweepA.GetTransform(&xfA, t);
         m_sweepB.GetTransform(&xfB, t);
 
         switch (m_type)
         {
         case e_points:
             {
                 b2Vec2 localPointA = m_proxyA->GetVertex(indexA);
                 b2Vec2 localPointB = m_proxyB->GetVertex(indexB);
 
                 b2Vec2 pointA = b2Mul(xfA, localPointA);
                 b2Vec2 pointB = b2Mul(xfB, localPointB);
                 float32 separation = b2Dot(pointB - pointA, m_axis);
 
                 return separation;
             }
 
         case e_faceA:
             {
                 b2Vec2 normal = b2Mul(xfA.q, m_axis);
                 b2Vec2 pointA = b2Mul(xfA, m_localPoint);
 
                 b2Vec2 localPointB = m_proxyB->GetVertex(indexB);
                 b2Vec2 pointB = b2Mul(xfB, localPointB);
 
                 float32 separation = b2Dot(pointB - pointA, normal);
                 return separation;
             }
 
         case e_faceB:
             {
                 b2Vec2 normal = b2Mul(xfB.q, m_axis);
                 b2Vec2 pointB = b2Mul(xfB, m_localPoint);
 
                 b2Vec2 localPointA = m_proxyA->GetVertex(indexA);
                 b2Vec2 pointA = b2Mul(xfA, localPointA);
 
                 float32 separation = b2Dot(pointA - pointB, normal);
                 return separation;
             }
 
         default:
             b2Assert(false);
             return 0.0f;
         }
     }
 
     const b2DistanceProxy* m_proxyA;
     const b2DistanceProxy* m_proxyB;
     b2Sweep m_sweepA, m_sweepB;
     Type m_type;
     b2Vec2 m_localPoint;
     b2Vec2 m_axis;
 };
 
 // CCD via the local separating axis method. This seeks progression
 // by computing the largest time at which separation is maintained.
 void b2TimeOfImpact(b2TOIOutput* output, const b2TOIInput* input)
 {
     b2Timer timer;
 
     ++b2_toiCalls;
 
     output->state = b2TOIOutput::e_unknown;
     output->t = input->tMax;
 
     const b2DistanceProxy* proxyA = &input->proxyA;
     const b2DistanceProxy* proxyB = &input->proxyB;
 
     b2Sweep sweepA = input->sweepA;
     b2Sweep sweepB = input->sweepB;
 
     // Large rotations can make the root finder fail, so we normalize the
     // sweep angles.
     sweepA.Normalize();
     sweepB.Normalize();
 
     float32 tMax = input->tMax;
 
     float32 totalRadius = proxyA->m_radius + proxyB->m_radius;
     float32 target = b2Max(b2_linearSlop, totalRadius - 3.0f * b2_linearSlop);
     float32 tolerance = 0.25f * b2_linearSlop;
     b2Assert(target > tolerance);
 
     float32 t1 = 0.0f;
     const int32 k_maxIterations = 20;   // TODO_ERIN b2Settings
     int32 iter = 0;
 
     // Prepare input for distance query.
     b2SimplexCache cache;
     cache.count = 0;
     b2DistanceInput distanceInput;
     distanceInput.proxyA = input->proxyA;
     distanceInput.proxyB = input->proxyB;
     distanceInput.useRadii = false;
 
     // The outer loop progressively attempts to compute new separating axes.
     // This loop terminates when an axis is repeated (no progress is made).
     for(;;)
     {
         b2Transform xfA, xfB;
         sweepA.GetTransform(&xfA, t1);
         sweepB.GetTransform(&xfB, t1);
 
         // Get the distance between shapes. We can also use the results
         // to get a separating axis.
         distanceInput.transformA = xfA;
         distanceInput.transformB = xfB;
         b2DistanceOutput distanceOutput;
         b2Distance(&distanceOutput, &cache, &distanceInput);
 
         // If the shapes are overlapped, we give up on continuous collision.
         if (distanceOutput.distance <= 0.0f)
         {
             // Failure!
             output->state = b2TOIOutput::e_overlapped;
             output->t = 0.0f;
             break;
         }
 
         if (distanceOutput.distance < target + tolerance)
         {
             // Victory!
             output->state = b2TOIOutput::e_touching;
             output->t = t1;
             break;
         }
 
         // Initialize the separating axis.
         b2SeparationFunction fcn;
         fcn.Initialize(&cache, proxyA, sweepA, proxyB, sweepB, t1);
 #if 0
         // Dump the curve seen by the root finder
         {
             const int32 N = 100;
             float32 dx = 1.0f / N;
             float32 xs[N+1];
             float32 fs[N+1];
 
             float32 x = 0.0f;
 
             for (int32 i = 0; i <= N; ++i)
             {
                 sweepA.GetTransform(&xfA, x);
                 sweepB.GetTransform(&xfB, x);
                 float32 f = fcn.Evaluate(xfA, xfB) - target;
 
                 printf("%g %g\n", x, f);
 
                 xs[i] = x;
                 fs[i] = f;
 
                 x += dx;
             }
         }
 #endif
 
         // Compute the TOI on the separating axis. We do this by successively
         // resolving the deepest point. This loop is bounded by the number of vertices.
         bool done = false;
         float32 t2 = tMax;
         int32 pushBackIter = 0;
         for (;;)
         {
             // Find the deepest point at t2. Store the witness point indices.
             int32 indexA, indexB;
             float32 s2 = fcn.FindMinSeparation(&indexA, &indexB, t2);
 
             // Is the final configuration separated?
             if (s2 > target + tolerance)
             {
                 // Victory!
                 output->state = b2TOIOutput::e_separated;
                 output->t = tMax;
                 done = true;
                 break;
             }
 
             // Has the separation reached tolerance?
             if (s2 > target - tolerance)
             {
                 // Advance the sweeps
                 t1 = t2;
                 break;
             }
 
             // Compute the initial separation of the witness points.
             float32 s1 = fcn.Evaluate(indexA, indexB, t1);
 
             // Check for initial overlap. This might happen if the root finder
             // runs out of iterations.
             if (s1 < target - tolerance)
             {
                 output->state = b2TOIOutput::e_failed;
                 output->t = t1;
                 done = true;
                 break;
             }
 
             // Check for touching
             if (s1 <= target + tolerance)
             {
                 // Victory! t1 should hold the TOI (could be 0.0).
                 output->state = b2TOIOutput::e_touching;
                 output->t = t1;
                 done = true;
                 break;
             }
 
             // Compute 1D root of: f(x) - target = 0
             int32 rootIterCount = 0;
             float32 a1 = t1, a2 = t2;
             for (;;)
             {
                 // Use a mix of the secant rule and bisection.
                 float32 t;
                 if (rootIterCount & 1)
                 {
                     // Secant rule to improve convergence.
                     t = a1 + (target - s1) * (a2 - a1) / (s2 - s1);
                 }
                 else
                 {
                     // Bisection to guarantee progress.
                     t = 0.5f * (a1 + a2);
                 }
 
                 ++rootIterCount;
                 ++b2_toiRootIters;
 
                 float32 s = fcn.Evaluate(indexA, indexB, t);
 
                 if (b2Abs(s - target) < tolerance)
                 {
                     // t2 holds a tentative value for t1
                     t2 = t;
                     break;
                 }
 
                 // Ensure we continue to bracket the root.
                 if (s > target)
                 {
                     a1 = t;
                     s1 = s;
                 }
                 else
                 {
                     a2 = t;
                     s2 = s;
                 }
                 
                 if (rootIterCount == 50)
                 {
                     break;
                 }
             }
 
             b2_toiMaxRootIters = b2Max(b2_toiMaxRootIters, rootIterCount);
 
             ++pushBackIter;
 
             if (pushBackIter == b2_maxPolygonVertices)
             {
                 break;
             }
         }
 
         ++iter;
         ++b2_toiIters;
 
         if (done)
         {
             break;
         }
 
         if (iter == k_maxIterations)
         {
             // Root finder got stuck. Semi-victory.
             output->state = b2TOIOutput::e_failed;
             output->t = t1;
             break;
         }
     }
 
     b2_toiMaxIters = b2Max(b2_toiMaxIters, iter);
 
     float32 time = timer.GetMilliseconds();
     b2_toiMaxTime = b2Max(b2_toiMaxTime, time);
     b2_toiTime += time;
 }