text: /*
  * 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>
  
  void b2WorldManifold::Initialize(const b2Manifold* manifold,
                            const b2Transform& xfA, float32 radiusA,
                            const b2Transform& xfB, float32 radiusB)
  {
      if (manifold->pointCount == 0)
      {
          return;
      }
  
      switch (manifold->type)
      {
      case b2Manifold::e_circles:
          {
              normal.Set(1.0f, 0.0f);
              b2Vec2 pointA = b2Mul(xfA, manifold->localPoint);
              b2Vec2 pointB = b2Mul(xfB, manifold->points[0].localPoint);
              if (b2DistanceSquared(pointA, pointB) > b2_epsilon * b2_epsilon)
              {
                  normal = pointB - pointA;
                  normal.Normalize();
              }
  
              b2Vec2 cA = pointA + radiusA * normal;
              b2Vec2 cB = pointB - radiusB * normal;
              points[0] = 0.5f * (cA + cB);
          }
          break;
  
      case b2Manifold::e_faceA:
          {
              normal = b2Mul(xfA.q, manifold->localNormal);
              b2Vec2 planePoint = b2Mul(xfA, manifold->localPoint);
              
              for (int32 i = 0; i < manifold->pointCount; ++i)
              {
                  b2Vec2 clipPoint = b2Mul(xfB, manifold->points[i].localPoint);
                  b2Vec2 cA = clipPoint + (radiusA - b2Dot(clipPoint - planePoint, normal)) * normal;
                  b2Vec2 cB = clipPoint - radiusB * normal;
                  points[i] = 0.5f * (cA + cB);
              }
          }
          break;
  
      case b2Manifold::e_faceB:
          {
              normal = b2Mul(xfB.q, manifold->localNormal);
              b2Vec2 planePoint = b2Mul(xfB, manifold->localPoint);
  
              for (int32 i = 0; i < manifold->pointCount; ++i)
              {
                  b2Vec2 clipPoint = b2Mul(xfA, manifold->points[i].localPoint);
                  b2Vec2 cB = clipPoint + (radiusB - b2Dot(clipPoint - planePoint, normal)) * normal;
                  b2Vec2 cA = clipPoint - radiusA * normal;
                  points[i] = 0.5f * (cA + cB);
              }
  
              // Ensure normal points from A to B.
              normal = -normal;
          }
          break;
      }
  }
  
  void b2GetPointStates(b2PointState state1[b2_maxManifoldPoints], b2PointState state2[b2_maxManifoldPoints],
                        const b2Manifold* manifold1, const b2Manifold* manifold2)
  {
      for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
      {
          state1[i] = b2_nullState;
          state2[i] = b2_nullState;
      }
  
      // Detect persists and removes.
      for (int32 i = 0; i < manifold1->pointCount; ++i)
      {
          b2ContactID id = manifold1->points[i].id;
  
          state1[i] = b2_removeState;
  
          for (int32 j = 0; j < manifold2->pointCount; ++j)
          {
              if (manifold2->points[j].id.key == id.key)
              {
                  state1[i] = b2_persistState;
                  break;
              }
          }
      }
  
      // Detect persists and adds.
      for (int32 i = 0; i < manifold2->pointCount; ++i)
      {
          b2ContactID id = manifold2->points[i].id;
  
          state2[i] = b2_addState;
  
          for (int32 j = 0; j < manifold1->pointCount; ++j)
          {
              if (manifold1->points[j].id.key == id.key)
              {
                  state2[i] = b2_persistState;
                  break;
              }
          }
      }
  }
  
  // From Real-time Collision Detection, p179.
  bool b2AABB::RayCast(b2RayCastOutput* output, const b2RayCastInput& input) const
  {
      float32 tmin = -b2_maxFloat;
      float32 tmax = b2_maxFloat;
  
      b2Vec2 p = input.p1;
      b2Vec2 d = input.p2 - input.p1;
      b2Vec2 absD = b2Abs(d);
  
      b2Vec2 normal;
  
      for (int32 i = 0; i < 2; ++i)
      {
          if (absD(i) < b2_epsilon)
          {
              // Parallel.
              if (p(i) < lowerBound(i) || upperBound(i) < p(i))
              {
                  return false;
              }
          }
          else
          {
              float32 inv_d = 1.0f / d(i);
              float32 t1 = (lowerBound(i) - p(i)) * inv_d;
              float32 t2 = (upperBound(i) - p(i)) * inv_d;
  
              // Sign of the normal vector.
              float32 s = -1.0f;
  
              if (t1 > t2)
              {
                  b2Swap(t1, t2);
                  s = 1.0f;
              }
  
              // Push the min up
              if (t1 > tmin)
              {
                  normal.SetZero();
                  normal(i) = s;
                  tmin = t1;
              }
  
              // Pull the max down
              tmax = b2Min(tmax, t2);
  
              if (tmin > tmax)
              {
                  return false;
              }
          }
      }
  
      // Does the ray start inside the box?
      // Does the ray intersect beyond the max fraction?
      if (tmin < 0.0f || input.maxFraction < tmin)
      {
          return false;
      }
  
      // Intersection.
      output->fraction = tmin;
      output->normal = normal;
      return true;
  }
  
  // Sutherland-Hodgman clipping.
  int32 b2ClipSegmentToLine(b2ClipVertex vOut[2], const b2ClipVertex vIn[2],
                          const b2Vec2& normal, float32 offset, int32 vertexIndexA)
  {
      // Start with no output points
      int32 numOut = 0;
  
      // Calculate the distance of end points to the line
      float32 distance0 = b2Dot(normal, vIn[0].v) - offset;
      float32 distance1 = b2Dot(normal, vIn[1].v) - offset;
  
      // If the points are behind the plane
      if (distance0 <= 0.0f) vOut[numOut++] = vIn[0];
      if (distance1 <= 0.0f) vOut[numOut++] = vIn[1];
  
      // If the points are on different sides of the plane
      if (distance0 * distance1 < 0.0f)
      {
          // Find intersection point of edge and plane
          float32 interp = distance0 / (distance0 - distance1);
          vOut[numOut].v = vIn[0].v + interp * (vIn[1].v - vIn[0].v);
  
          // VertexA is hitting edgeB.
          vOut[numOut].id.cf.indexA = vertexIndexA;
          vOut[numOut].id.cf.indexB = vIn[0].id.cf.indexB;
          vOut[numOut].id.cf.typeA = b2ContactFeature::e_vertex;
          vOut[numOut].id.cf.typeB = b2ContactFeature::e_face;
          ++numOut;
      }
  
      return numOut;
  }
  
  bool b2TestOverlap(    const b2Shape* shapeA, int32 indexA,
                      const b2Shape* shapeB, int32 indexB,
                      const b2Transform& xfA, const b2Transform& xfB)
  {
      b2DistanceInput input;
      input.proxyA.Set(shapeA, indexA);
      input.proxyB.Set(shapeB, indexB);
      input.transformA = xfA;
      input.transformB = xfB;
      input.useRadii = true;
  
      b2SimplexCache cache;
      cache.count = 0;
  
      b2DistanceOutput output;
  
      b2Distance(&output, &cache, &input);
  
      return output.distance < 10.0f * b2_epsilon;
  }
  