text: /*
  * Copyright (c) 2006-2009 Erin Catto http://www.box2d.org
  * Copyright (c) 2013 Google, Inc.
  *
  * 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/Shapes/b2CircleShape.h>
  #include <new>
  
  b2Shape* b2CircleShape::Clone(b2BlockAllocator* allocator) const
  {
  	void* mem = allocator->Allocate(sizeof(b2CircleShape));
  	b2CircleShape* clone = new (mem) b2CircleShape;
  	*clone = *this;
  	return clone;
  }
  
  int32 b2CircleShape::GetChildCount() const
  {
  	return 1;
  }
  
  bool b2CircleShape::TestPoint(const b2Transform& transform, const b2Vec2& p) const
  {
  	b2Vec2 center = transform.p + b2Mul(transform.q, m_p);
  	b2Vec2 d = p - center;
  	return b2Dot(d, d) <= m_radius * m_radius;
  }
  
  void b2CircleShape::ComputeDistance(const b2Transform& transform, const b2Vec2& p, float32* distance, b2Vec2* normal, int32 childIndex) const
  {
  	B2_NOT_USED(childIndex);
  
  	b2Vec2 center = transform.p + b2Mul(transform.q, m_p);
  	b2Vec2 d = p - center;
  	float32 d1 = d.Length();
  	*distance = d1 - m_radius;
  	*normal = 1 / d1 * d;
  }
  
  // Collision Detection in Interactive 3D Environments by Gino van den Bergen
  // From Section 3.1.2
  // x = s + a * r
  // norm(x) = radius
  bool b2CircleShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
  							const b2Transform& transform, int32 childIndex) const
  {
  	B2_NOT_USED(childIndex);
  
  	b2Vec2 position = transform.p + b2Mul(transform.q, m_p);
  	b2Vec2 s = input.p1 - position;
  	float32 b = b2Dot(s, s) - m_radius * m_radius;
  
  	// Solve quadratic equation.
  	b2Vec2 r = input.p2 - input.p1;
  	float32 c =  b2Dot(s, r);
  	float32 rr = b2Dot(r, r);
  	float32 sigma = c * c - rr * b;
  
  	// Check for negative discriminant and short segment.
  	if (sigma < 0.0f || rr < b2_epsilon)
  	{
  		return false;
  	}
  
  	// Find the point of intersection of the line with the circle.
  	float32 a = -(c + b2Sqrt(sigma));
  
  	// Is the intersection point on the segment?
  	if (0.0f <= a && a <= input.maxFraction * rr)
  	{
  		a /= rr;
  		output->fraction = a;
  		output->normal = s + a * r;
  		output->normal.Normalize();
  		return true;
  	}
  
  	return false;
  }
  
  void b2CircleShape::ComputeAABB(b2AABB* aabb, const b2Transform& transform, int32 childIndex) const
  {
  	B2_NOT_USED(childIndex);
  
  	b2Vec2 p = transform.p + b2Mul(transform.q, m_p);
  	aabb->lowerBound.Set(p.x - m_radius, p.y - m_radius);
  	aabb->upperBound.Set(p.x + m_radius, p.y + m_radius);
  }
  
  void b2CircleShape::ComputeMass(b2MassData* massData, float32 density) const
  {
  	massData->mass = density * b2_pi * m_radius * m_radius;
  	massData->center = m_p;
  
  	// inertia about the local origin
  	massData->I = massData->mass * (0.5f * m_radius * m_radius + b2Dot(m_p, m_p));
  }
  