text: /*
  * Copyright (c) 2011 Erin Catto http://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 <Rope/b2Rope.h>
  #include <Common/b2Draw.h>
  
  b2Rope::b2Rope()
  {
  	m_count = 0;
  	m_ps = NULL;
  	m_p0s = NULL;
  	m_vs = NULL;
  	m_ims = NULL;
  	m_Ls = NULL;
  	m_as = NULL;
  	m_gravity.SetZero();
  	m_k2 = 1.0f;
  	m_k3 = 0.1f;
  }
  
  b2Rope::~b2Rope()
  {
  	b2Free(m_ps);
  	b2Free(m_p0s);
  	b2Free(m_vs);
  	b2Free(m_ims);
  	b2Free(m_Ls);
  	b2Free(m_as);
  }
  
  void b2Rope::Initialize(const b2RopeDef* def)
  {
  	b2Assert(def->count >= 3);
  	m_count = def->count;
  	m_ps = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
  	m_p0s = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
  	m_vs = (b2Vec2*)b2Alloc(m_count * sizeof(b2Vec2));
  	m_ims = (b2_float32*)b2Alloc(m_count * sizeof(b2_float32));
  
  	for (b2_int32 i = 0; i < m_count; ++i)
  	{
  		m_ps[i] = def->vertices[i];
  		m_p0s[i] = def->vertices[i];
  		m_vs[i].SetZero();
  
  		b2_float32 m = def->masses[i];
  		if (m > 0.0f)
  		{
  			m_ims[i] = 1.0f / m;
  		}
  		else
  		{
  			m_ims[i] = 0.0f;
  		}
  	}
  
  	b2_int32 count2 = m_count - 1;
  	b2_int32 count3 = m_count - 2;
  	m_Ls = (b2_float32*)b2Alloc(count2 * sizeof(b2_float32));
  	m_as = (b2_float32*)b2Alloc(count3 * sizeof(b2_float32));
  
  	for (b2_int32 i = 0; i < count2; ++i)
  	{
  		b2Vec2 p1 = m_ps[i];
  		b2Vec2 p2 = m_ps[i+1];
  		m_Ls[i] = b2Distance(p1, p2);
  	}
  
  	for (b2_int32 i = 0; i < count3; ++i)
  	{
  		b2Vec2 p1 = m_ps[i];
  		b2Vec2 p2 = m_ps[i + 1];
  		b2Vec2 p3 = m_ps[i + 2];
  
  		b2Vec2 d1 = p2 - p1;
  		b2Vec2 d2 = p3 - p2;
  
  		b2_float32 a = b2Cross(d1, d2);
  		b2_float32 b = b2Dot(d1, d2);
  
  		m_as[i] = b2Atan2(a, b);
  	}
  
  	m_gravity = def->gravity;
  	m_damping = def->damping;
  	m_k2 = def->k2;
  	m_k3 = def->k3;
  }
  
  void b2Rope::Step(b2_float32 h, b2_int32 iterations)
  {
  	if (h == 0.0)
  	{
  		return;
  	}
  
  	b2_float32 d = expf(- h * m_damping);
  
  	for (b2_int32 i = 0; i < m_count; ++i)
  	{
  		m_p0s[i] = m_ps[i];
  		if (m_ims[i] > 0.0f)
  		{
  			m_vs[i] += h * m_gravity;
  		}
  		m_vs[i] *= d;
  		m_ps[i] += h * m_vs[i];
  
  	}
  
  	for (b2_int32 i = 0; i < iterations; ++i)
  	{
  		SolveC2();
  		SolveC3();
  		SolveC2();
  	}
  
  	b2_float32 inv_h = 1.0f / h;
  	for (b2_int32 i = 0; i < m_count; ++i)
  	{
  		m_vs[i] = inv_h * (m_ps[i] - m_p0s[i]);
  	}
  }
  
  void b2Rope::SolveC2()
  {
  	b2_int32 count2 = m_count - 1;
  
  	for (b2_int32 i = 0; i < count2; ++i)
  	{
  		b2Vec2 p1 = m_ps[i];
  		b2Vec2 p2 = m_ps[i + 1];
  
  		b2Vec2 d = p2 - p1;
  		b2_float32 L = d.Normalize();
  
  		b2_float32 im1 = m_ims[i];
  		b2_float32 im2 = m_ims[i + 1];
  
  		if (im1 + im2 == 0.0f)
  		{
  			continue;
  		}
  
  		b2_float32 s1 = im1 / (im1 + im2);
  		b2_float32 s2 = im2 / (im1 + im2);
  
  		p1 -= m_k2 * s1 * (m_Ls[i] - L) * d;
  		p2 += m_k2 * s2 * (m_Ls[i] - L) * d;
  
  		m_ps[i] = p1;
  		m_ps[i + 1] = p2;
  	}
  }
  
  void b2Rope::SetAngle(b2_float32 angle)
  {
  	b2_int32 count3 = m_count - 2;
  	for (b2_int32 i = 0; i < count3; ++i)
  	{
  		m_as[i] = angle;
  	}
  }
  
  void b2Rope::SolveC3()
  {
  	b2_int32 count3 = m_count - 2;
  
  	for (b2_int32 i = 0; i < count3; ++i)
  	{
  		b2Vec2 p1 = m_ps[i];
  		b2Vec2 p2 = m_ps[i + 1];
  		b2Vec2 p3 = m_ps[i + 2];
  
  		b2_float32 m1 = m_ims[i];
  		b2_float32 m2 = m_ims[i + 1];
  		b2_float32 m3 = m_ims[i + 2];
  
  		b2Vec2 d1 = p2 - p1;
  		b2Vec2 d2 = p3 - p2;
  
  		b2_float32 L1sqr = d1.LengthSquared();
  		b2_float32 L2sqr = d2.LengthSquared();
  
  		if (L1sqr * L2sqr == 0.0f)
  		{
  			continue;
  		}
  
  		b2_float32 a = b2Cross(d1, d2);
  		b2_float32 b = b2Dot(d1, d2);
  
  		b2_float32 angle = b2Atan2(a, b);
  
  		b2Vec2 Jd1 = (-1.0f / L1sqr) * d1.Skew();
  		b2Vec2 Jd2 = (1.0f / L2sqr) * d2.Skew();
  
  		b2Vec2 J1 = -Jd1;
  		b2Vec2 J2 = Jd1 - Jd2;
  		b2Vec2 J3 = Jd2;
  
  		b2_float32 mass = m1 * b2Dot(J1, J1) + m2 * b2Dot(J2, J2) + m3 * b2Dot(J3, J3);
  		if (mass == 0.0f)
  		{
  			continue;
  		}
  
  		mass = 1.0f / mass;
  
  		b2_float32 C = angle - m_as[i];
  
  		while (C > b2_pi)
  		{
  			angle -= 2 * b2_pi;
  			C = angle - m_as[i];
  		}
  
  		while (C < -b2_pi)
  		{
  			angle += 2.0f * b2_pi;
  			C = angle - m_as[i];
  		}
  
  		b2_float32 impulse = - m_k3 * mass * C;
  
  		p1 += (m1 * impulse) * J1;
  		p2 += (m2 * impulse) * J2;
  		p3 += (m3 * impulse) * J3;
  
  		m_ps[i] = p1;
  		m_ps[i + 1] = p2;
  		m_ps[i + 2] = p3;
  	}
  }
  
  void b2Rope::Draw(b2Draw* draw) const
  {
  	b2Color c(0.4f, 0.5f, 0.7f);
  
  	for (b2_int32 i = 0; i < m_count - 1; ++i)
  	{
  		draw->DrawSegment(m_ps[i], m_ps[i+1], c);
  	}
  }
  