487 lines
		
	
	
		
			11 KiB
		
	
	
	
		
			C++
		
	
	
	
			
		
		
	
	
			487 lines
		
	
	
		
			11 KiB
		
	
	
	
		
			C++
		
	
	
	
| /*
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| * Copyright (c) 2007-2009 Erin Catto http://www.box2d.org
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| *
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| * This software is provided 'as-is', without any express or implied
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| * warranty.  In no event will the authors be held liable for any damages
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| * arising from the use of this software.
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| * Permission is granted to anyone to use this software for any purpose,
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| * including commercial applications, and to alter it and redistribute it
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| * freely, subject to the following restrictions:
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| * 1. The origin of this software must not be misrepresented; you must not
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| * claim that you wrote the original software. If you use this software
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| * in a product, an acknowledgment in the product documentation would be
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| * appreciated but is not required.
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| * 2. Altered source versions must be plainly marked as such, and must not be
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| * misrepresented as being the original software.
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| * 3. This notice may not be removed or altered from any source distribution.
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| */
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| 
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| #include "Box2D/Collision/b2Collision.h"
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| #include "Box2D/Collision/b2Distance.h"
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| #include "Box2D/Collision/b2TimeOfImpact.h"
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| #include "Box2D/Collision/Shapes/b2CircleShape.h"
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| #include "Box2D/Collision/Shapes/b2PolygonShape.h"
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| #include "Box2D/Common/b2Timer.h"
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| 
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| #include <stdio.h>
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| 
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| float32 b2_toiTime, b2_toiMaxTime;
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| int32 b2_toiCalls, b2_toiIters, b2_toiMaxIters;
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| int32 b2_toiRootIters, b2_toiMaxRootIters;
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| 
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| //
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| struct b2SeparationFunction
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| {
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| 	enum Type
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| 	{
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| 		e_points,
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| 		e_faceA,
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| 		e_faceB
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| 	};
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| 
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| 	// TODO_ERIN might not need to return the separation
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| 
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| 	float32 Initialize(const b2SimplexCache* cache,
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| 		const b2DistanceProxy* proxyA, const b2Sweep& sweepA,
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| 		const b2DistanceProxy* proxyB, const b2Sweep& sweepB,
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| 		float32 t1)
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| 	{
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| 		m_proxyA = proxyA;
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| 		m_proxyB = proxyB;
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| 		int32 count = cache->count;
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| 		b2Assert(0 < count && count < 3);
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| 
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| 		m_sweepA = sweepA;
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| 		m_sweepB = sweepB;
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| 
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| 		b2Transform xfA, xfB;
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| 		m_sweepA.GetTransform(&xfA, t1);
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| 		m_sweepB.GetTransform(&xfB, t1);
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| 
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| 		if (count == 1)
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| 		{
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| 			m_type = e_points;
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| 			b2Vec2 localPointA = m_proxyA->GetVertex(cache->indexA[0]);
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| 			b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
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| 			b2Vec2 pointA = b2Mul(xfA, localPointA);
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| 			b2Vec2 pointB = b2Mul(xfB, localPointB);
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| 			m_axis = pointB - pointA;
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| 			float32 s = m_axis.Normalize();
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| 			return s;
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| 		}
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| 		else if (cache->indexA[0] == cache->indexA[1])
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| 		{
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| 			// Two points on B and one on A.
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| 			m_type = e_faceB;
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| 			b2Vec2 localPointB1 = proxyB->GetVertex(cache->indexB[0]);
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| 			b2Vec2 localPointB2 = proxyB->GetVertex(cache->indexB[1]);
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| 
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| 			m_axis = b2Cross(localPointB2 - localPointB1, 1.0f);
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| 			m_axis.Normalize();
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| 			b2Vec2 normal = b2Mul(xfB.q, m_axis);
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| 
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| 			m_localPoint = 0.5f * (localPointB1 + localPointB2);
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| 			b2Vec2 pointB = b2Mul(xfB, m_localPoint);
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| 
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| 			b2Vec2 localPointA = proxyA->GetVertex(cache->indexA[0]);
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| 			b2Vec2 pointA = b2Mul(xfA, localPointA);
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| 
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| 			float32 s = b2Dot(pointA - pointB, normal);
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| 			if (s < 0.0f)
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| 			{
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| 				m_axis = -m_axis;
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| 				s = -s;
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| 			}
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| 			return s;
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| 		}
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| 		else
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| 		{
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| 			// Two points on A and one or two points on B.
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| 			m_type = e_faceA;
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| 			b2Vec2 localPointA1 = m_proxyA->GetVertex(cache->indexA[0]);
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| 			b2Vec2 localPointA2 = m_proxyA->GetVertex(cache->indexA[1]);
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| 			
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| 			m_axis = b2Cross(localPointA2 - localPointA1, 1.0f);
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| 			m_axis.Normalize();
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| 			b2Vec2 normal = b2Mul(xfA.q, m_axis);
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| 
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| 			m_localPoint = 0.5f * (localPointA1 + localPointA2);
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| 			b2Vec2 pointA = b2Mul(xfA, m_localPoint);
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| 
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| 			b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
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| 			b2Vec2 pointB = b2Mul(xfB, localPointB);
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| 
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| 			float32 s = b2Dot(pointB - pointA, normal);
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| 			if (s < 0.0f)
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| 			{
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| 				m_axis = -m_axis;
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| 				s = -s;
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| 			}
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| 			return s;
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| 		}
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| 	}
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| 
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| 	//
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| 	float32 FindMinSeparation(int32* indexA, int32* indexB, float32 t) const
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| 	{
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| 		b2Transform xfA, xfB;
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| 		m_sweepA.GetTransform(&xfA, t);
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| 		m_sweepB.GetTransform(&xfB, t);
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| 
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| 		switch (m_type)
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| 		{
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| 		case e_points:
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| 			{
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| 				b2Vec2 axisA = b2MulT(xfA.q,  m_axis);
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| 				b2Vec2 axisB = b2MulT(xfB.q, -m_axis);
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| 
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| 				*indexA = m_proxyA->GetSupport(axisA);
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| 				*indexB = m_proxyB->GetSupport(axisB);
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| 
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| 				b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
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| 				b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
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| 				
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| 				b2Vec2 pointA = b2Mul(xfA, localPointA);
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| 				b2Vec2 pointB = b2Mul(xfB, localPointB);
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| 
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| 				float32 separation = b2Dot(pointB - pointA, m_axis);
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| 				return separation;
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| 			}
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| 
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| 		case e_faceA:
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| 			{
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| 				b2Vec2 normal = b2Mul(xfA.q, m_axis);
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| 				b2Vec2 pointA = b2Mul(xfA, m_localPoint);
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| 
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| 				b2Vec2 axisB = b2MulT(xfB.q, -normal);
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| 				
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| 				*indexA = -1;
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| 				*indexB = m_proxyB->GetSupport(axisB);
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| 
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| 				b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
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| 				b2Vec2 pointB = b2Mul(xfB, localPointB);
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| 
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| 				float32 separation = b2Dot(pointB - pointA, normal);
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| 				return separation;
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| 			}
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| 
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| 		case e_faceB:
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| 			{
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| 				b2Vec2 normal = b2Mul(xfB.q, m_axis);
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| 				b2Vec2 pointB = b2Mul(xfB, m_localPoint);
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| 
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| 				b2Vec2 axisA = b2MulT(xfA.q, -normal);
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| 
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| 				*indexB = -1;
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| 				*indexA = m_proxyA->GetSupport(axisA);
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| 
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| 				b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
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| 				b2Vec2 pointA = b2Mul(xfA, localPointA);
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| 
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| 				float32 separation = b2Dot(pointA - pointB, normal);
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| 				return separation;
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| 			}
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| 
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| 		default:
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| 			b2Assert(false);
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| 			*indexA = -1;
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| 			*indexB = -1;
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| 			return 0.0f;
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| 		}
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| 	}
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| 
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| 	//
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| 	float32 Evaluate(int32 indexA, int32 indexB, float32 t) const
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| 	{
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| 		b2Transform xfA, xfB;
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| 		m_sweepA.GetTransform(&xfA, t);
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| 		m_sweepB.GetTransform(&xfB, t);
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| 
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| 		switch (m_type)
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| 		{
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| 		case e_points:
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| 			{
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| 				b2Vec2 localPointA = m_proxyA->GetVertex(indexA);
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| 				b2Vec2 localPointB = m_proxyB->GetVertex(indexB);
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| 
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| 				b2Vec2 pointA = b2Mul(xfA, localPointA);
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| 				b2Vec2 pointB = b2Mul(xfB, localPointB);
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| 				float32 separation = b2Dot(pointB - pointA, m_axis);
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| 
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| 				return separation;
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| 			}
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| 
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| 		case e_faceA:
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| 			{
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| 				b2Vec2 normal = b2Mul(xfA.q, m_axis);
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| 				b2Vec2 pointA = b2Mul(xfA, m_localPoint);
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| 
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| 				b2Vec2 localPointB = m_proxyB->GetVertex(indexB);
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| 				b2Vec2 pointB = b2Mul(xfB, localPointB);
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| 
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| 				float32 separation = b2Dot(pointB - pointA, normal);
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| 				return separation;
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| 			}
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| 
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| 		case e_faceB:
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| 			{
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| 				b2Vec2 normal = b2Mul(xfB.q, m_axis);
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| 				b2Vec2 pointB = b2Mul(xfB, m_localPoint);
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| 
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| 				b2Vec2 localPointA = m_proxyA->GetVertex(indexA);
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| 				b2Vec2 pointA = b2Mul(xfA, localPointA);
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| 
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| 				float32 separation = b2Dot(pointA - pointB, normal);
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| 				return separation;
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| 			}
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| 
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| 		default:
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| 			b2Assert(false);
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| 			return 0.0f;
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| 		}
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| 	}
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| 
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| 	const b2DistanceProxy* m_proxyA;
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| 	const b2DistanceProxy* m_proxyB;
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| 	b2Sweep m_sweepA, m_sweepB;
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| 	Type m_type;
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| 	b2Vec2 m_localPoint;
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| 	b2Vec2 m_axis;
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| };
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| 
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| // CCD via the local separating axis method. This seeks progression
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| // by computing the largest time at which separation is maintained.
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| void b2TimeOfImpact(b2TOIOutput* output, const b2TOIInput* input)
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| {
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| 	b2Timer timer;
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| 
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| 	++b2_toiCalls;
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| 
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| 	output->state = b2TOIOutput::e_unknown;
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| 	output->t = input->tMax;
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| 
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| 	const b2DistanceProxy* proxyA = &input->proxyA;
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| 	const b2DistanceProxy* proxyB = &input->proxyB;
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| 
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| 	b2Sweep sweepA = input->sweepA;
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| 	b2Sweep sweepB = input->sweepB;
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| 
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| 	// Large rotations can make the root finder fail, so we normalize the
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| 	// sweep angles.
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| 	sweepA.Normalize();
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| 	sweepB.Normalize();
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| 
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| 	float32 tMax = input->tMax;
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| 
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| 	float32 totalRadius = proxyA->m_radius + proxyB->m_radius;
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| 	float32 target = b2Max(b2_linearSlop, totalRadius - 3.0f * b2_linearSlop);
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| 	float32 tolerance = 0.25f * b2_linearSlop;
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| 	b2Assert(target > tolerance);
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| 
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| 	float32 t1 = 0.0f;
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| 	const int32 k_maxIterations = 20;	// TODO_ERIN b2Settings
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| 	int32 iter = 0;
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| 
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| 	// Prepare input for distance query.
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| 	b2SimplexCache cache;
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| 	cache.count = 0;
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| 	b2DistanceInput distanceInput;
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| 	distanceInput.proxyA = input->proxyA;
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| 	distanceInput.proxyB = input->proxyB;
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| 	distanceInput.useRadii = false;
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| 
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| 	// The outer loop progressively attempts to compute new separating axes.
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| 	// This loop terminates when an axis is repeated (no progress is made).
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| 	for(;;)
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| 	{
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| 		b2Transform xfA, xfB;
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| 		sweepA.GetTransform(&xfA, t1);
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| 		sweepB.GetTransform(&xfB, t1);
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| 
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| 		// Get the distance between shapes. We can also use the results
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| 		// to get a separating axis.
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| 		distanceInput.transformA = xfA;
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| 		distanceInput.transformB = xfB;
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| 		b2DistanceOutput distanceOutput;
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| 		b2Distance(&distanceOutput, &cache, &distanceInput);
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| 
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| 		// If the shapes are overlapped, we give up on continuous collision.
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| 		if (distanceOutput.distance <= 0.0f)
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| 		{
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| 			// Failure!
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| 			output->state = b2TOIOutput::e_overlapped;
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| 			output->t = 0.0f;
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| 			break;
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| 		}
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| 
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| 		if (distanceOutput.distance < target + tolerance)
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| 		{
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| 			// Victory!
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| 			output->state = b2TOIOutput::e_touching;
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| 			output->t = t1;
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| 			break;
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| 		}
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| 
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| 		// Initialize the separating axis.
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| 		b2SeparationFunction fcn;
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| 		fcn.Initialize(&cache, proxyA, sweepA, proxyB, sweepB, t1);
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| #if 0
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| 		// Dump the curve seen by the root finder
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| 		{
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| 			const int32 N = 100;
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| 			float32 dx = 1.0f / N;
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| 			float32 xs[N+1];
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| 			float32 fs[N+1];
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| 
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| 			float32 x = 0.0f;
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| 
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| 			for (int32 i = 0; i <= N; ++i)
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| 			{
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| 				sweepA.GetTransform(&xfA, x);
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| 				sweepB.GetTransform(&xfB, x);
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| 				float32 f = fcn.Evaluate(xfA, xfB) - target;
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| 
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| 				printf("%g %g\n", x, f);
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| 
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| 				xs[i] = x;
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| 				fs[i] = f;
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| 
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| 				x += dx;
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| 			}
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| 		}
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| #endif
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| 
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| 		// Compute the TOI on the separating axis. We do this by successively
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| 		// resolving the deepest point. This loop is bounded by the number of vertices.
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| 		bool done = false;
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| 		float32 t2 = tMax;
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| 		int32 pushBackIter = 0;
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| 		for (;;)
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| 		{
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| 			// Find the deepest point at t2. Store the witness point indices.
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| 			int32 indexA, indexB;
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| 			float32 s2 = fcn.FindMinSeparation(&indexA, &indexB, t2);
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| 
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| 			// Is the final configuration separated?
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| 			if (s2 > target + tolerance)
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| 			{
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| 				// Victory!
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| 				output->state = b2TOIOutput::e_separated;
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| 				output->t = tMax;
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| 				done = true;
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| 				break;
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| 			}
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| 
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| 			// Has the separation reached tolerance?
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| 			if (s2 > target - tolerance)
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| 			{
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| 				// Advance the sweeps
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| 				t1 = t2;
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| 				break;
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| 			}
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| 
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| 			// Compute the initial separation of the witness points.
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| 			float32 s1 = fcn.Evaluate(indexA, indexB, t1);
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| 
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| 			// Check for initial overlap. This might happen if the root finder
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| 			// runs out of iterations.
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| 			if (s1 < target - tolerance)
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| 			{
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| 				output->state = b2TOIOutput::e_failed;
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| 				output->t = t1;
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| 				done = true;
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| 				break;
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| 			}
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| 
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| 			// Check for touching
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| 			if (s1 <= target + tolerance)
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| 			{
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| 				// Victory! t1 should hold the TOI (could be 0.0).
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| 				output->state = b2TOIOutput::e_touching;
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| 				output->t = t1;
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| 				done = true;
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| 				break;
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| 			}
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| 
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| 			// Compute 1D root of: f(x) - target = 0
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| 			int32 rootIterCount = 0;
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| 			float32 a1 = t1, a2 = t2;
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| 			for (;;)
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| 			{
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| 				// Use a mix of the secant rule and bisection.
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| 				float32 t;
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| 				if (rootIterCount & 1)
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| 				{
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| 					// Secant rule to improve convergence.
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| 					t = a1 + (target - s1) * (a2 - a1) / (s2 - s1);
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| 				}
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| 				else
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| 				{
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| 					// Bisection to guarantee progress.
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| 					t = 0.5f * (a1 + a2);
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| 				}
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| 
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| 				++rootIterCount;
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| 				++b2_toiRootIters;
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| 
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| 				float32 s = fcn.Evaluate(indexA, indexB, t);
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| 
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| 				if (b2Abs(s - target) < tolerance)
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| 				{
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| 					// t2 holds a tentative value for t1
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| 					t2 = t;
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| 					break;
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| 				}
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| 
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| 				// Ensure we continue to bracket the root.
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| 				if (s > target)
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| 				{
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| 					a1 = t;
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| 					s1 = s;
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| 				}
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| 				else
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| 				{
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| 					a2 = t;
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| 					s2 = s;
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| 				}
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| 				
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| 				if (rootIterCount == 50)
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| 				{
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| 					break;
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| 				}
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| 			}
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| 
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| 			b2_toiMaxRootIters = b2Max(b2_toiMaxRootIters, rootIterCount);
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| 
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| 			++pushBackIter;
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| 
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| 			if (pushBackIter == b2_maxPolygonVertices)
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| 			{
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| 				break;
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| 			}
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| 		}
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| 
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| 		++iter;
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| 		++b2_toiIters;
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| 
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| 		if (done)
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| 		{
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| 			break;
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| 		}
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| 
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| 		if (iter == k_maxIterations)
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| 		{
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| 			// Root finder got stuck. Semi-victory.
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| 			output->state = b2TOIOutput::e_failed;
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| 			output->t = t1;
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| 			break;
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| 		}
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| 	}
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| 
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| 	b2_toiMaxIters = b2Max(b2_toiMaxIters, iter);
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| 
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| 	float32 time = timer.GetMilliseconds();
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| 	b2_toiMaxTime = b2Max(b2_toiMaxTime, time);
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| 	b2_toiTime += time;
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| }
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