487 lines
11 KiB
C++
487 lines
11 KiB
C++
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/*
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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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#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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#include <stdio.h>
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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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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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// TODO_ERIN might not need to return the separation
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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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m_sweepA = sweepA;
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m_sweepB = sweepB;
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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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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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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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m_localPoint = 0.5f * (localPointB1 + localPointB2);
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b2Vec2 pointB = b2Mul(xfB, m_localPoint);
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b2Vec2 localPointA = proxyA->GetVertex(cache->indexA[0]);
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b2Vec2 pointA = b2Mul(xfA, localPointA);
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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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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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m_localPoint = 0.5f * (localPointA1 + localPointA2);
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b2Vec2 pointA = b2Mul(xfA, m_localPoint);
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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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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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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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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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*indexA = m_proxyA->GetSupport(axisA);
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*indexB = m_proxyB->GetSupport(axisB);
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b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
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b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
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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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return separation;
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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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b2Vec2 axisB = b2MulT(xfB.q, -normal);
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*indexA = -1;
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*indexB = m_proxyB->GetSupport(axisB);
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b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
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b2Vec2 pointB = b2Mul(xfB, localPointB);
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float32 separation = b2Dot(pointB - pointA, normal);
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return separation;
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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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b2Vec2 axisA = b2MulT(xfA.q, -normal);
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*indexB = -1;
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*indexA = m_proxyA->GetSupport(axisA);
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b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
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b2Vec2 pointA = b2Mul(xfA, localPointA);
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float32 separation = b2Dot(pointA - pointB, normal);
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return separation;
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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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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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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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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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return separation;
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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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b2Vec2 localPointB = m_proxyB->GetVertex(indexB);
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b2Vec2 pointB = b2Mul(xfB, localPointB);
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float32 separation = b2Dot(pointB - pointA, normal);
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return separation;
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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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b2Vec2 localPointA = m_proxyA->GetVertex(indexA);
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b2Vec2 pointA = b2Mul(xfA, localPointA);
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float32 separation = b2Dot(pointA - pointB, normal);
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return separation;
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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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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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// 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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++b2_toiCalls;
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output->state = b2TOIOutput::e_unknown;
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output->t = input->tMax;
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const b2DistanceProxy* proxyA = &input->proxyA;
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const b2DistanceProxy* proxyB = &input->proxyB;
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b2Sweep sweepA = input->sweepA;
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b2Sweep sweepB = input->sweepB;
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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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float32 tMax = input->tMax;
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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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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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// 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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// 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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// 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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// 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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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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// 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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float32 x = 0.0f;
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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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printf("%g %g\n", x, f);
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xs[i] = x;
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fs[i] = f;
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x += dx;
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}
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}
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#endif
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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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// 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;
|
||
|
|
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;
|
||
|
|
}
|