b2CollideEdge.cpp

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/*
 * 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/Shapes/b2CircleShape.h>
#include <Box2D/Collision/Shapes/b2EdgeShape.h>
#include <Box2D/Collision/Shapes/b2PolygonShape.h>


// Compute contact points for edge versus circle.
// This accounts for edge connectivity.
void b2CollideEdgeAndCircle(b2Manifold* manifold,
                                                        const b2EdgeShape* edgeA, const b2Transform& xfA,
                                                        const b2CircleShape* circleB, const b2Transform& xfB)
{
        manifold->pointCount = 0;
        
        // Compute circle in frame of edge
        b2Vec2 Q = b2MulT(xfA, b2Mul(xfB, circleB->m_p));
        
        b2Vec2 A = edgeA->m_vertex1, B = edgeA->m_vertex2;
        b2Vec2 e = B - A;
        
        // Barycentric coordinates
        float32 u = b2Dot(e, B - Q);
        float32 v = b2Dot(e, Q - A);
        
        float32 radius = edgeA->m_radius + circleB->m_radius;
        
        b2ContactFeature cf;
        cf.indexB = 0;
        cf.typeB = b2ContactFeature::e_vertex;
        
        // Region A
        if (v <= 0.0f)
        {
                b2Vec2 P = A;
                b2Vec2 d = Q - P;
                float32 dd = b2Dot(d, d);
                if (dd > radius * radius)
                {
                        return;
                }
                
                // Is there an edge connected to A?
                if (edgeA->m_hasVertex0)
                {
                        b2Vec2 A1 = edgeA->m_vertex0;
                        b2Vec2 B1 = A;
                        b2Vec2 e1 = B1 - A1;
                        float32 u1 = b2Dot(e1, B1 - Q);
                        
                        // Is the circle in Region AB of the previous edge?
                        if (u1 > 0.0f)
                        {
                                return;
                        }
                }
                
                cf.indexA = 0;
                cf.typeA = b2ContactFeature::e_vertex;
                manifold->pointCount = 1;
                manifold->type = b2Manifold::e_circles;
                manifold->localNormal.SetZero();
                manifold->localPoint = P;
                manifold->points[0].id.key = 0;
                manifold->points[0].id.cf = cf;
                manifold->points[0].localPoint = circleB->m_p;
                return;
        }
        
        // Region B
        if (u <= 0.0f)
        {
                b2Vec2 P = B;
                b2Vec2 d = Q - P;
                float32 dd = b2Dot(d, d);
                if (dd > radius * radius)
                {
                        return;
                }
                
                // Is there an edge connected to B?
                if (edgeA->m_hasVertex3)
                {
                        b2Vec2 B2 = edgeA->m_vertex3;
                        b2Vec2 A2 = B;
                        b2Vec2 e2 = B2 - A2;
                        float32 v2 = b2Dot(e2, Q - A2);
                        
                        // Is the circle in Region AB of the next edge?
                        if (v2 > 0.0f)
                        {
                                return;
                        }
                }
                
                cf.indexA = 1;
                cf.typeA = b2ContactFeature::e_vertex;
                manifold->pointCount = 1;
                manifold->type = b2Manifold::e_circles;
                manifold->localNormal.SetZero();
                manifold->localPoint = P;
                manifold->points[0].id.key = 0;
                manifold->points[0].id.cf = cf;
                manifold->points[0].localPoint = circleB->m_p;
                return;
        }
        
        // Region AB
        float32 den = b2Dot(e, e);
        b2Assert(den > 0.0f);
        b2Vec2 P = (1.0f / den) * (u * A + v * B);
        b2Vec2 d = Q - P;
        float32 dd = b2Dot(d, d);
        if (dd > radius * radius)
        {
                return;
        }
        
        b2Vec2 n(-e.y, e.x);
        if (b2Dot(n, Q - A) < 0.0f)
        {
                n.Set(-n.x, -n.y);
        }
        n.Normalize();
        
        cf.indexA = 0;
        cf.typeA = b2ContactFeature::e_face;
        manifold->pointCount = 1;
        manifold->type = b2Manifold::e_faceA;
        manifold->localNormal = n;
        manifold->localPoint = A;
        manifold->points[0].id.key = 0;
        manifold->points[0].id.cf = cf;
        manifold->points[0].localPoint = circleB->m_p;
}

// This structure is used to keep track of the best separating axis.
struct b2EPAxis
{
        enum Type
        {
                e_unknown,
                e_edgeA,
                e_edgeB
        };
        
        Type type;
        int32 index;
        float32 separation;
};

// This holds polygon B expressed in frame A.
struct b2TempPolygon
{
        b2Vec2 vertices[b2_maxPolygonVertices];
        b2Vec2 normals[b2_maxPolygonVertices];
        int32 count;
};

// Reference face used for clipping
struct b2ReferenceFace
{
        int32 i1, i2;
        
        b2Vec2 v1, v2;
        
        b2Vec2 normal;
        
        b2Vec2 sideNormal1;
        float32 sideOffset1;
        
        b2Vec2 sideNormal2;
        float32 sideOffset2;
};

// This class collides and edge and a polygon, taking into account edge adjacency.
struct b2EPCollider
{
        void Collide(b2Manifold* manifold, const b2EdgeShape* edgeA, const b2Transform& xfA,
                                 const b2PolygonShape* polygonB, const b2Transform& xfB);
        b2EPAxis ComputeEdgeSeparation();
        b2EPAxis ComputePolygonSeparation();
        
        enum VertexType
        {
                e_isolated,
                e_concave,
                e_convex
        };
        
        b2TempPolygon m_polygonB;
        
        b2Transform m_xf;
        b2Vec2 m_centroidB;
        b2Vec2 m_v0, m_v1, m_v2, m_v3;
        b2Vec2 m_normal0, m_normal1, m_normal2;
        b2Vec2 m_normal;
        VertexType m_type1, m_type2;
        b2Vec2 m_lowerLimit, m_upperLimit;
        float32 m_radius;
        bool m_front;
};

// Algorithm:
// 1. Classify v1 and v2
// 2. Classify polygon centroid as front or back
// 3. Flip normal if necessary
// 4. Initialize normal range to [-pi, pi] about face normal
// 5. Adjust normal range according to adjacent edges
// 6. Visit each separating axes, only accept axes within the range
// 7. Return if _any_ axis indicates separation
// 8. Clip
void b2EPCollider::Collide(b2Manifold* manifold, const b2EdgeShape* edgeA, const b2Transform& xfA,
                                                   const b2PolygonShape* polygonB, const b2Transform& xfB)
{
        m_xf = b2MulT(xfA, xfB);
        
        m_centroidB = b2Mul(m_xf, polygonB->m_centroid);
        
        m_v0 = edgeA->m_vertex0;
        m_v1 = edgeA->m_vertex1;
        m_v2 = edgeA->m_vertex2;
        m_v3 = edgeA->m_vertex3;
        
        bool hasVertex0 = edgeA->m_hasVertex0;
        bool hasVertex3 = edgeA->m_hasVertex3;
        
        b2Vec2 edge1 = m_v2 - m_v1;
        edge1.Normalize();
        m_normal1.Set(edge1.y, -edge1.x);
        float32 offset1 = b2Dot(m_normal1, m_centroidB - m_v1);
        float32 offset0 = 0.0f, offset2 = 0.0f;
        bool convex1 = false, convex2 = false;
        
        // Is there a preceding edge?
        if (hasVertex0)
        {
                b2Vec2 edge0 = m_v1 - m_v0;
                edge0.Normalize();
                m_normal0.Set(edge0.y, -edge0.x);
                convex1 = b2Cross(edge0, edge1) >= 0.0f;
                offset0 = b2Dot(m_normal0, m_centroidB - m_v0);
        }
        
        // Is there a following edge?
        if (hasVertex3)
        {
                b2Vec2 edge2 = m_v3 - m_v2;
                edge2.Normalize();
                m_normal2.Set(edge2.y, -edge2.x);
                convex2 = b2Cross(edge1, edge2) > 0.0f;
                offset2 = b2Dot(m_normal2, m_centroidB - m_v2);
        }
        
        // Determine front or back collision. Determine collision normal limits.
        if (hasVertex0 && hasVertex3)
        {
                if (convex1 && convex2)
                {
                        m_front = offset0 >= 0.0f || offset1 >= 0.0f || offset2 >= 0.0f;
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = m_normal0;
                                m_upperLimit = m_normal2;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = -m_normal1;
                                m_upperLimit = -m_normal1;
                        }
                }
                else if (convex1)
                {
                        m_front = offset0 >= 0.0f || (offset1 >= 0.0f && offset2 >= 0.0f);
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = m_normal0;
                                m_upperLimit = m_normal1;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = -m_normal2;
                                m_upperLimit = -m_normal1;
                        }
                }
                else if (convex2)
                {
                        m_front = offset2 >= 0.0f || (offset0 >= 0.0f && offset1 >= 0.0f);
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = m_normal1;
                                m_upperLimit = m_normal2;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = -m_normal1;
                                m_upperLimit = -m_normal0;
                        }
                }
                else
                {
                        m_front = offset0 >= 0.0f && offset1 >= 0.0f && offset2 >= 0.0f;
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = m_normal1;
                                m_upperLimit = m_normal1;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = -m_normal2;
                                m_upperLimit = -m_normal0;
                        }
                }
        }
        else if (hasVertex0)
        {
                if (convex1)
                {
                        m_front = offset0 >= 0.0f || offset1 >= 0.0f;
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = m_normal0;
                                m_upperLimit = -m_normal1;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = m_normal1;
                                m_upperLimit = -m_normal1;
                        }
                }
                else
                {
                        m_front = offset0 >= 0.0f && offset1 >= 0.0f;
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = m_normal1;
                                m_upperLimit = -m_normal1;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = m_normal1;
                                m_upperLimit = -m_normal0;
                        }
                }
        }
        else if (hasVertex3)
        {
                if (convex2)
                {
                        m_front = offset1 >= 0.0f || offset2 >= 0.0f;
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = -m_normal1;
                                m_upperLimit = m_normal2;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = -m_normal1;
                                m_upperLimit = m_normal1;
                        }
                }
                else
                {
                        m_front = offset1 >= 0.0f && offset2 >= 0.0f;
                        if (m_front)
                        {
                                m_normal = m_normal1;
                                m_lowerLimit = -m_normal1;
                                m_upperLimit = m_normal1;
                        }
                        else
                        {
                                m_normal = -m_normal1;
                                m_lowerLimit = -m_normal2;
                                m_upperLimit = m_normal1;
                        }
                }               
        }
        else
        {
                m_front = offset1 >= 0.0f;
                if (m_front)
                {
                        m_normal = m_normal1;
                        m_lowerLimit = -m_normal1;
                        m_upperLimit = -m_normal1;
                }
                else
                {
                        m_normal = -m_normal1;
                        m_lowerLimit = m_normal1;
                        m_upperLimit = m_normal1;
                }
        }
        
        // Get polygonB in frameA
        m_polygonB.count = polygonB->m_count;
        for (int32 i = 0; i < polygonB->m_count; ++i)
        {
                m_polygonB.vertices[i] = b2Mul(m_xf, polygonB->m_vertices[i]);
                m_polygonB.normals[i] = b2Mul(m_xf.q, polygonB->m_normals[i]);
        }
        
        m_radius = 2.0f * b2_polygonRadius;
        
        manifold->pointCount = 0;
        
        b2EPAxis edgeAxis = ComputeEdgeSeparation();
        
        // If no valid normal can be found than this edge should not collide.
        if (edgeAxis.type == b2EPAxis::e_unknown)
        {
                return;
        }
        
        if (edgeAxis.separation > m_radius)
        {
                return;
        }
        
        b2EPAxis polygonAxis = ComputePolygonSeparation();
        if (polygonAxis.type != b2EPAxis::e_unknown && polygonAxis.separation > m_radius)
        {
                return;
        }
        
        // Use hysteresis for jitter reduction.
        const float32 k_relativeTol = 0.98f;
        const float32 k_absoluteTol = 0.001f;
        
        b2EPAxis primaryAxis;
        if (polygonAxis.type == b2EPAxis::e_unknown)
        {
                primaryAxis = edgeAxis;
        }
        else if (polygonAxis.separation > k_relativeTol * edgeAxis.separation + k_absoluteTol)
        {
                primaryAxis = polygonAxis;
        }
        else
        {
                primaryAxis = edgeAxis;
        }
        
        b2ClipVertex ie[2];
        b2ReferenceFace rf;
        if (primaryAxis.type == b2EPAxis::e_edgeA)
        {
                manifold->type = b2Manifold::e_faceA;
                
                // Search for the polygon normal that is most anti-parallel to the edge normal.
                int32 bestIndex = 0;
                float32 bestValue = b2Dot(m_normal, m_polygonB.normals[0]);
                for (int32 i = 1; i < m_polygonB.count; ++i)
                {
                        float32 value = b2Dot(m_normal, m_polygonB.normals[i]);
                        if (value < bestValue)
                        {
                                bestValue = value;
                                bestIndex = i;
                        }
                }
                
                int32 i1 = bestIndex;
                int32 i2 = i1 + 1 < m_polygonB.count ? i1 + 1 : 0;
                
                ie[0].v = m_polygonB.vertices[i1];
                ie[0].id.cf.indexA = 0;
                ie[0].id.cf.indexB = static_cast<uint8>(i1);
                ie[0].id.cf.typeA = b2ContactFeature::e_face;
                ie[0].id.cf.typeB = b2ContactFeature::e_vertex;
                
                ie[1].v = m_polygonB.vertices[i2];
                ie[1].id.cf.indexA = 0;
                ie[1].id.cf.indexB = static_cast<uint8>(i2);
                ie[1].id.cf.typeA = b2ContactFeature::e_face;
                ie[1].id.cf.typeB = b2ContactFeature::e_vertex;
                
                if (m_front)
                {
                        rf.i1 = 0;
                        rf.i2 = 1;
                        rf.v1 = m_v1;
                        rf.v2 = m_v2;
                        rf.normal = m_normal1;
                }
                else
                {
                        rf.i1 = 1;
                        rf.i2 = 0;
                        rf.v1 = m_v2;
                        rf.v2 = m_v1;
                        rf.normal = -m_normal1;
                }               
        }
        else
        {
                manifold->type = b2Manifold::e_faceB;
                
                ie[0].v = m_v1;
                ie[0].id.cf.indexA = 0;
                ie[0].id.cf.indexB = static_cast<uint8>(primaryAxis.index);
                ie[0].id.cf.typeA = b2ContactFeature::e_vertex;
                ie[0].id.cf.typeB = b2ContactFeature::e_face;
                
                ie[1].v = m_v2;
                ie[1].id.cf.indexA = 0;
                ie[1].id.cf.indexB = static_cast<uint8>(primaryAxis.index);             
                ie[1].id.cf.typeA = b2ContactFeature::e_vertex;
                ie[1].id.cf.typeB = b2ContactFeature::e_face;
                
                rf.i1 = primaryAxis.index;
                rf.i2 = rf.i1 + 1 < m_polygonB.count ? rf.i1 + 1 : 0;
                rf.v1 = m_polygonB.vertices[rf.i1];
                rf.v2 = m_polygonB.vertices[rf.i2];
                rf.normal = m_polygonB.normals[rf.i1];
        }
        
        rf.sideNormal1.Set(rf.normal.y, -rf.normal.x);
        rf.sideNormal2 = -rf.sideNormal1;
        rf.sideOffset1 = b2Dot(rf.sideNormal1, rf.v1);
        rf.sideOffset2 = b2Dot(rf.sideNormal2, rf.v2);
        
        // Clip incident edge against extruded edge1 side edges.
        b2ClipVertex clipPoints1[2];
        b2ClipVertex clipPoints2[2];
        int32 np;
        
        // Clip to box side 1
        np = b2ClipSegmentToLine(clipPoints1, ie, rf.sideNormal1, rf.sideOffset1, rf.i1);
        
        if (np < b2_maxManifoldPoints)
        {
                return;
        }
        
        // Clip to negative box side 1
        np = b2ClipSegmentToLine(clipPoints2, clipPoints1, rf.sideNormal2, rf.sideOffset2, rf.i2);
        
        if (np < b2_maxManifoldPoints)
        {
                return;
        }
        
        // Now clipPoints2 contains the clipped points.
        if (primaryAxis.type == b2EPAxis::e_edgeA)
        {
                manifold->localNormal = rf.normal;
                manifold->localPoint = rf.v1;
        }
        else
        {
                manifold->localNormal = polygonB->m_normals[rf.i1];
                manifold->localPoint = polygonB->m_vertices[rf.i1];
        }
        
        int32 pointCount = 0;
        for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
        {
                float32 separation;
                
                separation = b2Dot(rf.normal, clipPoints2[i].v - rf.v1);
                
                if (separation <= m_radius)
                {
                        b2ManifoldPoint* cp = manifold->points + pointCount;
                        
                        if (primaryAxis.type == b2EPAxis::e_edgeA)
                        {
                                cp->localPoint = b2MulT(m_xf, clipPoints2[i].v);
                                cp->id = clipPoints2[i].id;
                        }
                        else
                        {
                                cp->localPoint = clipPoints2[i].v;
                                cp->id.cf.typeA = clipPoints2[i].id.cf.typeB;
                                cp->id.cf.typeB = clipPoints2[i].id.cf.typeA;
                                cp->id.cf.indexA = clipPoints2[i].id.cf.indexB;
                                cp->id.cf.indexB = clipPoints2[i].id.cf.indexA;
                        }
                        
                        ++pointCount;
                }
        }
        
        manifold->pointCount = pointCount;
}

b2EPAxis b2EPCollider::ComputeEdgeSeparation()
{
        b2EPAxis axis;
        axis.type = b2EPAxis::e_edgeA;
        axis.index = m_front ? 0 : 1;
        axis.separation = FLT_MAX;
        
        for (int32 i = 0; i < m_polygonB.count; ++i)
        {
                float32 s = b2Dot(m_normal, m_polygonB.vertices[i] - m_v1);
                if (s < axis.separation)
                {
                        axis.separation = s;
                }
        }
        
        return axis;
}

b2EPAxis b2EPCollider::ComputePolygonSeparation()
{
        b2EPAxis axis;
        axis.type = b2EPAxis::e_unknown;
        axis.index = -1;
        axis.separation = -FLT_MAX;

        b2Vec2 perp(-m_normal.y, m_normal.x);

        for (int32 i = 0; i < m_polygonB.count; ++i)
        {
                b2Vec2 n = -m_polygonB.normals[i];
                
                float32 s1 = b2Dot(n, m_polygonB.vertices[i] - m_v1);
                float32 s2 = b2Dot(n, m_polygonB.vertices[i] - m_v2);
                float32 s = b2Min(s1, s2);
                
                if (s > m_radius)
                {
                        // No collision
                        axis.type = b2EPAxis::e_edgeB;
                        axis.index = i;
                        axis.separation = s;
                        return axis;
                }
                
                // Adjacency
                if (b2Dot(n, perp) >= 0.0f)
                {
                        if (b2Dot(n - m_upperLimit, m_normal) < -b2_angularSlop)
                        {
                                continue;
                        }
                }
                else
                {
                        if (b2Dot(n - m_lowerLimit, m_normal) < -b2_angularSlop)
                        {
                                continue;
                        }
                }
                
                if (s > axis.separation)
                {
                        axis.type = b2EPAxis::e_edgeB;
                        axis.index = i;
                        axis.separation = s;
                }
        }
        
        return axis;
}

void b2CollideEdgeAndPolygon(   b2Manifold* manifold,
                                                         const b2EdgeShape* edgeA, const b2Transform& xfA,
                                                         const b2PolygonShape* polygonB, const b2Transform& xfB)
{
        b2EPCollider collider;
        collider.Collide(manifold, edgeA, xfA, polygonB, xfB);
}