axmol/external/Box2D/Collision/b2CollidePolygon.cpp

/*
* Copyright (c) 2006-2009 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/b2PolygonShape.h>

// Find the separation between poly1 and poly2 for a give edge normal on poly1.
static float32 b2EdgeSeparation(const b2PolygonShape* poly1, const b2Transform& xf1, int32 edge1,
                              const b2PolygonShape* poly2, const b2Transform& xf2)
{
    const b2Vec2* vertices1 = poly1->m_vertices;
    const b2Vec2* normals1 = poly1->m_normals;

    int32 count2 = poly2->m_vertexCount;
    const b2Vec2* vertices2 = poly2->m_vertices;

    b2Assert(0 <= edge1 && edge1 < poly1->m_vertexCount);

    // Convert normal from poly1's frame into poly2's frame.
    b2Vec2 normal1World = b2Mul(xf1.q, normals1[edge1]);
    b2Vec2 normal1 = b2MulT(xf2.q, normal1World);

    // Find support vertex on poly2 for -normal.
    int32 index = 0;
    float32 minDot = b2_maxFloat;

    for (int32 i = 0; i < count2; ++i)
    {
        float32 dot = b2Dot(vertices2[i], normal1);
        if (dot < minDot)
        {
            minDot = dot;
            index = i;
        }
    }

    b2Vec2 v1 = b2Mul(xf1, vertices1[edge1]);
    b2Vec2 v2 = b2Mul(xf2, vertices2[index]);
    float32 separation = b2Dot(v2 - v1, normal1World);
    return separation;
}

// Find the max separation between poly1 and poly2 using edge normals from poly1.
static float32 b2FindMaxSeparation(int32* edgeIndex,
                                 const b2PolygonShape* poly1, const b2Transform& xf1,
                                 const b2PolygonShape* poly2, const b2Transform& xf2)
{
    int32 count1 = poly1->m_vertexCount;
    const b2Vec2* normals1 = poly1->m_normals;

    // Vector pointing from the centroid of poly1 to the centroid of poly2.
    b2Vec2 d = b2Mul(xf2, poly2->m_centroid) - b2Mul(xf1, poly1->m_centroid);
    b2Vec2 dLocal1 = b2MulT(xf1.q, d);

    // Find edge normal on poly1 that has the largest projection onto d.
    int32 edge = 0;
    float32 maxDot = -b2_maxFloat;
    for (int32 i = 0; i < count1; ++i)
    {
        float32 dot = b2Dot(normals1[i], dLocal1);
        if (dot > maxDot)
        {
            maxDot = dot;
            edge = i;
        }
    }

    // Get the separation for the edge normal.
    float32 s = b2EdgeSeparation(poly1, xf1, edge, poly2, xf2);

    // Check the separation for the previous edge normal.
    int32 prevEdge = edge - 1 >= 0 ? edge - 1 : count1 - 1;
    float32 sPrev = b2EdgeSeparation(poly1, xf1, prevEdge, poly2, xf2);

    // Check the separation for the next edge normal.
    int32 nextEdge = edge + 1 < count1 ? edge + 1 : 0;
    float32 sNext = b2EdgeSeparation(poly1, xf1, nextEdge, poly2, xf2);

    // Find the best edge and the search direction.
    int32 bestEdge;
    float32 bestSeparation;
    int32 increment;
    if (sPrev > s && sPrev > sNext)
    {
        increment = -1;
        bestEdge = prevEdge;
        bestSeparation = sPrev;
    }
    else if (sNext > s)
    {
        increment = 1;
        bestEdge = nextEdge;
        bestSeparation = sNext;
    }
    else
    {
        *edgeIndex = edge;
        return s;
    }

    // Perform a local search for the best edge normal.
    for ( ; ; )
    {
        if (increment == -1)
            edge = bestEdge - 1 >= 0 ? bestEdge - 1 : count1 - 1;
        else
            edge = bestEdge + 1 < count1 ? bestEdge + 1 : 0;

        s = b2EdgeSeparation(poly1, xf1, edge, poly2, xf2);

        if (s > bestSeparation)
        {
            bestEdge = edge;
            bestSeparation = s;
        }
        else
        {
            break;
        }
    }

    *edgeIndex = bestEdge;
    return bestSeparation;
}

static void b2FindIncidentEdge(b2ClipVertex c[2],
                             const b2PolygonShape* poly1, const b2Transform& xf1, int32 edge1,
                             const b2PolygonShape* poly2, const b2Transform& xf2)
{
    const b2Vec2* normals1 = poly1->m_normals;

    int32 count2 = poly2->m_vertexCount;
    const b2Vec2* vertices2 = poly2->m_vertices;
    const b2Vec2* normals2 = poly2->m_normals;

    b2Assert(0 <= edge1 && edge1 < poly1->m_vertexCount);

    // Get the normal of the reference edge in poly2's frame.
    b2Vec2 normal1 = b2MulT(xf2.q, b2Mul(xf1.q, normals1[edge1]));

    // Find the incident edge on poly2.
    int32 index = 0;
    float32 minDot = b2_maxFloat;
    for (int32 i = 0; i < count2; ++i)
    {
        float32 dot = b2Dot(normal1, normals2[i]);
        if (dot < minDot)
        {
            minDot = dot;
            index = i;
        }
    }

    // Build the clip vertices for the incident edge.
    int32 i1 = index;
    int32 i2 = i1 + 1 < count2 ? i1 + 1 : 0;

    c[0].v = b2Mul(xf2, vertices2[i1]);
    c[0].id.cf.indexA = (uint8)edge1;
    c[0].id.cf.indexB = (uint8)i1;
    c[0].id.cf.typeA = b2ContactFeature::e_face;
    c[0].id.cf.typeB = b2ContactFeature::e_vertex;

    c[1].v = b2Mul(xf2, vertices2[i2]);
    c[1].id.cf.indexA = (uint8)edge1;
    c[1].id.cf.indexB = (uint8)i2;
    c[1].id.cf.typeA = b2ContactFeature::e_face;
    c[1].id.cf.typeB = b2ContactFeature::e_vertex;
}

// Find edge normal of max separation on A - return if separating axis is found
// Find edge normal of max separation on B - return if separation axis is found
// Choose reference edge as min(minA, minB)
// Find incident edge
// Clip

// The normal points from 1 to 2
void b2CollidePolygons(b2Manifold* manifold,
                      const b2PolygonShape* polyA, const b2Transform& xfA,
                      const b2PolygonShape* polyB, const b2Transform& xfB)
{
    manifold->pointCount = 0;
    float32 totalRadius = polyA->m_radius + polyB->m_radius;

    int32 edgeA = 0;
    float32 separationA = b2FindMaxSeparation(&edgeA, polyA, xfA, polyB, xfB);
    if (separationA > totalRadius)
        return;

    int32 edgeB = 0;
    float32 separationB = b2FindMaxSeparation(&edgeB, polyB, xfB, polyA, xfA);
    if (separationB > totalRadius)
        return;

    const b2PolygonShape* poly1;    // reference polygon
    const b2PolygonShape* poly2;    // incident polygon
    b2Transform xf1, xf2;
    int32 edge1;        // reference edge
    uint8 flip;
    const float32 k_relativeTol = 0.98f;
    const float32 k_absoluteTol = 0.001f;

    if (separationB > k_relativeTol * separationA + k_absoluteTol)
    {
        poly1 = polyB;
        poly2 = polyA;
        xf1 = xfB;
        xf2 = xfA;
        edge1 = edgeB;
        manifold->type = b2Manifold::e_faceB;
        flip = 1;
    }
    else
    {
        poly1 = polyA;
        poly2 = polyB;
        xf1 = xfA;
        xf2 = xfB;
        edge1 = edgeA;
        manifold->type = b2Manifold::e_faceA;
        flip = 0;
    }

    b2ClipVertex incidentEdge[2];
    b2FindIncidentEdge(incidentEdge, poly1, xf1, edge1, poly2, xf2);

    int32 count1 = poly1->m_vertexCount;
    const b2Vec2* vertices1 = poly1->m_vertices;

    int32 iv1 = edge1;
    int32 iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0;

    b2Vec2 v11 = vertices1[iv1];
    b2Vec2 v12 = vertices1[iv2];

    b2Vec2 localTangent = v12 - v11;
    localTangent.Normalize();
    
    b2Vec2 localNormal = b2Cross(localTangent, 1.0f);
    b2Vec2 planePoint = 0.5f * (v11 + v12);

    b2Vec2 tangent = b2Mul(xf1.q, localTangent);
    b2Vec2 normal = b2Cross(tangent, 1.0f);
    
    v11 = b2Mul(xf1, v11);
    v12 = b2Mul(xf1, v12);

    // Face offset.
    float32 frontOffset = b2Dot(normal, v11);

    // Side offsets, extended by polytope skin thickness.
    float32 sideOffset1 = -b2Dot(tangent, v11) + totalRadius;
    float32 sideOffset2 = b2Dot(tangent, v12) + totalRadius;

    // Clip incident edge against extruded edge1 side edges.
    b2ClipVertex clipPoints1[2];
    b2ClipVertex clipPoints2[2];
    int np;

    // Clip to box side 1
    np = b2ClipSegmentToLine(clipPoints1, incidentEdge, -tangent, sideOffset1, iv1);

    if (np < 2)
        return;

    // Clip to negative box side 1
    np = b2ClipSegmentToLine(clipPoints2, clipPoints1,  tangent, sideOffset2, iv2);

    if (np < 2)
    {
        return;
    }

    // Now clipPoints2 contains the clipped points.
    manifold->localNormal = localNormal;
    manifold->localPoint = planePoint;

    int32 pointCount = 0;
    for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
    {
        float32 separation = b2Dot(normal, clipPoints2[i].v) - frontOffset;

        if (separation <= totalRadius)
        {
            b2ManifoldPoint* cp = manifold->points + pointCount;
            cp->localPoint = b2MulT(xf2, clipPoints2[i].v);
            cp->id = clipPoints2[i].id;
            if (flip)
            {
                // Swap features
                b2ContactFeature cf = cp->id.cf;
                cp->id.cf.indexA = cf.indexB;
                cp->id.cf.indexB = cf.indexA;
                cp->id.cf.typeA = cf.typeB;
                cp->id.cf.typeB = cf.typeA;
            }
            ++pointCount;
        }
    }

    manifold->pointCount = pointCount;
}