axmol/Box2D/Collision/Shapes/b2PolygonShape.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/Shapes/b2PolygonShape.h>
#include <new>

b2Shape* b2PolygonShape::Clone(b2BlockAllocator* allocator) const
{
    void* mem = allocator->Allocate(sizeof(b2PolygonShape));
    b2PolygonShape* clone = new (mem) b2PolygonShape;
    *clone = *this;
    return clone;
}

void b2PolygonShape::SetAsBox(float32 hx, float32 hy)
{
    m_vertexCount = 4;
    m_vertices[0].Set(-hx, -hy);
    m_vertices[1].Set( hx, -hy);
    m_vertices[2].Set( hx,  hy);
    m_vertices[3].Set(-hx,  hy);
    m_normals[0].Set(0.0f, -1.0f);
    m_normals[1].Set(1.0f, 0.0f);
    m_normals[2].Set(0.0f, 1.0f);
    m_normals[3].Set(-1.0f, 0.0f);
    m_centroid.SetZero();
}

void b2PolygonShape::SetAsBox(float32 hx, float32 hy, const b2Vec2& center, float32 angle)
{
    m_vertexCount = 4;
    m_vertices[0].Set(-hx, -hy);
    m_vertices[1].Set( hx, -hy);
    m_vertices[2].Set( hx,  hy);
    m_vertices[3].Set(-hx,  hy);
    m_normals[0].Set(0.0f, -1.0f);
    m_normals[1].Set(1.0f, 0.0f);
    m_normals[2].Set(0.0f, 1.0f);
    m_normals[3].Set(-1.0f, 0.0f);
    m_centroid = center;

    b2Transform xf;
    xf.p = center;
    xf.q.Set(angle);

    // Transform vertices and normals.
    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        m_vertices[i] = b2Mul(xf, m_vertices[i]);
        m_normals[i] = b2Mul(xf.q, m_normals[i]);
    }
}

int32 b2PolygonShape::GetChildCount() const
{
    return 1;
}

static b2Vec2 ComputeCentroid(const b2Vec2* vs, int32 count)
{
    b2Assert(count >= 3);

    b2Vec2 c; c.Set(0.0f, 0.0f);
    float32 area = 0.0f;

    // pRef is the reference point for forming triangles.
    // It's location doesn't change the result (except for rounding error).
    b2Vec2 pRef(0.0f, 0.0f);
#if 0
    // This code would put the reference point inside the polygon.
    for (int32 i = 0; i < count; ++i)
    {
        pRef += vs[i];
    }
    pRef *= 1.0f / count;
#endif

    const float32 inv3 = 1.0f / 3.0f;

    for (int32 i = 0; i < count; ++i)
    {
        // Triangle vertices.
        b2Vec2 p1 = pRef;
        b2Vec2 p2 = vs[i];
        b2Vec2 p3 = i + 1 < count ? vs[i+1] : vs[0];

        b2Vec2 e1 = p2 - p1;
        b2Vec2 e2 = p3 - p1;

        float32 D = b2Cross(e1, e2);

        float32 triangleArea = 0.5f * D;
        area += triangleArea;

        // Area weighted centroid
        c += triangleArea * inv3 * (p1 + p2 + p3);
    }

    // Centroid
    b2Assert(area > b2_epsilon);
    c *= 1.0f / area;
    return c;
}

void b2PolygonShape::Set(const b2Vec2* vertices, int32 count)
{
    b2Assert(3 <= count && count <= b2_maxPolygonVertices);
    m_vertexCount = count;

    // Copy vertices.
    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        m_vertices[i] = vertices[i];
    }

    // Compute normals. Ensure the edges have non-zero length.
    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        int32 i1 = i;
        int32 i2 = i + 1 < m_vertexCount ? i + 1 : 0;
        b2Vec2 edge = m_vertices[i2] - m_vertices[i1];
        b2Assert(edge.LengthSquared() > b2_epsilon * b2_epsilon);
        m_normals[i] = b2Cross(edge, 1.0f);
        m_normals[i].Normalize();
    }

#ifdef _DEBUG
    // Ensure the polygon is convex and the interior
    // is to the left of each edge.
    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        int32 i1 = i;
        int32 i2 = i + 1 < m_vertexCount ? i + 1 : 0;
        b2Vec2 edge = m_vertices[i2] - m_vertices[i1];

        for (int32 j = 0; j < m_vertexCount; ++j)
        {
            // Don't check vertices on the current edge.
            if (j == i1 || j == i2)
            {
                continue;
            }
            
            b2Vec2 r = m_vertices[j] - m_vertices[i1];

            // If this crashes, your polygon is non-convex, has colinear edges,
            // or the winding order is wrong.
            float32 s = b2Cross(edge, r);
            b2Assert(s > 0.0f && "ERROR: Please ensure your polygon is convex and has a CCW winding order");
        }
    }
#endif

    // Compute the polygon centroid.
    m_centroid = ComputeCentroid(m_vertices, m_vertexCount);
}

bool b2PolygonShape::TestPoint(const b2Transform& xf, const b2Vec2& p) const
{
    b2Vec2 pLocal = b2MulT(xf.q, p - xf.p);

    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        float32 dot = b2Dot(m_normals[i], pLocal - m_vertices[i]);
        if (dot > 0.0f)
        {
            return false;
        }
    }

    return true;
}

bool b2PolygonShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
                                const b2Transform& xf, int32 childIndex) const
{
    B2_NOT_USED(childIndex);

    // Put the ray into the polygon's frame of reference.
    b2Vec2 p1 = b2MulT(xf.q, input.p1 - xf.p);
    b2Vec2 p2 = b2MulT(xf.q, input.p2 - xf.p);
    b2Vec2 d = p2 - p1;

    float32 lower = 0.0f, upper = input.maxFraction;

    int32 index = -1;

    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        // p = p1 + a * d
        // dot(normal, p - v) = 0
        // dot(normal, p1 - v) + a * dot(normal, d) = 0
        float32 numerator = b2Dot(m_normals[i], m_vertices[i] - p1);
        float32 denominator = b2Dot(m_normals[i], d);

        if (denominator == 0.0f)
        {    
            if (numerator < 0.0f)
            {
                return false;
            }
        }
        else
        {
            // Note: we want this predicate without division:
            // lower < numerator / denominator, where denominator < 0
            // Since denominator < 0, we have to flip the inequality:
            // lower < numerator / denominator <==> denominator * lower > numerator.
            if (denominator < 0.0f && numerator < lower * denominator)
            {
                // Increase lower.
                // The segment enters this half-space.
                lower = numerator / denominator;
                index = i;
            }
            else if (denominator > 0.0f && numerator < upper * denominator)
            {
                // Decrease upper.
                // The segment exits this half-space.
                upper = numerator / denominator;
            }
        }

        // The use of epsilon here causes the assert on lower to trip
        // in some cases. Apparently the use of epsilon was to make edge
        // shapes work, but now those are handled separately.
        //if (upper < lower - b2_epsilon)
        if (upper < lower)
        {
            return false;
        }
    }

    b2Assert(0.0f <= lower && lower <= input.maxFraction);

    if (index >= 0)
    {
        output->fraction = lower;
        output->normal = b2Mul(xf.q, m_normals[index]);
        return true;
    }

    return false;
}

void b2PolygonShape::ComputeAABB(b2AABB* aabb, const b2Transform& xf, int32 childIndex) const
{
    B2_NOT_USED(childIndex);

    b2Vec2 lower = b2Mul(xf, m_vertices[0]);
    b2Vec2 upper = lower;

    for (int32 i = 1; i < m_vertexCount; ++i)
    {
        b2Vec2 v = b2Mul(xf, m_vertices[i]);
        lower = b2Min(lower, v);
        upper = b2Max(upper, v);
    }

    b2Vec2 r(m_radius, m_radius);
    aabb->lowerBound = lower - r;
    aabb->upperBound = upper + r;
}

void b2PolygonShape::ComputeMass(b2MassData* massData, float32 density) const
{
    // Polygon mass, centroid, and inertia.
    // Let rho be the polygon density in mass per unit area.
    // Then:
    // mass = rho * int(dA)
    // centroid.x = (1/mass) * rho * int(x * dA)
    // centroid.y = (1/mass) * rho * int(y * dA)
    // I = rho * int((x*x + y*y) * dA)
    //
    // We can compute these integrals by summing all the integrals
    // for each triangle of the polygon. To evaluate the integral
    // for a single triangle, we make a change of variables to
    // the (u,v) coordinates of the triangle:
    // x = x0 + e1x * u + e2x * v
    // y = y0 + e1y * u + e2y * v
    // where 0 <= u && 0 <= v && u + v <= 1.
    //
    // We integrate u from [0,1-v] and then v from [0,1].
    // We also need to use the Jacobian of the transformation:
    // D = cross(e1, e2)
    //
    // Simplification: triangle centroid = (1/3) * (p1 + p2 + p3)
    //
    // The rest of the derivation is handled by computer algebra.

    b2Assert(m_vertexCount >= 3);

    b2Vec2 center; center.Set(0.0f, 0.0f);
    float32 area = 0.0f;
    float32 I = 0.0f;

    // s is the reference point for forming triangles.
    // It's location doesn't change the result (except for rounding error).
    b2Vec2 s(0.0f, 0.0f);

    // This code would put the reference point inside the polygon.
    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        s += m_vertices[i];
    }
    s *= 1.0f / m_vertexCount;

    const float32 k_inv3 = 1.0f / 3.0f;

    for (int32 i = 0; i < m_vertexCount; ++i)
    {
        // Triangle vertices.
        b2Vec2 e1 = m_vertices[i] - s;
        b2Vec2 e2 = i + 1 < m_vertexCount ? m_vertices[i+1] - s : m_vertices[0] - s;

        float32 D = b2Cross(e1, e2);

        float32 triangleArea = 0.5f * D;
        area += triangleArea;

        // Area weighted centroid
        center += triangleArea * k_inv3 * (e1 + e2);

        float32 ex1 = e1.x, ey1 = e1.y;
        float32 ex2 = e2.x, ey2 = e2.y;

        float32 intx2 = ex1*ex1 + ex2*ex1 + ex2*ex2;
        float32 inty2 = ey1*ey1 + ey2*ey1 + ey2*ey2;

        I += (0.25f * k_inv3 * D) * (intx2 + inty2);
    }

    // Total mass
    massData->mass = density * area;

    // Center of mass
    b2Assert(area > b2_epsilon);
    center *= 1.0f / area;
    massData->center = center + s;

    // Inertia tensor relative to the local origin (point s).
    massData->I = density * I;
    
    // Shift to center of mass then to original body origin.
    massData->I += massData->mass * (b2Dot(massData->center, massData->center) - b2Dot(center, center));
}