b2PolygonShape.cpp

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/*
* 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_count = 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_count = 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_count; ++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);
        if (count < 3)
        {
                SetAsBox(1.0f, 1.0f);
                return;
        }
        
        int32 n = b2Min(count, b2_maxPolygonVertices);

        // Perform welding and copy vertices into local buffer.
        b2Vec2 ps[b2_maxPolygonVertices];
        int32 tempCount = 0;
        for (int32 i = 0; i < n; ++i)
        {
                b2Vec2 v = vertices[i];

                bool unique = true;
                for (int32 j = 0; j < tempCount; ++j)
                {
                        if (b2DistanceSquared(v, ps[j]) < 0.5f * b2_linearSlop)
                        {
                                unique = false;
                                break;
                        }
                }

                if (unique)
                {
                        ps[tempCount++] = v;
                }
        }

        n = tempCount;
        if (n < 3)
        {
                // Polygon is degenerate.
                b2Assert(false);
                SetAsBox(1.0f, 1.0f);
                return;
        }

        // Create the convex hull using the Gift wrapping algorithm
        // http://en.wikipedia.org/wiki/Gift_wrapping_algorithm

        // Find the right most point on the hull
        int32 i0 = 0;
        float32 x0 = ps[0].x;
        for (int32 i = 1; i < n; ++i)
        {
                float32 x = ps[i].x;
                if (x > x0 || (x == x0 && ps[i].y < ps[i0].y))
                {
                        i0 = i;
                        x0 = x;
                }
        }

        int32 hull[b2_maxPolygonVertices];
        int32 m = 0;
        int32 ih = i0;

        for (;;)
        {
                hull[m] = ih;

                int32 ie = 0;
                for (int32 j = 1; j < n; ++j)
                {
                        if (ie == ih)
                        {
                                ie = j;
                                continue;
                        }

                        b2Vec2 r = ps[ie] - ps[hull[m]];
                        b2Vec2 v = ps[j] - ps[hull[m]];
                        float32 c = b2Cross(r, v);
                        if (c < 0.0f)
                        {
                                ie = j;
                        }

                        // Collinearity check
                        if (c == 0.0f && v.LengthSquared() > r.LengthSquared())
                        {
                                ie = j;
                        }
                }

                ++m;
                ih = ie;

                if (ie == i0)
                {
                        break;
                }
        }
        
        if (m < 3)
        {
                // Polygon is degenerate.
                b2Assert(false);
                SetAsBox(1.0f, 1.0f);
                return;
        }

        m_count = m;

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

        // Compute normals. Ensure the edges have non-zero length.
        for (int32 i = 0; i < m; ++i)
        {
                int32 i1 = i;
                int32 i2 = i + 1 < m ? 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();
        }

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

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

        for (int32 i = 0; i < m_count; ++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_count; ++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_count; ++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_count >= 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_count; ++i)
        {
                s += m_vertices[i];
        }
        s *= 1.0f / m_count;

        const float32 k_inv3 = 1.0f / 3.0f;

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

bool b2PolygonShape::Validate() const
{
        for (int32 i = 0; i < m_count; ++i)
        {
                int32 i1 = i;
                int32 i2 = i < m_count - 1 ? i1 + 1 : 0;
                b2Vec2 p = m_vertices[i1];
                b2Vec2 e = m_vertices[i2] - p;

                for (int32 j = 0; j < m_count; ++j)
                {
                        if (j == i1 || j == i2)
                        {
                                continue;
                        }

                        b2Vec2 v = m_vertices[j] - p;
                        float32 c = b2Cross(e, v);
                        if (c < 0.0f)
                        {
                                return false;
                        }
                }
        }

        return true;
}