File indexing completed on 2024-06-02 03:42:36

 /*
 * 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;
 }