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Diffstat (limited to 'src/3rdparty/Box2D/Collision/Shapes/b2PolygonShape.cpp')
-rw-r--r-- | src/3rdparty/Box2D/Collision/Shapes/b2PolygonShape.cpp | 468 |
1 files changed, 468 insertions, 0 deletions
diff --git a/src/3rdparty/Box2D/Collision/Shapes/b2PolygonShape.cpp b/src/3rdparty/Box2D/Collision/Shapes/b2PolygonShape.cpp new file mode 100644 index 0000000..3c8c47d --- /dev/null +++ b/src/3rdparty/Box2D/Collision/Shapes/b2PolygonShape.cpp @@ -0,0 +1,468 @@ +/* +* 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) * (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 (;;) + { + b2Assert(m < b2_maxPolygonVertices); + 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; +} |