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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) * (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;
+}