bool PolyhedronIntersectsAABB_OBB(const Polyhedron &p, const T &obj)
{
if (p.Contains(obj.CenterPoint()))
return true;
if (obj.Contains(p.Centroid()))
return true;
// Test for each edge of the AABB/OBB whether this polyhedron intersects it.
for(int i = 0; i < obj.NumEdges(); ++i)
if (p.Intersects(obj.Edge(i)))
return true;
// Test for each edge of this polyhedron whether the AABB/OBB intersects it.
for(size_t i = 0; i < p.f.size(); ++i)
{
assert(!p.f[i].v.empty()); // Cannot have degenerate faces here, and for performance reasons, don't start checking for this condition in release mode!
int v0 = p.f[i].v.back();
float3 l0 = p.v[v0];
for(size_t j = 0; j < p.f[i].v.size(); ++j)
{
int v1 = p.f[i].v[j];
float3 l1 = p.v[v1];
if (v0 < v1 && obj.Intersects(LineSegment(l0, l1))) // If v0 < v1, then this line segment is the canonical one.
return true;
l0 = l1;
v0 = v1;
}
}
return false;
}
/** The algorithm for Polyhedron-Polyhedron intersection is from Christer Ericson's Real-Time Collision Detection, p. 384.
As noted by the author, the algorithm is very naive (and here unoptimized), and better methods exist. [groupSyntax] */
bool Polyhedron::Intersects(const Polyhedron &polyhedron) const
{
if (polyhedron.Contains(this->Centroid()))
return true;
if (this->Contains(polyhedron.Centroid()))
return true;
// This test assumes that both this and the other polyhedron are closed.
// This means that for each edge running through vertices i and j, there's a face
// that contains the line segment (i,j) and another neighboring face that contains
// the line segment (j,i). These represent the same line segment (but in opposite direction)
// so we only have to test one of them for intersection. Take i < j as the canonical choice
// and skip the other winding order.
// Test for each edge of this polyhedron whether the other polyhedron intersects it.
for(size_t i = 0; i < f.size(); ++i)
{
assert(!f[i].v.empty()); // Cannot have degenerate faces here, and for performance reasons, don't start checking for this condition in release mode!
int v0 = f[i].v.back();
float3 l0 = v[v0];
for(size_t j = 0; j < f[i].v.size(); ++j)
{
int v1 = f[i].v[j];
float3 l1 = v[v1];
if (v0 < v1 && polyhedron.Intersects(LineSegment(l0, l1))) // If v0 < v1, then this line segment is the canonical one.
return true;
l0 = l1;
v0 = v1;
}
}
// Test for each edge of the other polyhedron whether this polyhedron intersects it.
for(size_t i = 0; i < polyhedron.f.size(); ++i)
{
assert(!polyhedron.f[i].v.empty()); // Cannot have degenerate faces here, and for performance reasons, don't start checking for this condition in release mode!
int v0 = polyhedron.f[i].v.back();
float3 l0 = polyhedron.v[v0];
for(size_t j = 0; j < polyhedron.f[i].v.size(); ++j)
{
int v1 = polyhedron.f[i].v[j];
float3 l1 = polyhedron.v[v1];
if (v0 < v1 && Intersects(LineSegment(l0, l1))) // If v0 < v1, then this line segment is the canonical one.
return true;
l0 = l1;
v0 = v1;
}
}
return false;
}
Polyhedron AABB::ToPolyhedron() const
{
// Note to maintainer: This function is an exact copy of OBB:ToPolyhedron() and Frustum::ToPolyhedron().
Polyhedron p;
// Populate the corners of this AABB.
// The will be in the order 0: ---, 1: --+, 2: -+-, 3: -++, 4: +--, 5: +-+, 6: ++-, 7: +++.
for(int i = 0; i < 8; ++i)
p.v.push_back(CornerPoint(i));
// Generate the 6 faces of this AABB.
const int faces[6][4] =
{
{ 0, 1, 3, 2 }, // X-
{ 4, 6, 7, 5 }, // X+
{ 0, 4, 5, 1 }, // Y-
{ 7, 6, 2, 3 }, // Y+
{ 0, 2, 6, 4 }, // Z-
{ 1, 5, 7, 3 }, // Z+
};
for(int f = 0; f < 6; ++f)
{
Polyhedron::Face face;
for(int v = 0; v < 4; ++v)
face.v.push_back(faces[f][v]);
p.f.push_back(face);
}
assume(p.IsClosed());
assume(p.IsConvex());
assume(p.EulerFormulaHolds());
assume(p.FaceIndicesValid());
assume(p.FacesAreNondegeneratePlanar());
assume(p.Contains(this->CenterPoint()));
return p;
}
