bool Polyhedron::IsConvex() const
{
// This function is O(n^2).
/** @todo Real-Time Collision Detection, p. 64:
A faster O(n) approach is to compute for each face F of P the centroid C of F,
and for all neighboring faces G of F test if C lies behind the supporting plane of
G. If some C fails to lie behind the supporting plane of one or more neighboring
faces, P is concave, and is otherwise assumed convex. However, note that just as the
corresponding polygonal convexity test may fail for a pentagram this test may fail for,
for example, a pentagram extruded out of its plane and capped at the ends. */
for(int f = 0; f < NumFaces(); ++f)
{
Plane p = FacePlane(f);
for(int i = 0; i < NumVertices(); ++i)
{
float d = p.SignedDistance(Vertex(i));
if (d > 1e-3f) // Tolerate a small epsilon error.
{
printf("Distance of vertex %d from plane %d: %f", i, f, d);
return false;
}
}
}
return true;
}
bool Polygon::Intersects(const Plane &plane) const
{
// Project the points of this polygon onto the 1D axis of the plane normal.
// If there are points on both sides of the plane, then the polygon intersects the plane.
float minD = inf;
float maxD = -inf;
for(size_t i = 0; i < p.size(); ++i)
{
float d = plane.SignedDistance(p[i]);
minD = Min(minD, d);
maxD = Max(maxD, d);
}
// Allow a very small epsilon tolerance.
return minD <= 1e-4f && maxD >= -1e-4f;
}
void Polyhedron::MergeConvex(const float3 &point)
{
// LOGI("mergeconvex.");
std::set<std::pair<int, int> > deletedEdges;
std::map<std::pair<int, int>, int> remainingEdges;
for(size_t i = 0; i < v.size(); ++i)
if (point.DistanceSq(v[i]) < 1e-3f)
return;
// bool hadDisconnectedHorizon = false;
for(int i = 0; i < (int)f.size(); ++i)
{
// Delete all faces that don't contain the given point. (they have point in their positive side)
Plane p = FacePlane(i);
Face &face = f[i];
if (p.SignedDistance(point) > 1e-5f)
{
bool isConnected = (deletedEdges.empty());
int v0 = face.v.back();
for(size_t j = 0; j < face.v.size() && !isConnected; ++j)
{
int v1 = face.v[j];
if (deletedEdges.find(std::make_pair(v1, v0)) != deletedEdges.end())
{
isConnected = true;
break;
}
v0 = v1;
}
if (isConnected)
{
v0 = face.v.back();
for(size_t j = 0; j < face.v.size(); ++j)
{
int v1 = face.v[j];
deletedEdges.insert(std::make_pair(v0, v1));
// LOGI("Edge %d,%d is to be deleted.", v0, v1);
v0 = v1;
}
// LOGI("Deleting face %d: %s. Distance to vertex %f", i, face.ToString().c_str(), p.SignedDistance(point));
std::swap(f[i], f.back());
f.pop_back();
--i;
continue;
}
// else
// hadDisconnectedHorizon = true;
}
int v0 = face.v.back();
for(size_t j = 0; j < face.v.size(); ++j)
{
int v1 = face.v[j];
remainingEdges[std::make_pair(v0, v1)] = i;
// LOGI("Edge %d,%d is to be deleted.", v0, v1);
v0 = v1;
}
}
// The polyhedron contained our point, nothing to merge.
if (deletedEdges.empty())
return;
// Add the new point to this polyhedron.
// if (!v.back().Equals(point))
v.push_back(point);
/*
// Create a look-up index of all remaining uncapped edges of the polyhedron.
std::map<std::pair<int,int>, int> edgesToFaces;
for(size_t i = 0; i < f.size(); ++i)
{
Face &face = f[i];
int v0 = face.v.back();
for(size_t j = 0; j < face.v.size(); ++j)
{
int v1 = face.v[j];
edgesToFaces[std::make_pair(v1, v0)] = i;
v0 = v1;
}
}
*/
// Now fix all edges by adding new triangular faces for the point.
// for(size_t i = 0; i < deletedEdges.size(); ++i)
for(std::set<std::pair<int, int> >::iterator iter = deletedEdges.begin(); iter != deletedEdges.end(); ++iter)
{
std::pair<int, int> opposite = std::make_pair(iter->second, iter->first);
if (deletedEdges.find(opposite) != deletedEdges.end())
continue;
// std::map<std::pair<int,int>, int>::iterator iter = edgesToFaces.find(deletedEdges[i]);
// std::map<std::pair<int,int>, int>::iterator iter = edgesToFaces.find(deletedEdges[i]);
// if (iter != edgesToFaces.end())
{
// If the adjoining face is planar to the triangle we'd like to add, instead extend the face to enclose
// this vertex.
//float3 newTriangleNormal = (v[v.size()-1]-v[iter->second]).Cross(v[iter->first]-v[iter->second]).Normalized();
std::map<std::pair<int, int>, int>::iterator existing = remainingEdges.find(opposite);
assert(existing != remainingEdges.end());
MARK_UNUSED(existing);
#if 0
int adjoiningFace = existing->second;
if (FaceNormal(adjoiningFace).Dot(newTriangleNormal) >= 0.99999f) ///\todo float3::IsCollinear
{
bool added = false;
Face &adjoining = f[adjoiningFace];
for(size_t i = 0; i < adjoining.v.size(); ++i)
if (adjoining.v[i] == iter->second)
{
adjoining.v.insert(adjoining.v.begin() + i + 1, v.size()-1);
added = true;
/*
int prev2 = (i + adjoining.v.size() - 1) % adjoining.v.size();
int prev = i;
int cur = i + 1;
int next = (i + 2) % adjoining.v.size();
int next2 = (i + 3) % adjoining.v.size();
if (float3::AreCollinear(v[prev2], v[prev], v[cur]))
adjoining.v.erase(adjoining.v.begin() + prev);
else if (float3::AreCollinear(v[prev], v[cur], v[next]))
adjoining.v.erase(adjoining.v.begin() + cur);
else if (float3::AreCollinear(v[cur], v[next], v[next2]))
adjoining.v.erase(adjoining.v.begin() + next2);
*/
break;
}
assert(added);
assume(added);
}
else
#endif
// if (!v[deletedEdges[i].first].Equals(point) && !v[deletedEdges[i].second].Equals(point))
{
Face tri;
tri.v.push_back(iter->second);
tri.v.push_back((int)v.size()-1);
tri.v.push_back(iter->first);
f.push_back(tri);
// LOGI("Added face %d: %s.", (int)f.size()-1, tri.ToString().c_str());
}
}
}
#define mathasserteq(lhs, op, rhs) do { if (!((lhs) op (rhs))) { LOGE("Condition %s %s %s (%g %s %g) failed!", #lhs, #op, #rhs, (double)(lhs), #op, (double)(rhs)); assert(false); } } while(0)
// mathasserteq(NumVertices() + NumFaces(), ==, 2 + NumEdges());
assert(FaceIndicesValid());
// assert(EulerFormulaHolds());
// assert(IsClosed());
// assert(FacesAreNondegeneratePlanar());
// assert(IsConvex());
// if (hadDisconnectedHorizon)
// MergeConvex(point);
}