double Mesh::ComputeVolume() const
{
const size_t nV = GetNPoints();
const size_t nT = GetNTriangles();
if (nV == 0 || nT == 0)
{
return 0.0;
}
Vec3<double> bary(0.0, 0.0, 0.0);
for (size_t v = 0; v < nV; v++)
{
bary += GetPoint(v);
}
bary /= static_cast<double>(nV);
Vec3<double> ver0, ver1, ver2;
double totalVolume = 0.0;
for(size_t t = 0; t < nT; t++)
{
const Vec3<int> & tri = GetTriangle(t);
ver0 = GetPoint(tri[0]);
ver1 = GetPoint(tri[1]);
ver2 = GetPoint(tri[2]);
totalVolume += ComputeVolume4(ver0, ver1, ver2, bary);
}
return totalVolume/6.0;
}
bool ICHull::IsInside(const Vec3<double>& pt0, const double eps)
{
const Vec3<double> pt(pt0.X(), pt0.Y(), pt0.Z());
if (m_isFlat)
{
size_t nT = m_mesh.m_triangles.GetSize();
Vec3<double> ver0, ver1, ver2, a, b, c;
double u, v;
for (size_t t = 0; t < nT; t++)
{
ver0.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.X();
ver0.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Y();
ver0.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Z();
ver1.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.X();
ver1.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Y();
ver1.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Z();
ver2.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.X();
ver2.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Y();
ver2.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Z();
a = ver1 - ver0;
b = ver2 - ver0;
c = pt - ver0;
u = c * a;
v = c * b;
if (u >= 0.0 && u <= 1.0 && v >= 0.0 && u + v <= 1.0)
{
return true;
}
m_mesh.m_triangles.Next();
}
return false;
}
else
{
size_t nT = m_mesh.m_triangles.GetSize();
Vec3<double> ver0, ver1, ver2;
double vol;
for (size_t t = 0; t < nT; t++)
{
ver0.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.X();
ver0.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Y();
ver0.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Z();
ver1.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.X();
ver1.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Y();
ver1.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Z();
ver2.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.X();
ver2.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Y();
ver2.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Z();
vol = ComputeVolume4(ver0, ver1, ver2, pt);
if (vol < eps)
{
return false;
}
m_mesh.m_triangles.Next();
}
return true;
}
}
bool ICHull::ComputePointVolume(double& totalVolume, bool markVisibleFaces)
{
// mark visible faces
CircularListElement<TMMTriangle>* fHead = m_mesh.GetTriangles().GetHead();
CircularListElement<TMMTriangle>* f = fHead;
CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
CircularListElement<TMMVertex>* vertex0 = vertices.GetHead();
bool visible = false;
Vec3<double> pos0 = Vec3<double>(vertex0->GetData().m_pos.X(),
vertex0->GetData().m_pos.Y(),
vertex0->GetData().m_pos.Z());
double vol = 0.0;
totalVolume = 0.0;
Vec3<double> ver0, ver1, ver2;
do
{
ver0.X() = f->GetData().m_vertices[0]->GetData().m_pos.X();
ver0.Y() = f->GetData().m_vertices[0]->GetData().m_pos.Y();
ver0.Z() = f->GetData().m_vertices[0]->GetData().m_pos.Z();
ver1.X() = f->GetData().m_vertices[1]->GetData().m_pos.X();
ver1.Y() = f->GetData().m_vertices[1]->GetData().m_pos.Y();
ver1.Z() = f->GetData().m_vertices[1]->GetData().m_pos.Z();
ver2.X() = f->GetData().m_vertices[2]->GetData().m_pos.X();
ver2.Y() = f->GetData().m_vertices[2]->GetData().m_pos.Y();
ver2.Z() = f->GetData().m_vertices[2]->GetData().m_pos.Z();
vol = ComputeVolume4(ver0, ver1, ver2, pos0);
if (vol < -sc_eps)
{
vol = fabs(vol);
totalVolume += vol;
if (markVisibleFaces)
{
f->GetData().m_visible = true;
m_trianglesToDelete.PushBack(f);
}
visible = true;
}
f = f->GetNext();
} while (f != fHead);
if (m_trianglesToDelete.Size() == m_mesh.m_triangles.GetSize())
{
for (size_t i = 0; i < m_trianglesToDelete.Size(); i++)
{
m_trianglesToDelete[i]->GetData().m_visible = false;
}
visible = false;
}
// if no faces visible from p then p is inside the hull
if (!visible && markVisibleFaces)
{
vertices.Delete();
m_trianglesToDelete.Resize(0);
return false;
}
return true;
}
bool Mesh::IsInside(const Vec3<double> & pt) const
{
const size_t nV = GetNPoints();
const size_t nT = GetNTriangles();
if (nV == 0 || nT == 0)
{
return false;
}
Vec3<double> ver0, ver1, ver2;
double volume;
for (size_t t = 0; t < nT; t++)
{
const Vec3<int> & tri = GetTriangle(t);
ver0 = GetPoint(tri[0]);
ver1 = GetPoint(tri[1]);
ver2 = GetPoint(tri[2]);
volume = ComputeVolume4(ver0, ver1, ver2, pt);
if (volume < 0.0)
{
return false;
}
}
return true;
}
ICHullError ICHull::DoubleTriangle()
{
// find three non colinear points
m_isFlat = false;
CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
CircularListElement<TMMVertex>* v0 = vertices.GetHead();
while (Colinear(v0->GetData().m_pos,
v0->GetNext()->GetData().m_pos,
v0->GetNext()->GetNext()->GetData().m_pos)) {
if ((v0 = v0->GetNext()) == vertices.GetHead()) {
return ICHullErrorCoplanarPoints;
}
}
CircularListElement<TMMVertex>* v1 = v0->GetNext();
CircularListElement<TMMVertex>* v2 = v1->GetNext();
// mark points as processed
v0->GetData().m_tag = v1->GetData().m_tag = v2->GetData().m_tag = true;
// create two triangles
CircularListElement<TMMTriangle>* f0 = MakeFace(v0, v1, v2, 0);
MakeFace(v2, v1, v0, f0);
// find a fourth non-coplanar point to form tetrahedron
CircularListElement<TMMVertex>* v3 = v2->GetNext();
vertices.GetHead() = v3;
double vol = ComputeVolume4(v0->GetData().m_pos, v1->GetData().m_pos, v2->GetData().m_pos, v3->GetData().m_pos);
while (fabs(vol) < sc_eps && !v3->GetNext()->GetData().m_tag) {
v3 = v3->GetNext();
vol = ComputeVolume4(v0->GetData().m_pos, v1->GetData().m_pos, v2->GetData().m_pos, v3->GetData().m_pos);
}
if (fabs(vol) < sc_eps) {
// compute the barycenter
Vec3<double> bary(0.0, 0.0, 0.0);
CircularListElement<TMMVertex>* vBary = v0;
do {
bary += vBary->GetData().m_pos;
} while ((vBary = vBary->GetNext()) != v0);
bary /= static_cast<double>(vertices.GetSize());
// Compute the normal to the plane
Vec3<double> p0 = v0->GetData().m_pos;
Vec3<double> p1 = v1->GetData().m_pos;
Vec3<double> p2 = v2->GetData().m_pos;
m_normal = (p1 - p0) ^ (p2 - p0);
m_normal.Normalize();
// add dummy vertex placed at (bary + normal)
vertices.GetHead() = v2;
Vec3<double> newPt = bary + m_normal;
AddPoint(newPt, sc_dummyIndex);
m_isFlat = true;
return ICHullErrorOK;
}
else if (v3 != vertices.GetHead()) {
TMMVertex temp;
temp.m_name = v3->GetData().m_name;
temp.m_pos = v3->GetData().m_pos;
v3->GetData().m_name = vertices.GetHead()->GetData().m_name;
v3->GetData().m_pos = vertices.GetHead()->GetData().m_pos;
vertices.GetHead()->GetData().m_name = temp.m_name;
vertices.GetHead()->GetData().m_pos = temp.m_pos;
}
return ICHullErrorOK;
}
