bool ICHull::ProcessPoint()
{
double totalVolume = 0.0;
if (!ComputePointVolume(totalVolume, true)) {
return false;
}
// Mark edges in interior of visible region for deletion.
// Create a new face based on each border edge
CircularListElement<TMMVertex>* v0 = m_mesh.GetVertices().GetHead();
CircularListElement<TMMEdge>* eHead = m_mesh.GetEdges().GetHead();
CircularListElement<TMMEdge>* e = eHead;
CircularListElement<TMMEdge>* tmp = 0;
int nvisible = 0;
m_edgesToDelete.Resize(0);
m_edgesToUpdate.Resize(0);
do {
tmp = e->GetNext();
nvisible = 0;
for (int k = 0; k < 2; k++) {
if (e->GetData().m_triangles[k]->GetData().m_visible) {
nvisible++;
}
}
if (nvisible == 2) {
m_edgesToDelete.PushBack(e);
}
else if (nvisible == 1) {
e->GetData().m_newFace = MakeConeFace(e, v0);
m_edgesToUpdate.PushBack(e);
}
e = tmp;
} while (e != eHead);
return true;
}
bool ICHull::CleanVertices(unsigned int& addedPoints)
{
// mark all vertices incident to some undeleted edge as on the hull
CircularList<TMMEdge>& edges = m_mesh.GetEdges();
CircularListElement<TMMEdge>* e = edges.GetHead();
size_t nE = edges.GetSize();
for (size_t i = 0; i < nE; i++) {
e->GetData().m_vertices[0]->GetData().m_onHull = true;
e->GetData().m_vertices[1]->GetData().m_onHull = true;
e = e->GetNext();
}
// delete all the vertices that have been processed but are not on the hull
CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
CircularListElement<TMMVertex>* vHead = vertices.GetHead();
CircularListElement<TMMVertex>* v = vHead;
v = v->GetPrev();
do {
if (v->GetData().m_tag && !v->GetData().m_onHull) {
CircularListElement<TMMVertex>* tmp = v->GetPrev();
vertices.Delete(v);
v = tmp;
addedPoints--;
}
else {
v->GetData().m_duplicate = 0;
v->GetData().m_onHull = false;
v = v->GetPrev();
}
} while (v->GetData().m_tag && v != vHead);
return true;
}
bool ICHull::MakeCCW(CircularListElement<TMMTriangle>* f,
CircularListElement<TMMEdge>* e,
CircularListElement<TMMVertex>* v)
{
// the visible face adjacent to e
CircularListElement<TMMTriangle>* fv;
if (e->GetData().m_triangles[0]->GetData().m_visible) {
fv = e->GetData().m_triangles[0];
}
else {
fv = e->GetData().m_triangles[1];
}
// set vertex[0] and vertex[1] to have the same orientation as the corresponding vertices of fv.
int i; // index of e->m_vertices[0] in fv
CircularListElement<TMMVertex>* v0 = e->GetData().m_vertices[0];
CircularListElement<TMMVertex>* v1 = e->GetData().m_vertices[1];
for (i = 0; fv->GetData().m_vertices[i] != v0; i++)
;
if (fv->GetData().m_vertices[(i + 1) % 3] != e->GetData().m_vertices[1]) {
f->GetData().m_vertices[0] = v1;
f->GetData().m_vertices[1] = v0;
}
else {
f->GetData().m_vertices[0] = v0;
f->GetData().m_vertices[1] = v1;
// swap edges
CircularListElement<TMMEdge>* tmp = f->GetData().m_edges[0];
f->GetData().m_edges[0] = f->GetData().m_edges[1];
f->GetData().m_edges[1] = tmp;
}
f->GetData().m_vertices[2] = v;
return true;
}
CircularListElement<TMMTriangle>* ICHull::MakeConeFace(CircularListElement<TMMEdge>* e, CircularListElement<TMMVertex>* p)
{
// create two new edges if they don't already exist
CircularListElement<TMMEdge>* newEdges[2];
for (int i = 0; i < 2; ++i) {
if (!(newEdges[i] = e->GetData().m_vertices[i]->GetData().m_duplicate)) { // if the edge doesn't exits add it and mark the vertex as duplicated
newEdges[i] = m_mesh.AddEdge();
newEdges[i]->GetData().m_vertices[0] = e->GetData().m_vertices[i];
newEdges[i]->GetData().m_vertices[1] = p;
e->GetData().m_vertices[i]->GetData().m_duplicate = newEdges[i];
}
}
// make the new face
CircularListElement<TMMTriangle>* newFace = m_mesh.AddTriangle();
newFace->GetData().m_edges[0] = e;
newFace->GetData().m_edges[1] = newEdges[0];
newFace->GetData().m_edges[2] = newEdges[1];
MakeCCW(newFace, e, p);
for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) {
if (!newEdges[i]->GetData().m_triangles[j]) {
newEdges[i]->GetData().m_triangles[j] = newFace;
break;
}
}
}
return newFace;
}
bool ICHull::AddPoints(const Vec3<double>* points, size_t nPoints)
{
if (!points) {
return false;
}
CircularListElement<TMMVertex>* vertex = NULL;
for (size_t i = 0; i < nPoints; i++) {
vertex = m_mesh.AddVertex();
vertex->GetData().m_pos.X() = points[i].X();
vertex->GetData().m_pos.Y() = points[i].Y();
vertex->GetData().m_pos.Z() = points[i].Z();
vertex->GetData().m_name = static_cast<int>(i);
}
return true;
}
bool ICHull::CleanEdges()
{
// integrate the new faces into the data structure
CircularListElement<TMMEdge>* e;
const size_t ne_update = m_edgesToUpdate.Size();
for (size_t i = 0; i < ne_update; ++i) {
e = m_edgesToUpdate[i];
if (e->GetData().m_newFace) {
if (e->GetData().m_triangles[0]->GetData().m_visible) {
e->GetData().m_triangles[0] = e->GetData().m_newFace;
}
else {
e->GetData().m_triangles[1] = e->GetData().m_newFace;
}
e->GetData().m_newFace = 0;
}
}
// delete edges maked for deletion
CircularList<TMMEdge>& edges = m_mesh.GetEdges();
const size_t ne_delete = m_edgesToDelete.Size();
for (size_t i = 0; i < ne_delete; ++i) {
edges.Delete(m_edgesToDelete[i]);
}
m_edgesToDelete.Resize(0);
m_edgesToUpdate.Resize(0);
return true;
}
bool ICHull::FindMaxVolumePoint(const double minVolume)
{
CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
CircularListElement<TMMVertex>* vMaxVolume = 0;
CircularListElement<TMMVertex>* vHeadPrev = vertices.GetHead()->GetPrev();
double maxVolume = minVolume;
double volume = 0.0;
while (!vertices.GetData().m_tag) // not processed
{
if (ComputePointVolume(volume, false)) {
if (maxVolume < volume) {
maxVolume = volume;
vMaxVolume = vertices.GetHead();
}
vertices.Next();
}
}
CircularListElement<TMMVertex>* vHead = vHeadPrev->GetNext();
vertices.GetHead() = vHead;
if (!vMaxVolume) {
return false;
}
if (vMaxVolume != vHead) {
Vec3<double> pos = vHead->GetData().m_pos;
int id = vHead->GetData().m_name;
vHead->GetData().m_pos = vMaxVolume->GetData().m_pos;
vHead->GetData().m_name = vMaxVolume->GetData().m_name;
vMaxVolume->GetData().m_pos = pos;
vHead->GetData().m_name = id;
}
return true;
}
CircularListElement<TMMTriangle>* ICHull::MakeFace(CircularListElement<TMMVertex>* v0,
CircularListElement<TMMVertex>* v1,
CircularListElement<TMMVertex>* v2,
CircularListElement<TMMTriangle>* fold)
{
CircularListElement<TMMEdge>* e0;
CircularListElement<TMMEdge>* e1;
CircularListElement<TMMEdge>* e2;
int index = 0;
if (!fold) // if first face to be created
{
e0 = m_mesh.AddEdge(); // create the three edges
e1 = m_mesh.AddEdge();
e2 = m_mesh.AddEdge();
}
else // otherwise re-use existing edges (in reverse order)
{
e0 = fold->GetData().m_edges[2];
e1 = fold->GetData().m_edges[1];
e2 = fold->GetData().m_edges[0];
index = 1;
}
e0->GetData().m_vertices[0] = v0;
e0->GetData().m_vertices[1] = v1;
e1->GetData().m_vertices[0] = v1;
e1->GetData().m_vertices[1] = v2;
e2->GetData().m_vertices[0] = v2;
e2->GetData().m_vertices[1] = v0;
// create the new face
CircularListElement<TMMTriangle>* f = m_mesh.AddTriangle();
f->GetData().m_edges[0] = e0;
f->GetData().m_edges[1] = e1;
f->GetData().m_edges[2] = e2;
f->GetData().m_vertices[0] = v0;
f->GetData().m_vertices[1] = v1;
f->GetData().m_vertices[2] = v2;
// link edges to face f
e0->GetData().m_triangles[index] = e1->GetData().m_triangles[index] = e2->GetData().m_triangles[index] = f;
return f;
}
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;
}
ICHullError ICHull::Process()
{
unsigned int addedPoints = 0;
if (m_mesh.GetNVertices() < 3) {
return ICHullErrorNotEnoughPoints;
}
if (m_mesh.GetNVertices() == 3) {
m_isFlat = true;
CircularListElement<TMMTriangle>* t1 = m_mesh.AddTriangle();
CircularListElement<TMMTriangle>* t2 = m_mesh.AddTriangle();
CircularListElement<TMMVertex>* v0 = m_mesh.m_vertices.GetHead();
CircularListElement<TMMVertex>* v1 = v0->GetNext();
CircularListElement<TMMVertex>* v2 = v1->GetNext();
// 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();
t1->GetData().m_vertices[0] = v0;
t1->GetData().m_vertices[1] = v1;
t1->GetData().m_vertices[2] = v2;
t2->GetData().m_vertices[0] = v1;
t2->GetData().m_vertices[1] = v2;
t2->GetData().m_vertices[2] = v2;
return ICHullErrorOK;
}
if (m_isFlat) {
m_mesh.m_edges.Clear();
m_mesh.m_triangles.Clear();
m_isFlat = false;
}
if (m_mesh.GetNTriangles() == 0) // we have to create the first polyhedron
{
ICHullError res = DoubleTriangle();
if (res != ICHullErrorOK) {
return res;
}
else {
addedPoints += 3;
}
}
CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
// go to the first added and not processed vertex
while (!(vertices.GetHead()->GetPrev()->GetData().m_tag)) {
vertices.Prev();
}
while (!vertices.GetData().m_tag) // not processed
{
vertices.GetData().m_tag = true;
if (ProcessPoint()) {
addedPoints++;
CleanUp(addedPoints);
vertices.Next();
if (!GetMesh().CheckConsistancy()) {
size_t nV = m_mesh.GetNVertices();
CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
for (size_t v = 0; v < nV; ++v) {
if (vertices.GetData().m_name == sc_dummyIndex) {
vertices.Delete();
break;
}
vertices.Next();
}
return ICHullErrorInconsistent;
}
}
}
if (m_isFlat) {
SArray<CircularListElement<TMMTriangle>*> trianglesToDuplicate;
size_t nT = m_mesh.GetNTriangles();
for (size_t f = 0; f < nT; f++) {
TMMTriangle& currentTriangle = m_mesh.m_triangles.GetHead()->GetData();
if (currentTriangle.m_vertices[0]->GetData().m_name == sc_dummyIndex || currentTriangle.m_vertices[1]->GetData().m_name == sc_dummyIndex || currentTriangle.m_vertices[2]->GetData().m_name == sc_dummyIndex) {
m_trianglesToDelete.PushBack(m_mesh.m_triangles.GetHead());
for (int k = 0; k < 3; k++) {
for (int h = 0; h < 2; h++) {
if (currentTriangle.m_edges[k]->GetData().m_triangles[h] == m_mesh.m_triangles.GetHead()) {
currentTriangle.m_edges[k]->GetData().m_triangles[h] = 0;
break;
}
}
}
}
else {
trianglesToDuplicate.PushBack(m_mesh.m_triangles.GetHead());
}
m_mesh.m_triangles.Next();
}
size_t nE = m_mesh.GetNEdges();
for (size_t e = 0; e < nE; e++) {
TMMEdge& currentEdge = m_mesh.m_edges.GetHead()->GetData();
if (currentEdge.m_triangles[0] == 0 && currentEdge.m_triangles[1] == 0) {
m_edgesToDelete.PushBack(m_mesh.m_edges.GetHead());
}
m_mesh.m_edges.Next();
}
size_t nV = m_mesh.GetNVertices();
CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
for (size_t v = 0; v < nV; ++v) {
if (vertices.GetData().m_name == sc_dummyIndex) {
vertices.Delete();
}
else {
vertices.GetData().m_tag = false;
vertices.Next();
}
}
CleanEdges();
CleanTriangles();
CircularListElement<TMMTriangle>* newTriangle;
for (size_t t = 0; t < trianglesToDuplicate.Size(); t++) {
newTriangle = m_mesh.AddTriangle();
newTriangle->GetData().m_vertices[0] = trianglesToDuplicate[t]->GetData().m_vertices[1];
newTriangle->GetData().m_vertices[1] = trianglesToDuplicate[t]->GetData().m_vertices[0];
newTriangle->GetData().m_vertices[2] = trianglesToDuplicate[t]->GetData().m_vertices[2];
}
}
return ICHullErrorOK;
}
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;
}