VertexIter HalfedgeMesh::splitEdge( EdgeIter e0 )
{
// TODO This method should split the given edge and return an iterator to the newly inserted vertex.
// TODO The halfedge of this vertex should point along the edge that was split, rather than the new edges.
//1. collect elements
//Halfedges
HalfedgeIter h0 = e0->halfedge();
HalfedgeIter h3 = h0->twin();
//Faces
FaceIter f0 = h0->face();
FaceIter f1 = h3->face();
//Ignore requests to split boundary edges
if(f0->isBoundary() && f1->isBoundary())
return verticesEnd();
else if(f0->isBoundary())
{
//1. collent elements (continue)
HalfedgeIter h1 = h0->next();
HalfedgeIter h4 = h3->next();
HalfedgeIter h5 = h4->next();
//Vertices
VertexIter v0 = h0->vertex();
VertexIter v1 = h3->vertex();
VertexIter v3 = h5->vertex();
//Edges
//e0 is given
//2. allocate new elements
HalfedgeIter h11 = newHalfedge();
HalfedgeIter h13 = newHalfedge();
HalfedgeIter h14 = newHalfedge();
HalfedgeIter h15 = newHalfedge();
FaceIter f3 = newFace();
EdgeIter e6 = newEdge();
EdgeIter e7 = newEdge();
VertexIter v4 = newVertex();
v4->position = 0.5f * (v0->position + v1->position);
//3. reassign elements
//Halfedges
h0->next() = h11;
h11->setNeighbors(h1, h14, v4, e7, f0);
h3->vertex() = v4;
h4->next() = h13;
h13->setNeighbors(h3, h15, v3, e6, f1);
h14->setNeighbors(h15, h11, v1, e7, f3);
h15->setNeighbors(h5, h13, v4, e6, f3);
h5->next() = h14; h5->face() = f3;
//Vertices
v0->halfedge() = h0;
v1->halfedge() = h14;
v3->halfedge() = h13;
v4->halfedge() = h3;
//Edges
e6->halfedge() = h13;
e7->halfedge() = h14;
//Faces
f1->halfedge() = h3;
f3->halfedge() = h14;
return v4;
}
else if(f1->isBoundary())
{
//1. collent elements (continue)
HalfedgeIter h1 = h0->next();
HalfedgeIter h2 = h1->next();
//HalfedgeIter h4 = h3->next();
HalfedgeIter h5 = h3;
do
h5 = h5->next();
while(h5->next() != h3);
//Vertices
VertexIter v0 = h0->vertex();
VertexIter v1 = h3->vertex();
VertexIter v2 = h2->vertex();
//Edges
//e0 is given
//2. allocate new elements
HalfedgeIter h10 = newHalfedge();
HalfedgeIter h11 = newHalfedge();
HalfedgeIter h12 = newHalfedge();
HalfedgeIter h14 = newHalfedge();
FaceIter f2 = newFace();
EdgeIter e5 = newEdge();
EdgeIter e7 = newEdge();
VertexIter v4 = newVertex();
v4->position = 0.5f * (v0->position + v1->position);
//3. reassign elements
//Halfedges
h0->next() = h10;
h10->setNeighbors(h2, h12, v4, e5, f0);
h11->setNeighbors(h1, h14, v4, e7, f2);
h1->next() = h12; h1->face() = f2;
h12->setNeighbors(h11, h10, v2, e5, f2);
h3->vertex() = v4;
h5->next() = h14;
h14->setNeighbors(h3, h11, v1, e7, f1);
//Vertices
v0->halfedge() = h0;
v1->halfedge() = h14;
v2->halfedge() = h12;
v4->halfedge() = h3;
//Edges
e7->halfedge() = h11;
e5->halfedge() = h10;
//Faces
f0->halfedge() = h0;
f1->halfedge() = h3;
f2->halfedge() = h1;
return v4;
}
else
{
//1. collent elements (continue)
HalfedgeIter h1 = h0->next();
HalfedgeIter h2 = h1->next();
HalfedgeIter h4 = h3->next();
HalfedgeIter h5 = h4->next();
// HalfedgeIter h6 = h1->twin();
// HalfedgeIter h7 = h2->twin();
// HalfedgeIter h8 = h4->twin();
// HalfedgeIter h9 = h5->twin();
//Vertices
VertexIter v0 = h0->vertex();
VertexIter v1 = h3->vertex();
VertexIter v2 = h2->vertex();
VertexIter v3 = h5->vertex();
//Edges
//e0 is given
EdgeIter e1 = h1->edge();
EdgeIter e2 = h2->edge();
EdgeIter e3 = h4->edge();
EdgeIter e4 = h5->edge();
//2. allocate new elements
HalfedgeIter h10 = newHalfedge();
HalfedgeIter h11 = newHalfedge();
HalfedgeIter h12 = newHalfedge();
HalfedgeIter h13 = newHalfedge();
HalfedgeIter h14 = newHalfedge();
HalfedgeIter h15 = newHalfedge();
FaceIter f2 = newFace();
FaceIter f3 = newFace();
EdgeIter e5 = newEdge();
EdgeIter e6 = newEdge();
EdgeIter e7 = newEdge();
VertexIter v4 = newVertex();
v4->position = 0.5f * (v0->position + v1->position);
//3. reassign elements
//Halfedges
h0->next() = h10; h0->twin() = h3; h0->vertex() = v0; h0->edge() = e0; h0->face() = f0;
h1->next() = h12; /*h1->twin() = h6;*/ h1->vertex() = v1; h1->edge() = e1; h1->face() = f2;
h2->next() = h0; /*h2->twin() = h7;*/ h2->vertex() = v2; h2->edge() = e2; h2->face() = f0;
h3->next() = h4; h3->twin() = h0; h3->vertex() = v4; h3->edge() = e0; h3->face() = f1;
h4->next() = h13; /*h4->twin() = h8;*/ h4->vertex() = v0; h4->edge() = e3; h4->face() = f1;
h5->next() = h14; /*h5->twin() = h9;*/ h5->vertex() = v3; h5->edge() = e4; h5->face() = f3;
// h6->twin() = h1; h6->vertex() = v2; h6->edge() = e1;
// h7->twin() = h2; h7->vertex() = v0; h7->edge() = e2;
// h8->twin() = h4; h8->vertex() = v3; h8->edge() = e3;
// h9->twin() = h5; h9->vertex() = v1; h9->edge() = e4;
h10->next() = h2; h10->twin() = h12; h10->vertex() = v4; h10->edge() = e5; h10->face() = f0;
h11->next() = h1; h11->twin() = h14; h11->vertex() = v4; h11->edge() = e7; h11->face() = f2;
h12->next() = h11; h12->twin() = h10; h12->vertex() = v2; h12->edge() = e5; h12->face() = f2;
h13->next() = h3; h13->twin() = h15; h13->vertex() = v3; h13->edge() = e6; h13->face() = f1;
h14->next() = h15; h14->twin() = h11; h14->vertex() = v1; h14->edge() = e7; h14->face() = f3;
h15->next() = h5; h15->twin() = h13; h15->vertex() = v4; h15->edge() = e6; h15->face() = f3;
//Vertices
v0->halfedge() = h0;
v1->halfedge() = h1;
v2->halfedge() = h2;
v3->halfedge() = h5;
v4->halfedge() = h3;
//Edges
e0->halfedge() = h0;
e1->halfedge() = h1;
e2->halfedge() = h2;
e3->halfedge() = h4;
e4->halfedge() = h5;
e5->halfedge() = h10;
e6->halfedge() = h13;
e7->halfedge() = h11;
//Faces
f0->halfedge() = h0;
f1->halfedge() = h3;
f2->halfedge() = h1;
f3->halfedge() = h5;
return v4;
}
}
void HalfedgeMesh::build(const vector<vector<Index> >& polygons,
const vector<Vector3D>& vertexPositions)
// This method initializes the halfedge data structure from a raw list of
// polygons, where each input polygon is specified as a list of vertex indices.
// The input must describe a manifold, oriented surface, where the orientation
// of a polygon is determined by the order of vertices in the list. Polygons
// must have at least three vertices. Note that there are no special conditions
// on the vertex indices, i.e., they do not have to start at 0 or 1, nor does
// the collection of indices have to be contiguous. Overall, this initializer
// is designed to be robust but perhaps not incredibly fast (though of course
// this does not affect the performance of the resulting data structure). One
// could also implement faster initializers that handle important special cases
// (e.g., all triangles, or data that is known to be manifold). Since there are
// no strong conditions on the indices of polygons, we assume that the list of
// vertex positions is given in lexicographic order (i.e., that the lowest index
// appearing in any polygon corresponds to the first entry of the list of
// positions and so on).
{
// define some types, to improve readability
typedef vector<Index> IndexList;
typedef IndexList::const_iterator IndexListCIter;
typedef vector<IndexList> PolygonList;
typedef PolygonList::const_iterator PolygonListCIter;
typedef pair<Index, Index> IndexPair; // ordered pair of vertex indices,
// corresponding to an edge of an
// oriented polygon
// Clear any existing elements.
halfedges.clear();
vertices.clear();
edges.clear();
faces.clear();
boundaries.clear();
// Since the vertices in our halfedge mesh are stored in a linked list,
// we will temporarily need to keep track of the correspondence between
// indices of vertices in our input and pointers to vertices in the new
// mesh (which otherwise can't be accessed by index). Note that since
// we're using a general-purpose map (rather than, say, a vector), we can
// be a bit more flexible about the indexing scheme: input vertex indices
// aren't required to be 0-based or 1-based; in fact, the set of indices
// doesn't even have to be contiguous. Taking advantage of this fact makes
// our conversion a bit more robust to different types of input, including
// data that comes from a subset of a full mesh.
// maps a vertex index to the corresponding vertex
map<Index, VertexIter> indexToVertex;
// Also store the vertex degree, i.e., the number of polygons that use each
// vertex; this information will be used to check that the mesh is manifold.
map<VertexIter, Size> vertexDegree;
// First, we do some basic sanity checks on the input.
for (PolygonListCIter p = polygons.begin(); p != polygons.end(); p++) {
if (p->size() < 3) {
// Refuse to build the mesh if any of the polygons have fewer than three
// vertices.(Note that if we omit this check the code will still
// constructsomething fairlymeaningful for 1- and 2-point polygons, but
// enforcing this stricterrequirementon the input will help simplify code
// further downstream, since it canbe certainit doesn't have to check for
// these rather degenerate cases.)
cerr << "Error converting polygons to halfedge mesh: each polygon must "
"have at least three vertices." << endl;
exit(1);
}
// We want to count the number of distinct vertex indices in this
// polygon, to make sure it's the same as the number of vertices
// in the polygon---if they disagree, then the polygon is not valid
// (or at least, for simplicity we don't handle polygons of this type!).
set<Index> polygonIndices;
// loop over polygon vertices
for (IndexListCIter i = p->begin(); i != p->end(); i++) {
polygonIndices.insert(*i);
// allocate one vertex for each new index we encounter
if (indexToVertex.find(*i) == indexToVertex.end()) {
VertexIter v = newVertex();
v->halfedge() =
halfedges.end(); // this vertex doesn't yet point to any halfedge
indexToVertex[*i] = v;
vertexDegree[v] = 1; // we've now seen this vertex only once
} else {
// keep track of the number of times we've seen this vertex
vertexDegree[indexToVertex[*i]]++;
}
} // end loop over polygon vertices
// check that all vertices of the current polygon are distinct
Size degree = p->size(); // number of vertices in this polygon
if (polygonIndices.size() < degree) {
cerr << "Error converting polygons to halfedge mesh: one of the input "
"polygons does not have distinct vertices!" << endl;
cerr << "(vertex indices:";
for (IndexListCIter i = p->begin(); i != p->end(); i++) {
cerr << " " << *i;
}
cerr << ")" << endl;
exit(1);
} // end check that polygon vertices are distinct
} // end basic sanity checks on input
// The number of vertices in the mesh is the
// number of unique indices seen in the input.
Size nVertices = indexToVertex.size();
// The number of faces is just the number of polygons in the input.
Size nFaces = polygons.size();
faces.resize(nFaces); // allocate storage for faces in our new mesh
// We will store a map from ordered pairs of vertex indices to
// the corresponding halfedge object in our new (halfedge) mesh;
// this map gets constructed during the next loop over polygons.
map<IndexPair, HalfedgeIter> pairToHalfedge;
// Next, we actually build the halfedge connectivity by again looping over
// polygons
PolygonListCIter p;
FaceIter f;
for (p = polygons.begin(), f = faces.begin(); p != polygons.end(); p++, f++) {
vector<HalfedgeIter> faceHalfedges; // cyclically ordered list of the half
// edges of this face
Size degree = p->size(); // number of vertices in this polygon
// loop over the halfedges of this face (equivalently, the ordered pairs of
// consecutive vertices)
for (Index i = 0; i < degree; i++) {
Index a = (*p)[i]; // current index
Index b = (*p)[(i + 1) % degree]; // next index, in cyclic order
IndexPair ab(a, b);
HalfedgeIter hab;
// check if this halfedge already exists; if so, we have a problem!
if (pairToHalfedge.find(ab) != pairToHalfedge.end()) {
cerr << "Error converting polygons to halfedge mesh: found multiple "
"oriented edges with indices (" << a << ", " << b << ")."
<< endl;
cerr << "This means that either (i) more than two faces contain this "
"edge (hence the surface is nonmanifold), or" << endl;
cerr << "(ii) there are exactly two faces containing this edge, but "
"they have the same orientation (hence the surface is" << endl;
cerr << "not consistently oriented." << endl;
exit(1);
} else // otherwise, the halfedge hasn't been allocated yet
{
// so, we point this vertex pair to a new halfedge
hab = newHalfedge();
pairToHalfedge[ab] = hab;
// link the new halfedge to its face
hab->face() = f;
hab->face()->halfedge() = hab;
// also link it to its starting vertex
hab->vertex() = indexToVertex[a];
hab->vertex()->halfedge() = hab;
// keep a list of halfedges in this face, so that we can later
// link them together in a loop (via their "next" pointers)
faceHalfedges.push_back(hab);
}
// Also, check if the twin of this halfedge has already been constructed
// (during construction of a different face). If so, link the twins
// together and allocate their shared halfedge. By the end of this pass
// over polygons, the only halfedges that will not have a twin will hence
// be those that sit along the domain boundary.
IndexPair ba(b, a);
map<IndexPair, HalfedgeIter>::iterator iba = pairToHalfedge.find(ba);
if (iba != pairToHalfedge.end()) {
HalfedgeIter hba = iba->second;
// link the twins
hab->twin() = hba;
hba->twin() = hab;
// allocate and link their edge
EdgeIter e = newEdge();
hab->edge() = e;
hba->edge() = e;
e->halfedge() = hab;
} else { // If we didn't find a twin...
// ...mark this halfedge as being twinless by pointing
// it to the end of the list of halfedges. If it remains
// twinless by the end of the current loop over polygons,
// it will be linked to a boundary face in the next pass.
hab->twin() = halfedges.end();
}
} // end loop over the current polygon's halfedges
// Now that all the halfedges of this face have been allocated,
// we can link them together via their "next" pointers.
for (Index i = 0; i < degree; i++) {
Index j =
(i + 1) % degree; // index of the next halfedge, in cyclic order
faceHalfedges[i]->next() = faceHalfedges[j];
}
} // done building basic halfedge connectivity
// For each vertex on the boundary, advance its halfedge pointer to one that
// is also on the boundary.
for (VertexIter v = verticesBegin(); v != verticesEnd(); v++) {
// loop over halfedges around vertex
HalfedgeIter h = v->halfedge();
do {
if (h->twin() == halfedges.end()) {
v->halfedge() = h;
break;
}
h = h->twin()->next();
} while (h != v->halfedge()); // end loop over halfedges around vertex
} // done advancing halfedge pointers for boundary vertices
// Next we construct new faces for each boundary component.
for (HalfedgeIter h = halfedgesBegin(); h != halfedgesEnd();
h++) // loop over all halfedges
{
// Any halfedge that does not yet have a twin is on the boundary of the
// domain. If we follow the boundary around long enough we will of course
// eventually make a closed loop; we can represent this boundary loop by a
// new face. To make clear the distinction between faces and boundary loops,
// the boundary face will (i) have a flag indicating that it is a boundary
// loop, and (ii) be stored in a list of boundaries, rather than the usual
// list of faces. The reason we need the both the flag *and* the separate
// list is that faces are often accessed in two fundamentally different
// ways: either by (i) local traversal of the neighborhood of some mesh
// element using the halfedge structure, or (ii) global traversal of all
// faces (or boundary loops).
if (h->twin() == halfedges.end()) {
FaceIter b = newBoundary();
vector<HalfedgeIter> boundaryHalfedges; // keep a list of halfedges along
// the boundary, so we can link
// them together
// We now need to walk around the boundary, creating new
// halfedges and edges along the boundary loop as we go.
HalfedgeIter i = h;
do {
// create a twin, which becomes a halfedge of the boundary loop
HalfedgeIter t = newHalfedge();
boundaryHalfedges.push_back(
t); // keep a list of all boundary halfedges, in cyclic order
i->twin() = t;
t->twin() = i;
t->face() = b;
t->vertex() = i->next()->vertex();
// create the shared edge
EdgeIter e = newEdge();
e->halfedge() = i;
i->edge() = e;
t->edge() = e;
// Advance i to the next halfedge along the current boundary loop
// by walking around its target vertex and stopping as soon as we
// find a halfedge that does not yet have a twin defined.
i = i->next();
while (i != h && // we're done if we end up back at the beginning of
// the loop
i->twin() != halfedges.end()) // otherwise, we're looking for
// the next twinless halfedge
// along the loop
{
i = i->twin();
i = i->next();
}
} while (i != h);
// The only pointers that still need to be set are the "next" pointers of
// the twins; these we can set from the list of boundary halfedges, but we
// must use the opposite order from the order in the list, since the
// orientation of the boundary loop is opposite the orientation of the
// halfedges "inside" the domain boundary.
Size degree = boundaryHalfedges.size();
for (Index p = 0; p < degree; p++) {
Index q = (p - 1 + degree) % degree;
boundaryHalfedges[p]->next() = boundaryHalfedges[q];
}
} // end construction of one of the boundary loops
// Note that even though we are looping over all halfedges, we will still
// construct the appropriate number of boundary loops (and not, say, one
// loop per boundary halfedge). The reason is that as we continue to
// iterate through halfedges, we check whether their twin has been assigned,
// and since new twins may have been assigned earlier in this loop, we will
// end up skipping many subsequent halfedges.
} // done adding "virtual" faces corresponding to boundary loops
// To make later traversal of the mesh easier, we will now advance the
// halfedge
// associated with each vertex such that it refers to the *first* non-boundary
// halfedge, rather than the last one.
for (VertexIter v = verticesBegin(); v != verticesEnd(); v++) {
v->halfedge() = v->halfedge()->twin()->next();
}
// Finally, we check that all vertices are manifold.
for (VertexIter v = vertices.begin(); v != vertices.end(); v++) {
// First check that this vertex is not a "floating" vertex;
// if it is then we do not have a valid 2-manifold surface.
if (v->halfedge() == halfedges.end()) {
cerr << "Error converting polygons to halfedge mesh: some vertices are "
"not referenced by any polygon." << endl;
exit(1);
}
// Next, check that the number of halfedges emanating from this vertex in
// our half edge data structure equals the number of polygons containing
// this vertex, which we counted during our first pass over the mesh. If
// not, then our vertex is not a "fan" of polygons, but instead has some
// other (nonmanifold) structure.
Size count = 0;
HalfedgeIter h = v->halfedge();
do {
if (!h->face()->isBoundary()) {
count++;
}
h = h->twin()->next();
} while (h != v->halfedge());
if (count != vertexDegree[v]) {
cerr << "Error converting polygons to halfedge mesh: at least one of the "
"vertices is nonmanifold." << endl;
exit(1);
}
} // end loop over vertices
// Now that we have the connectivity, we copy the list of vertex
// positions into member variables of the individual vertices.
if (vertexPositions.size() != vertices.size()) {
cerr << "Error converting polygons to halfedge mesh: number of vertex "
"positions is different from the number of distinct vertices!"
<< endl;
cerr << "(number of positions in input: " << vertexPositions.size() << ")"
<< endl;
cerr << "( number of vertices in mesh: " << vertices.size() << ")" << endl;
exit(1);
}
// Since an STL map internally sorts its keys, we can iterate over the map
// from vertex indices to vertex iterators to visit our (input) vertices in
// lexicographic order
int i = 0;
for (map<Index, VertexIter>::const_iterator e = indexToVertex.begin();
e != indexToVertex.end(); e++) {
// grab a pointer to the vertex associated with the current key (i.e., the
// current index)
VertexIter v = e->second;
// set the att of this vertex to the corresponding
// position in the input
v->position = vertexPositions[i];
i++;
}
// compute initial normals
for (VertexIter v = verticesBegin(); v != verticesEnd(); v++) {
v->computeNormal();
}
} // end HalfedgeMesh::build()
