const HalfedgeMesh& HalfedgeMesh::operator=(const HalfedgeMesh& mesh)
// The assignment operator does a "deep" copy of the halfedge mesh data
// structure; in other words, it makes new instances of each mesh element, and
// ensures that pointers in the copy point to the newly allocated elements
// rather than elements in the original mesh. This behavior is especially
// important for making assignments, since the mesh on the right-hand side of an
// assignment may be temporary (hence any pointers to elements in this mesh will
// become invalid as soon as it is released.)
{
// Clear any existing elements.
halfedges.clear();
vertices.clear();
edges.clear();
faces.clear();
boundaries.clear();
// These maps will be used to identify elements of the old mesh
// with elements of the new mesh. (Note that we can use a single
// map for both interior and boundary faces, because the map
// doesn't care which list of faces these iterators come from.)
map<HalfedgeCIter, HalfedgeIter> halfedgeOldToNew;
map<VertexCIter, VertexIter> vertexOldToNew;
map<EdgeCIter, EdgeIter> edgeOldToNew;
map<FaceCIter, FaceIter> faceOldToNew;
// Copy geometry from the original mesh and create a map from
// pointers in the original mesh to those in the new mesh.
for (HalfedgeCIter h = mesh.halfedgesBegin(); h != mesh.halfedgesEnd(); h++)
halfedgeOldToNew[h] = halfedges.insert(halfedges.end(), *h);
for (VertexCIter v = mesh.verticesBegin(); v != mesh.verticesEnd(); v++)
vertexOldToNew[v] = vertices.insert(vertices.end(), *v);
for (EdgeCIter e = mesh.edgesBegin(); e != mesh.edgesEnd(); e++)
edgeOldToNew[e] = edges.insert(edges.end(), *e);
for (FaceCIter f = mesh.facesBegin(); f != mesh.facesEnd(); f++)
faceOldToNew[f] = faces.insert(faces.end(), *f);
for (FaceCIter b = mesh.boundariesBegin(); b != mesh.boundariesEnd(); b++)
faceOldToNew[b] = boundaries.insert(boundaries.end(), *b);
// "Search and replace" old pointers with new ones.
for (HalfedgeIter he = halfedgesBegin(); he != halfedgesEnd(); he++) {
he->next() = halfedgeOldToNew[he->next()];
he->twin() = halfedgeOldToNew[he->twin()];
he->vertex() = vertexOldToNew[he->vertex()];
he->edge() = edgeOldToNew[he->edge()];
he->face() = faceOldToNew[he->face()];
}
for (VertexIter v = verticesBegin(); v != verticesEnd(); v++)
v->halfedge() = halfedgeOldToNew[v->halfedge()];
for (EdgeIter e = edgesBegin(); e != edgesEnd(); e++)
e->halfedge() = halfedgeOldToNew[e->halfedge()];
for (FaceIter f = facesBegin(); f != facesEnd(); f++)
f->halfedge() = halfedgeOldToNew[f->halfedge()];
for (FaceIter b = boundariesBegin(); b != boundariesEnd(); b++)
b->halfedge() = halfedgeOldToNew[b->halfedge()];
// Return a reference to the new mesh.
return *this;
}
void MeshResampler::upsample( HalfedgeMesh& mesh )
// This routine should increase the number of triangles in the mesh using Loop subdivision.
{
// Each vertex and edge of the original surface can be associated with a vertex in the new (subdivided) surface.
// Therefore, our strategy for computing the subdivided vertex locations is to *first* compute the new positions
// using the connectity of the original (coarse) mesh; navigating this mesh will be much easier than navigating
// the new subdivided (fine) mesh, which has more elements to traverse. We will then assign vertex positions in
// the new mesh based on the values we computed for the original mesh.
// TODO Compute new positions for all the vertices in the input mesh, using the Loop subdivision rule,
// TODO and store them in Vertex::newPosition. At this point, we also want to mark each vertex as being
// TODO a vertex of the original mesh.
for(VertexIter v = mesh.verticesBegin(); v != mesh.verticesEnd(); ++v )
{
v->isNew = false;
if(!v->isBoundary())
{
//By convention, Vertex::degree() returns the face degree,
//not the edge degree. The edge degree can be computed by finding the face
//degree, and adding 1 if the vertex is a boundary vertex.
int degree = v->degree();
double u = degree == 3 ? 0.1875 : (3.0 / (8.0 * degree)); //0.1875 = 3/16
v->newPosition = v->position * (1.0 - u * degree);
HalfedgeIter h = v->halfedge();
do
{
h = h->twin();
v->newPosition += (h->vertex()->position * u);
h = h->next();
}
while(h != v->halfedge());
}
else
{
HalfedgeIter h0_b = v->halfedge();
while(!h0_b->isBoundary())
h0_b = h0_b->twin()->next();
VertexIter v0_b = h0_b->twin()->vertex();
HalfedgeIter h1_b = v->halfedge();
do
{
h1_b = h1_b->twin();
if(h1_b->isBoundary())
break;
h1_b = h1_b->next();
}
while(h1_b != v->halfedge());
VertexIter v1_b = h1_b->vertex();
v->newPosition = 0.75 * v->position + 0.125 * (v0_b->position + v1_b->position);
}
}
// TODO Next, compute the updated vertex positions associated with edges, and store it in Edge::newPosition.
for(EdgeIter e = mesh.edgesBegin(); e != mesh.edgesEnd(); ++e)
{
e->isNew = false;
FaceIter f0 = e->halfedge()->face();
FaceIter f1 = e->halfedge()->twin()->face();
if(f0->isBoundary() || f1->isBoundary())
{
VertexIter v0_b = e->halfedge()->vertex();
VertexIter v1_b = e->halfedge()->twin()->vertex();
e->newPosition = 0.5 * (v0_b->position + v1_b->position);
}
else
{
Vector3D v0,v1; //this diagonal
v0 = e->halfedge()->vertex()->position;
v1 = e->halfedge()->twin()->vertex()->position;
e->newPosition = 0.375 * (v0 + v1);
Vector3D v2,v3; //opposite diagonal
v2 = e->halfedge()->next()->next()->vertex()->position;
v3 = e->halfedge()->twin()->next()->next()->vertex()->position;
e->newPosition += 0.125 * (v2 + v3);
}
}
// TODO Next, we're going to split every edge in the mesh, in any order. For future
// TODO reference, we're also going to store some information about which subdivided
// TODO edges come from splitting an edge in the original mesh, and which edges are new,
// TODO by setting the flat Edge::isNew. Note that in this loop, we only want to iterate
// TODO over edges of the original mesh---otherwise, we'll end up splitting edges that we
// TODO just split (and the loop will never end!)
EdgeIter e = mesh.edgesBegin();
while(e != mesh.edgesEnd())
{
EdgeIter next = e;
++next;
if(!e->isNew &&
!e->halfedge()->vertex()->isNew &&
!e->halfedge()->twin()->vertex()->isNew)
{
VertexIter e_v0 = e->halfedge()->vertex();
VertexIter e_v1 = e->halfedge()->twin()->vertex();
VertexIter v_new = mesh.splitEdge(e);
v_new->isNew = true;
v_new->position = e->newPosition;
HalfedgeIter h = v_new->halfedge();
do
{
h = h->twin();
VertexIter v = h->vertex();
h->edge()->isNew = (v != e_v0 && v != e_v1);
h = h->next();
}
while(h != v_new->halfedge());
}
e = next;
}
// TODO Now flip any new edge that connects an old and new vertex.
for(EdgeIter e = mesh.edgesBegin(); e!= mesh.edgesEnd(); ++e)
{
VertexIter v0 = e->halfedge()->vertex();
VertexIter v1 = e->halfedge()->twin()->vertex();
bool v_old_new = (v0->isNew && !v1->isNew) || (!v0->isNew && v1->isNew);
if(v_old_new && e->isNew)
mesh.flipEdge(e);
}
// TODO Finally, copy the new vertex positions into final Vertex::position.
for(VertexIter v = mesh.verticesBegin(); v != mesh.verticesEnd(); ++v)
{
if(!v->isNew)
v->position = v->newPosition;
}
}
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()