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;
}
Пример #2
0
Interface0DIterator Stroke::pointsBegin(float /*t*/)
{
  return verticesBegin();  // FIXME
}
Пример #3
0
Interface0DIterator ViewEdge::pointsBegin(float /*t*/)
{
	return verticesBegin();
}
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()