void PoseGraph::clearGraph (void)
{
/// Clear out data associated with the graph
_graph.clear();
_nextVertexId = VertexId(1);
_nextEdgeId = EdgeId(1);
_vertexMap.clear();
_edgeMap.clear();
//graphCleared();
}
GEODE_NEVER_INLINE static void add_constraint_edges(MutableTriangleTopology& mesh, RawField<const EV,VertexId> X,
RawArray<const Vector<int,2>> edges, const bool validate) {
if (!edges.size())
return;
IntervalScope scope;
Hashtable<Vector<VertexId,2>> constrained;
Array<VertexId> left_cavity, right_cavity; // List of vertices for both cavities
const auto random = new_<Random>(key+7);
for (int i=0;i<edges.size();i++) {
// Randomly choose an edge to ensure optimal time complexity
const auto edge = edges[int(random_permute(edges.size(),key+5,i))].sorted();
auto v0 = VertexId(edge.x),
v1 = VertexId(edge.y);
const auto vs = vec(v0,v1);
GEODE_ASSERT(mesh.valid(v0) && mesh.valid(v1));
{
// Check if the edge already exists in the triangulation. To ensure optimal complexity,
// we loop around both vertices interleaved so that our time is O(min(degree(v0),degree(v1))).
const auto s0 = mesh.halfedge(v0),
s1 = mesh.halfedge(v1);
{
auto e0 = s0,
e1 = s1;
do {
if (mesh.dst(e0)==v1 || mesh.dst(e1)==v0)
goto success; // The edge already exists, so there's nothing to be done.
e0 = mesh.left(e0);
e1 = mesh.left(e1);
} while (e0!=s0 && e1!=s1);
}
// Find a triangle touching v0 or v1 containing part of the v0-v1 segment.
// As above, we loop around both vertices interleaved.
auto e0 = s0;
{
auto e1 = s1;
if (mesh.is_boundary(e0)) e0 = mesh.left(e0);
if (mesh.is_boundary(e1)) e1 = mesh.left(e1);
const auto x0 = Perturbed2(v0.id,X[v0]),
x1 = Perturbed2(v1.id,X[v1]);
const auto e0d = mesh.dst(e0),
e1d = mesh.dst(e1);
bool e0o = triangle_oriented(x0,Perturbed2(e0d.id,X[e0d]),x1),
e1o = triangle_oriented(x1,Perturbed2(e1d.id,X[e1d]),x0);
for (;;) { // No need to check for an end condition, since we're guaranteed to terminate
const auto n0 = mesh.left(e0),
n1 = mesh.left(e1);
const auto n0d = mesh.dst(n0),
n1d = mesh.dst(n1);
const bool n0o = triangle_oriented(x0,Perturbed2(n0d.id,X[n0d]),x1),
n1o = triangle_oriented(x1,Perturbed2(n1d.id,X[n1d]),x0);
if (e0o && !n0o)
break;
if (e1o && !n1o) {
// Swap v0 with v1 and e0 with e1 so that our ray starts at v0
swap(v0,v1);
swap(e0,e1);
break;
}
e0 = n0;
e1 = n1;
e0o = n0o;
e1o = n1o;
}
}
// If we only need to walk one step, the retriangulation is a single edge flip
auto cut = mesh.reverse(mesh.next(e0));
if (mesh.dst(mesh.next(cut))==v1) {
if (constrained.contains(vec(mesh.src(cut),mesh.dst(cut)).sorted()))
throw DelaunayConstraintConflict(vec(v0.id,v1.id),vec(mesh.src(cut).id,mesh.dst(cut).id));
cut = mesh.flip_edge(cut);
goto success;
}
// Walk from v0 to v1, collecting the two cavities.
const auto x0 = Perturbed2(v0.id,X[v0]),
x1 = Perturbed2(v1.id,X[v1]);
right_cavity.copy(vec(v0,mesh.dst(cut)));
left_cavity .copy(vec(v0,mesh.src(cut)));
mesh.erase(mesh.face(e0));
for (;;) {
if (constrained.contains(vec(mesh.src(cut),mesh.dst(cut)).sorted()))
throw DelaunayConstraintConflict(vec(v0.id,v1.id),vec(mesh.src(cut).id,mesh.dst(cut).id));
const auto n = mesh.reverse(mesh.next(cut)),
p = mesh.reverse(mesh.prev(cut));
const auto v = mesh.src(n);
mesh.erase(mesh.face(cut));
if (v == v1) {
left_cavity.append(v);
right_cavity.append(v);
break;
} else if (triangle_oriented(x0,x1,Perturbed2(v.id,X[v]))) {
left_cavity.append(v);
cut = n;
} else {
right_cavity.append(v);
cut = p;
}
}
// Retriangulate both cavities
left_cavity.reverse();
cavity_delaunay(mesh,X,left_cavity,random),
cavity_delaunay(mesh,X,right_cavity,random);
}
success:
constrained.set(vs);
}
// If desired, check that the final mesh is constrained Delaunay
if (validate)
assert_delaunay("constrained delaunay validate: ",mesh,X,constrained);
}
// Retriangulate a cavity formed when a constraint edge is inserted, following Shewchuck and Brown.
// The cavity is defined by a counterclockwise list of vertices v[0] to v[m-1] as in Shewchuck and Brown, Figure 5.
static void cavity_delaunay(MutableTriangleTopology& parent_mesh, RawField<const EV,VertexId> X,
RawArray<const VertexId> cavity, Random& random) {
// Since the algorithm generates meshes which may be inconsistent with the outer mesh, and the cavity
// array may have duplicate vertices, we use a temporary mesh and then copy the triangles over when done.
// In the temporary, vertices are indexed consecutively from 0 to m-1.
const int m = cavity.size();
assert(m >= 3);
const auto mesh = new_<MutableTriangleTopology>();
Field<Perturbed2,VertexId> Xc(m,uninit);
for (const int i : range(m))
Xc.flat[i] = Perturbed2(cavity[i].id,X[cavity[i]]);
mesh->add_vertices(m);
const auto xs = Xc.flat[0],
xe = Xc.flat[m-1];
// Set up data structures for prev, next, pi in the paper
const Field<VertexId,VertexId> prev(m,uninit),
next(m,uninit);
for (int i=0;i<m-1;i++) {
next.flat[i] = VertexId(i+1);
prev.flat[i+1] = VertexId(i);
}
const Array<VertexId> pi_(m-2,uninit);
for (int i=1;i<=m-2;i++)
pi_[i-1] = VertexId(i);
#define PI(i) pi_[(i)-1]
// Randomly shuffle [1,m-2], subject to vertices closer to xs-xe than both their neighbors occurring later
for (int i=m-2;i>=2;i--) {
int j;
for (;;) {
j = random.uniform<int>(0,i)+1;
const auto pj = PI(j);
if (!( segment_directions_oriented(xe,xs,Xc[pj],Xc[prev[pj]])
&& segment_directions_oriented(xe,xs,Xc[pj],Xc[next[pj]])))
break;
}
swap(PI(i),PI(j));
// Remove PI(i) from the list
const auto pi = PI(i);
next[prev[pi]] = next[pi];
prev[next[pi]] = prev[pi];
}
// Add the first triangle
mesh->add_face(vec(VertexId(0),PI(1),VertexId(m-1)));
// Add remaining triangles, flipping to ensure Delaunay
const Field<bool,VertexId> marked(m);
Array<HalfedgeId> fan;
bool used_chew = false;
for (int i=2;i<m-1;i++) {
const auto pi = PI(i);
insert_cavity_vertex(mesh,Xc,marked,pi,next[pi],prev[pi]);
if (marked[pi]) {
used_chew = true;
marked[pi] = false;
// Retriangulate the fans of triangles that have all three vertices marked
auto e = mesh->reverse(mesh->halfedge(pi));
auto v = mesh->src(e);
bool mv = marked[v];
marked[v] = false;
fan.clear();
do {
const auto h = mesh->prev(e);
e = mesh->reverse(mesh->next(e));
v = mesh->src(e);
const bool mv2 = marked[v];
marked[v] = false;
if (mv) {
if (mv2)
fan.append(h);
if (!mv2 || mesh->is_boundary(e)) {
chew_fan(mesh,Xc,pi,fan,random);
fan.clear();
}
}
mv = mv2;
} while (!mesh->is_boundary(e));
}
}
#undef PI
// If we ran Chew's algorithm, validate the output. I haven't tested this
// case enough to be confident of its correctness.
if (used_chew)
assert_delaunay("Failure in extreme special case. If this triggers, please email [email protected]: ",
mesh,Xc,Tuple<>(),false,false);
// Copy triangles from temporary mesh to real mesh
for (const auto f : mesh->faces()) {
const auto v = mesh->vertices(f);
parent_mesh.add_face(vec(cavity[v.x.id],cavity[v.y.id],cavity[v.z.id]));
}
}
// This routine assumes the sentinel points have already been added, and processes points in order
GEODE_NEVER_INLINE static Ref<MutableTriangleTopology> deterministic_exact_delaunay(RawField<const Perturbed2,VertexId> X, const bool validate) {
const int n = X.size()-3;
const auto mesh = new_<MutableTriangleTopology>();
IntervalScope scope;
// Initialize the mesh to a Delaunay triangle containing the sentinels at infinity.
mesh->add_vertices(n+3);
mesh->add_face(vec(VertexId(n+0),VertexId(n+1),VertexId(n+2)));
if (self_check) {
mesh->assert_consistent();
assert_delaunay("self check 0: ",mesh,X);
}
// The randomized incremental construction algorithm uses the history of the triangles
// as the acceleration structure. Specifically, we maintain a BSP tree where the nodes
// are edge tests (are we only the left or right of an edge) and the leaves are triangles.
// There are two operations that modify this tree:
//
// 1. Split: A face is split into three by the insertion of an interior vertex.
// 2. Flip: An edge is flipped, turning two triangles into two different triangles.
//
// The three starts out empty, since one triangle needs zero tests.
Array<Node> bsp; // All BSP nodes including leaves
bsp.preallocate(3*n); // The minimum number of possible BSP nodes
Field<Vector<int,2>,FaceId> face_to_bsp; // Map from FaceId to up to two BSP leaf points (2*node+(right?0:1))
face_to_bsp.flat.preallocate(2*n+1); // The exact maximum number of faces
face_to_bsp.flat.append_assuming_enough_space(vec(0,-1)); // By the time we call set_links, node 0 will be valid
if (self_check)
check_bsp(*mesh,bsp,face_to_bsp,X);
// Allocate a stack to simulate recursion when flipping non-Delaunay edges.
// Invariant: if edge is on the stack, the other edges of face(edge) are Delaunay.
// Since halfedge ids change during edge flips in a corner mesh, we store half edges as directed vertex pairs.
Array<Tuple<HalfedgeId,Vector<VertexId,2>>> stack;
stack.preallocate(8);
// Insert all vertices into the mesh in random order, maintaining the Delaunay property
for (const auto i : range(n)) {
const VertexId v(i);
check_interrupts();
// Search through the BSP tree to find the containing triangle
const auto f0 = bsp_search(bsp,X,v);
const auto vs = mesh->vertices(f0);
// Split the face by inserting the new vertex and update the BSP tree accordingly.
mesh->split_face(f0,v);
const auto e0 = mesh->halfedge(v),
e1 = mesh->left(e0),
e2 = mesh->right(e0);
assert(mesh->dst(e0)==vs.x);
const auto f1 = mesh->face(e1),
f2 = mesh->face(e2);
const int base = bsp.extend(3,uninit);
set_links(bsp,face_to_bsp[f0],base);
bsp[base+0] = Node(vec(v,vs.x),base+2,base+1);
bsp[base+1] = Node(vec(v,vs.y),~f0.id,~f1.id);
bsp[base+2] = Node(vec(v,vs.z),~f1.id,~f2.id);
face_to_bsp[f0] = vec(2*(base+1)+0,-1);
face_to_bsp.flat.append_assuming_enough_space(vec(2*(base+1)+1,2*(base+2)+0));
face_to_bsp.flat.append_assuming_enough_space(vec(2*(base+2)+1,-1));
if (self_check) {
mesh->assert_consistent();
check_bsp(*mesh,bsp,face_to_bsp,X);
}
// Fix all non-Delaunay edges
stack.copy(vec(tuple(mesh->next(e0),vec(vs.x,vs.y)),
tuple(mesh->next(e1),vec(vs.y,vs.z)),
tuple(mesh->next(e2),vec(vs.z,vs.x))));
if (self_check)
assert_delaunay("self check 1: ",mesh,X,Tuple<>(),true);
while (stack.size()) {
const auto evs = stack.pop();
auto e = mesh->vertices(evs.x)==evs.y ? evs.x : mesh->halfedge(evs.y.x,evs.y.y);
if (e.valid() && !is_delaunay(*mesh,X,e)) {
// Our mesh is linearly embedded in the plane, so edge flips are always safe
assert(mesh->is_flip_safe(e));
e = mesh->unsafe_flip_edge(e);
GEODE_ASSERT(is_delaunay(*mesh,X,e));
// Update the BSP tree for the triangle flip
const auto f0 = mesh->face(e),
f1 = mesh->face(mesh->reverse(e));
const int node = bsp.append(Node(mesh->vertices(e),~f1.id,~f0.id));
set_links(bsp,face_to_bsp[f0],node);
set_links(bsp,face_to_bsp[f1],node);
face_to_bsp[f0] = vec(2*node+1,-1);
face_to_bsp[f1] = vec(2*node+0,-1);
if (self_check) {
mesh->assert_consistent();
check_bsp(*mesh,bsp,face_to_bsp,X);
}
// Recurse to successor edges to e
const auto e0 = mesh->next(e),
e1 = mesh->prev(mesh->reverse(e));
stack.extend(vec(tuple(e0,mesh->vertices(e0)),
tuple(e1,mesh->vertices(e1))));
if (self_check)
assert_delaunay("self check 2: ",mesh,X,Tuple<>(),true);
}
}
if (self_check) {
mesh->assert_consistent();
assert_delaunay("self check 3: ",mesh,X);
}
}
// Remove sentinels
for (int i=0;i<3;i++)
mesh->erase_last_vertex_with_reordering();
// If desired, check that the final mesh is Delaunay
if (validate)
assert_delaunay("delaunay validate: ",mesh,X);
// Return the mesh with the sentinels removed
return mesh;
}