/// <summary>
/// Find the set of boundary EdgeLoops. Note that if we encounter topological
/// issues, we will throw MeshBoundaryLoopsException w/ more info (if possible)
/// </summary>
public bool Compute()
{
// This algorithm assumes that triangles are oriented consistently,
// so closed boundary-loop can be followed by walking edges in-order
Loops = new List <EdgeLoop>();
int NE = Mesh.MaxEdgeID;
// Temporary memory used to indicate when we have "used" an edge.
BitArray used_edge = new BitArray(NE);
used_edge.SetAll(false);
// current loop is stored here, cleared after each loop extracted
List <int> loop_edges = new List <int>(); // [RMS] not sure we need this...
List <int> loop_verts = new List <int>();
List <int> bowties = new List <int>();
// Temp buffer for reading back all boundary edges of a vertex.
// probably always small but in pathological cases it could be large...
int[] all_e = new int[16];
// process all edges of mesh
for (int eid = 0; eid < NE; ++eid)
{
if (!Mesh.IsEdge(eid))
{
continue;
}
if (used_edge[eid] == true)
{
continue;
}
if (Mesh.IsBoundaryEdge(eid) == false)
{
continue;
}
if (EdgeFilterF != null && EdgeFilterF(eid) == false)
{
used_edge[eid] = true;
continue;
}
// ok this is start of a boundary chain
int eStart = eid;
used_edge[eStart] = true;
loop_edges.Add(eStart);
int eCur = eid;
// follow the chain in order of oriented edges
bool bClosed = false;
while (!bClosed)
{
Index2i ev = Mesh.GetOrientedBoundaryEdgeV(eCur);
int cure_a = ev.a, cure_b = ev.b;
loop_verts.Add(cure_a);
int e0 = -1, e1 = 1;
int bdry_nbrs = Mesh.VtxBoundaryEdges(cure_b, ref e0, ref e1);
// have to filter this list, if we are filtering. this is ugly.
if (EdgeFilterF != null)
{
if (bdry_nbrs > 2)
{
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[bdry_nbrs];
}
// we may repreat this below...irritating...
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
num_be = BufferUtil.CountValid(all_e, EdgeFilterF, num_be);
}
else
{
if (EdgeFilterF(e0) == false)
{
bdry_nbrs--;
}
if (EdgeFilterF(e1) == false)
{
bdry_nbrs--;
}
}
}
if (bdry_nbrs < 2)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: found broken neighbourhood at vertex " + cure_b)
{
UnclosedLoop = true
}
}
;
int eNext = -1;
if (bdry_nbrs > 2)
{
// found "bowtie" vertex...things just got complicated!
if (cure_b == loop_verts[0])
{
// The "end" of the current edge is the same as the start vertex.
// This means we can close the loop here. Might as well!
eNext = -2; // sentinel value used below
}
else
{
// try to find an unused outgoing edge that is oriented properly.
// This could create sub-loops, we will handle those later
if (bdry_nbrs >= all_e.Length)
{
all_e = new int[bdry_nbrs];
}
int num_be = Mesh.VtxAllBoundaryEdges(cure_b, all_e);
if (EdgeFilterF != null)
{
num_be = BufferUtil.FilterInPlace(all_e, EdgeFilterF, num_be);
}
Debug.Assert(num_be == bdry_nbrs);
// Try to pick the best "turn left" vertex.
eNext = find_left_turn_edge(eCur, cure_b, all_e, num_be, used_edge);
if (eNext == -1)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: cannot find valid outgoing edge at bowtie vertex " + cure_b)
{
BowtieFailure = true
}
}
;
}
if (bowties.Contains(cure_b) == false)
{
bowties.Add(cure_b);
}
}
else
{
Debug.Assert(e0 == eCur || e1 == eCur);
eNext = (e0 == eCur) ? e1 : e0;
}
if (eNext == -2)
{
// found a bowtie vert that is the same as start-of-loop, so we
// are just closing it off explicitly
bClosed = true;
}
else if (eNext == eStart)
{
// found edge at start of loop, so loop is done.
bClosed = true;
}
else
{
// push onto accumulated list
Debug.Assert(used_edge[eNext] == false);
loop_edges.Add(eNext);
eCur = eNext;
used_edge[eCur] = true;
}
}
// if we saw a bowtie vertex, we might need to break up this loop,
// so call extract_subloops
if (bowties.Count > 0)
{
List <EdgeLoop> subloops = extract_subloops(loop_verts, loop_edges, bowties);
for (int i = 0; i < subloops.Count; ++i)
{
Loops.Add(subloops[i]);
}
}
else
{
// clean simple loop, convert to EdgeLoop instance
EdgeLoop loop = new EdgeLoop(Mesh);
loop.Vertices = loop_verts.ToArray();
loop.Edges = loop_edges.ToArray();
Loops.Add(loop);
}
// reset these lists
loop_edges.Clear();
loop_verts.Clear();
bowties.Clear();
}
return(true);
}
// [TODO] cache this in a dictionary? we will not need very many, but we will
// need each multiple times!
Vector3D get_vtx_normal(int vid)
{
Vector3D n = Vector3D.Zero;
foreach (int ti in Mesh.VtxTrianglesItr(vid))
{
n += Mesh.GetTriNormal(ti);
}
n.Normalize();
return(n);
}
// ok, bdry_edges[0...bdry_edges_count] contains the boundary edges coming out of bowtie_v.
// We want to pick the best one to continue the loop that came in to bowtie_v on incoming_e.
// If the loops are all sane, then we will get the smallest loops by "turning left" at bowtie_v.
// So, we compute the tangent plane at bowtie_v, and then the signed angle for each
// viable edge in this plane.
//
// [TODO] handle degenerate edges. what do we do then? Currently will only chose
// degenerate edge if there are no other options (I think...)
int find_left_turn_edge(int incoming_e, int bowtie_v, int[] bdry_edges, int bdry_edges_count, BitArray used_edges)
{
// compute normal and edge [a,bowtie]
Vector3D n = get_vtx_normal(bowtie_v);
int other_v = Mesh.Edge_other_v(incoming_e, bowtie_v);
Vector3D ab = Mesh.GetVertex(bowtie_v) - Mesh.GetVertex(other_v);
// our winner
int best_e = -1;
double best_angle = double.MaxValue;
for (int i = 0; i < bdry_edges_count; ++i)
{
int bdry_eid = bdry_edges[i];
if (used_edges[bdry_eid] == true)
{
continue; // this edge is already used
}
Index2i bdry_ev = Mesh.GetOrientedBoundaryEdgeV(bdry_eid);
if (bdry_ev.a != bowtie_v)
{
continue; // have to be able to chain to end of current edge, orientation-wise
}
// compute projected angle
Vector3D bc = Mesh.GetVertex(bdry_ev.b) - Mesh.GetVertex(bowtie_v);
float fAngleS = math.MathUtil.PlaneAngleSignedD((Vector3F)ab, (Vector3F)bc, (Vector3F)n);
// turn left!
if (best_angle == double.MaxValue || fAngleS < best_angle)
{
best_angle = fAngleS;
best_e = bdry_eid;
}
}
Debug.Assert(best_e != -1);
return(best_e);
}
// This is called when loopV contains one or more "bowtie" vertices.
// These vertices *might* be duplicated in loopV (but not necessarily)
// If they are, we have to break loopV into subloops that don't contain duplicates.
//
// The list bowties contains all the possible duplicates
// (all v in bowties occur in loopV at least once)
//
// Currently loopE is not used, and the returned EdgeLoop objects do not have their Edges
// arrays initialized. Perhaps to improve in future.
List <EdgeLoop> extract_subloops(List <int> loopV, List <int> loopE, List <int> bowties)
{
List <EdgeLoop> subs = new List <EdgeLoop>();
// figure out which bowties we saw are actually duplicated in loopV
List <int> dupes = new List <int>();
foreach (int bv in bowties)
{
if (count_in_list(loopV, bv) > 1)
{
dupes.Add(bv);
}
}
// we might not actually have any duplicates, if we got luck. Early out in that case
if (dupes.Count == 0)
{
subs.Add(new EdgeLoop(Mesh)
{
Vertices = loopV.ToArray(), Edges = loopE.ToArray(), BowtieVertices = bowties.ToArray()
});
return(subs);
}
// This loop extracts subloops until we have dealt with all the
// duplicate vertices in loopV
while (dupes.Count > 0)
{
// Find shortest "simple" loop, ie a loop from a bowtie to itself that
// does not contain any other bowties. This is an independent loop.
// We're doing a lot of extra work here if we only have one element in dupes...
int bi = 0, bv = 0;
int start_i = -1, end_i = -1;
int bv_shortest = -1; int shortest = int.MaxValue;
for ( ; bi < dupes.Count; ++bi)
{
bv = dupes[bi];
if (is_simple_bowtie_loop(loopV, dupes, bv, out start_i, out end_i))
{
int len = count_span(loopV, start_i, end_i);
if (len < shortest)
{
bv_shortest = bv;
shortest = len;
}
}
}
if (bv_shortest == -1)
{
throw new MeshBoundaryLoopsException("MeshBoundaryLoops.Compute: Cannot find a valid simple loop");
}
if (bv != bv_shortest)
{
bv = bv_shortest;
// running again just to get start_i and end_i...
is_simple_bowtie_loop(loopV, dupes, bv, out start_i, out end_i);
}
Debug.Assert(loopV[start_i] == bv && loopV[end_i] == bv);
EdgeLoop loop = new EdgeLoop(Mesh);
loop.Vertices = extract_span(loopV, start_i, end_i, true);
loop.Edges = EdgeLoop.VertexLoopToEdgeLoop(Mesh, loop.Vertices);
loop.BowtieVertices = bowties.ToArray();
subs.Add(loop);
// If there are no more duplicates of this bowtie, we can treat
// it like a regular vertex now
if (count_in_list(loopV, bv) < 2)
{
dupes.Remove(bv);
}
}
// Should have one loop left that contains duplicates.
// Extract this as a separate loop
int nLeft = 0;
for (int i = 0; i < loopV.Count; ++i)
{
if (loopV[i] != -1)
{
nLeft++;
}
}
if (nLeft > 0)
{
EdgeLoop loop = new EdgeLoop(Mesh);
loop.Vertices = new int[nLeft];
int vi = 0;
for (int i = 0; i < loopV.Count; ++i)
{
if (loopV[i] != -1)
{
loop.Vertices[vi++] = loopV[i];
}
}
loop.Edges = EdgeLoop.VertexLoopToEdgeLoop(Mesh, loop.Vertices);
loop.BowtieVertices = bowties.ToArray();
subs.Add(loop);
}
return(subs);
}
/*
* In all the functions below, the list loopV is assumed to possibly
* contain "removed" vertices indicated by -1. These are ignored.
*/
// Check if the loop from bowtieV to bowtieV inside loopV contains any other bowtie verts.
// Also returns start and end indices in loopV of "clean" loop
// Note that start may be < end, if the "clean" loop wraps around the end
bool is_simple_bowtie_loop(List <int> loopV, List <int> bowties, int bowtieV, out int start_i, out int end_i)
{
// find two indices of bowtie vert
start_i = find_index(loopV, 0, bowtieV);
end_i = find_index(loopV, start_i + 1, bowtieV);
if (is_simple_path(loopV, bowties, bowtieV, start_i, end_i))
{
return(true);
}
else if (is_simple_path(loopV, bowties, bowtieV, end_i, start_i))
{
int tmp = start_i; start_i = end_i; end_i = tmp;
return(true);
}
else
{
return(false); // not a simple bowtie loop!
}
}
// check if forward path from loopV[i1] to loopV[i2] contains any bowtie verts other than bowtieV
bool is_simple_path(List <int> loopV, List <int> bowties, int bowtieV, int i1, int i2)
{
int N = loopV.Count;
for (int i = i1; i != i2; i = (i + 1) % N)
{
int vi = loopV[i];
if (vi == -1)
{
continue; // skip removed vertices
}
if (vi != bowtieV && bowties.Contains(vi))
{
return(false);
}
}
return(true);
}
// Read out the span from loop[i0] to loop [i1-1] into an array.
// If bMarkInvalid, then these values are set to -1 in loop
int[] extract_span(List <int> loop, int i0, int i1, bool bMarkInvalid)
{
int num = count_span(loop, i0, i1);
int[] a = new int[num];
int ai = 0;
int N = loop.Count;
for (int i = i0; i != i1; i = (i + 1) % N)
{
if (loop[i] != -1)
{
a[ai++] = loop[i];
if (bMarkInvalid)
{
loop[i] = -1;
}
}
}
return(a);
}
// count number of valid vertices in l between loop[i0] and loop[i1-1]
int count_span(List <int> l, int i0, int i1)
{
int c = 0;
int N = l.Count;
for (int i = i0; i != i1; i = (i + 1) % N)
{
if (l[i] != -1)
{
c++;
}
}
return(c);
}
// find the index of item in loop, starting at start index
int find_index(List <int> loop, int start, int item)
{
for (int i = start; i < loop.Count; ++i)
{
if (loop[i] == item)
{
return(i);
}
}
return(-1);
}
// count number of times item appears in loop
int count_in_list(List <int> loop, int item)
{
int c = 0;
for (int i = 0; i < loop.Count; ++i)
{
if (loop[i] == item)
{
c++;
}
}
return(c);
}
}