// return point that minimizes quadric error for edge [ea,eb]
Vector3d OptimalPoint(QuadricError q, int ea, int eb)
{
if (MinimizeQuadricPositionError == false)
{
return((mesh.GetVertex(ea) + mesh.GetVertex(eb)) * 0.5);
}
else
{
try {
return(q.OptimalPoint());
} catch {
// degenerate matrix, evaluate quadric at edge end and midpoints
// (could do line search here...)
Vector3d va = mesh.GetVertex(ea);
Vector3d vb = mesh.GetVertex(eb);
Vector3d c = (va + vb) * 0.5;
double fa = q.Evaluate(va);
double fb = q.Evaluate(vb);
double fc = q.Evaluate(c);
double m = MathUtil.Min(fa, fb, fc);
if (m == fa)
{
return(va);
}
else if (m == fb)
{
return(vb);
}
return(c);
}
}
}
// return point that minimizes quadric error for edge [ea,eb]
protected Vector3d OptimalPoint(int eid, ref QuadricError q, int ea, int eb)
{
// if we would like to preserve boundary, we need to know that here
// so that we properly score these edges
if (HaveBoundary && PreserveBoundaryShape)
{
if (mesh.IsBoundaryEdge(eid))
{
return((mesh.GetVertex(ea) + mesh.GetVertex(eb)) * 0.5);
}
else
{
if (IsBoundaryV(ea))
{
return(mesh.GetVertex(ea));
}
else if (IsBoundaryV(eb))
{
return(mesh.GetVertex(eb));
}
}
}
// [TODO] if we have constraints, we should apply them here, for same reason as bdry above...
if (MinimizeQuadricPositionError == false)
{
return(project((mesh.GetVertex(ea) + mesh.GetVertex(eb)) * 0.5));
}
else
{
Vector3d result = Vector3d.Zero;
if (q.OptimalPoint(ref result))
{
return(project(result));
}
// degenerate matrix, evaluate quadric at edge end and midpoints
// (could do line search here...)
Vector3d va = mesh.GetVertex(ea);
Vector3d vb = mesh.GetVertex(eb);
Vector3d c = project((va + vb) * 0.5);
double fa = q.Evaluate(ref va);
double fb = q.Evaluate(ref vb);
double fc = q.Evaluate(ref c);
double m = MathUtil.Min(fa, fb, fc);
if (m == fa)
{
return(va);
}
else if (m == fb)
{
return(vb);
}
return(c);
}
}
protected virtual void InitializeQueue()
{
int NE = mesh.EdgeCount;
Nodes = new QEdge[2 * NE]; // [RMS] do we need this many?
NodePool = new MemoryPool <QEdge>(NE);
EdgeQueue = new g3ext.FastPriorityQueue <QEdge>(NE);
int cur_eid = start_edges();
bool done = false;
do
{
if (mesh.IsEdge(cur_eid))
{
Index2i ev = mesh.GetEdgeV(cur_eid);
QuadricError Q = new QuadricError(ref vertQuadrics[ev.a], ref vertQuadrics[ev.b]);
Vector3d opt = OptimalPoint(Q, ev.a, ev.b);
double err = Q.Evaluate(opt);
QEdge ee = NodePool.Allocate();
ee.Initialize(cur_eid, Q, opt);
Nodes[cur_eid] = ee;
EdgeQueue.Enqueue(ee, (float)err);
}
cur_eid = next_edge(cur_eid, out done);
} while (done == false);
}
protected virtual void InitializeQueue()
{
int NE = mesh.EdgeCount;
int MaxEID = mesh.MaxEdgeID;
EdgeQuadrics = new QEdge[MaxEID];
EdgeQueue = new IndexPriorityQueue(MaxEID);
float[] edgeErrors = new float[MaxEID];
// vertex quadrics can be computed in parallel
gParallel.BlockStartEnd(0, MaxEID - 1, (start_eid, end_eid) => {
for (int eid = start_eid; eid <= end_eid; eid++)
{
if (mesh.IsEdge(eid))
{
Index2i ev = mesh.GetEdgeV(eid);
QuadricError Q = new QuadricError(ref vertQuadrics[ev.a], ref vertQuadrics[ev.b]);
Vector3d opt = OptimalPoint(eid, ref Q, ev.a, ev.b);
edgeErrors[eid] = (float)Q.Evaluate(ref opt);
EdgeQuadrics[eid] = new QEdge(eid, ref Q, ref opt);
}
}
});
// sorted pq insert is faster, so sort edge errors array and index map
int[] indices = new int[MaxEID];
for (int i = 0; i < MaxEID; ++i)
{
indices[i] = i;
}
Array.Sort(edgeErrors, indices);
// now do inserts
for (int i = 0; i < edgeErrors.Length; ++i)
{
int eid = indices[i];
if (mesh.IsEdge(eid))
{
QEdge edge = EdgeQuadrics[eid];
EdgeQueue.Insert(edge.eid, edgeErrors[i]);
}
}
/*
* // previous code that does unsorted insert. This is marginally slower, but
* // might get even slower on larger meshes? have only tried up to about 350k.
* // (still, this function is not the bottleneck...)
* int cur_eid = start_edges();
* bool done = false;
* do {
* if (mesh.IsEdge(cur_eid)) {
* QEdge edge = EdgeQuadrics[cur_eid];
* double err = errList[cur_eid];
* EdgeQueue.Enqueue(cur_eid, (float)err);
* }
* cur_eid = next_edge(cur_eid, out done);
* } while (done == false);
*/
}
// update queue weight for each edge in vertex one-ring
protected virtual void UpdateNeighbours(int vid)
{
foreach (int eid in mesh.VtxEdgesItr(vid))
{
Index2i nev = mesh.GetEdgeV(eid);
QuadricError Q = new QuadricError(ref vertQuadrics[nev.a], ref vertQuadrics[nev.b]);
Vector3d opt = OptimalPoint(eid, ref Q, nev.a, nev.b);
double err = Q.Evaluate(ref opt);
EdgeQuadrics[eid] = new QEdge(eid, ref Q, ref opt);
if (EdgeQueue.Contains(eid))
{
EdgeQueue.Update(eid, (float)err);
}
else
{
EdgeQueue.Insert(eid, (float)err);
}
}
}
// update queue weight for each edge in vertex one-ring
protected virtual void UpdateNeighbours(int vid)
{
foreach (int eid in mesh.VtxEdgesItr(vid))
{
Index2i nev = mesh.GetEdgeV(eid);
QuadricError Q = new QuadricError(ref vertQuadrics[nev.a], ref vertQuadrics[nev.b]);
Vector3d opt = OptimalPoint(Q, nev.a, nev.b);
double err = Q.Evaluate(opt);
QEdge eid_node = Nodes[eid];
if (eid_node != null)
{
eid_node.q = Q;
eid_node.collapse_pt = opt;
EdgeQueue.UpdatePriority(eid_node, (float)err);
}
else
{
QEdge ee = NodePool.Allocate();
ee.Initialize(eid, Q, opt);
Nodes[eid] = ee;
EdgeQueue.Enqueue(ee, (float)err);
}
}
}
