/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="position"></param>
private static void QuadSplitGeometry <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
// create face vertices
foreach (var f in mesh.Faces)
{
var v = mesh.AddVertex();
if (!f.IsUnused)
{
position.Set(v, f.Vertices.Mean(position.Get));
}
}
// create edge vertices
foreach (var he in mesh.Edges)
{
var v = mesh.AddVertex();
if (!he.IsUnused)
{
var p = (position.Get(he.Start) + position.Get(he.End)) * 0.5;
position.Set(v, p);
}
}
}
/// <summary>
///
/// </summary>
/// <param name="mesh"></param>
/// <returns></returns>
public G CreateFromFaceTopology(HeMesh <HeMesh3d.Vertex, HeMesh3d.Halfedge, HeMesh3d.Face> mesh)
{
var graph = Create(mesh.Faces.Count, mesh.Halfedges.Count);
graph.AppendFaceTopology(mesh);
return(graph);
}
/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="start"></param>
/// <param name="setEdge"></param>
public static void DetachFaceCycles <V, E, F>(HeMesh <V, E, F> mesh, F start, Action <E, E> setEdge)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
Impl <V, E, F> .DetachFaceCycles(mesh, start, setEdge);
}
/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="start"></param>
/// <param name="getPosition"></param>
/// <param name="setUnrolledPosition"></param>
/// <param name="getUnrollFactor"></param>
public static void Unroll <V, E, F>(HeMesh <V, E, F> mesh, F start, Func <V, Vector3d> getPosition, Action <V, Vector3d> setUnrolledPosition, Func <E, double> getUnrollFactor = null)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
Impl <V, E, F> .Unroll(mesh, start, getPosition, setUnrolledPosition, getUnrollFactor);
}
/// <summary>
///
/// </summary>
/// <param name="mesh"></param>
/// <param name="start"></param>
/// <param name="setEdge"></param>
public static void DetachFaceCycles(HeMesh <V, E, F> mesh, F start, Action <E, E> setEdge)
{
var currTag = mesh.Halfedges.NextTag;
// tag traversed edges during BFS
foreach (var he in mesh.GetFacesBreadthFirst2(start.Yield()))
{
he.Edge.Tag = currTag;
}
var edges = mesh.Edges;
var ne = edges.Count;
// detach all untagged edges
for (int i = 0; i < ne; i++)
{
var he0 = edges[i];
if (he0.IsUnused || he0.IsBoundary || he0.Tag == currTag)
{
continue;
}
var he1 = mesh.DetachEdgeImpl(he0);
setEdge(he1, he0);
}
}
/// <summary>
///
/// </summary>
private static void CatmullClarkSmoothFixed <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
var verts = mesh.Vertices;
int ev0 = verts.Count - mesh.Edges.Count; // index of first edge vertex
int fv0 = ev0 - mesh.Faces.Count; // index of first face vertex
// set old vertices
for (int i = 0; i < fv0; i++)
{
var v = verts[i];
if (v.IsUnused || v.IsBoundary)
{
continue; // skip boundary verts
}
var fsum = new Vector3d();
var esum = new Vector3d();
int n = 0;
foreach (var he in v.OutgoingHalfedges)
{
fsum += position.Get(verts[he.Face.Index + fv0]);
esum += position.Get(verts[(he.Index >> 1) + ev0]);
n++;
}
var t = 1.0 / n;
position.Set(v, (position.Get(v) * (n - 3) + fsum * t + 2 * esum * t) * t);
}
}
/// <summary>
/// Returns all quad strips in the given mesh.
/// </summary>
public static IEnumerable <QuadStrip <V, E, F> > GetQuadStrips <V, E, F>(HeMesh <V, E, F> mesh, bool flip)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
var faces = mesh.Faces;
var result = new List <QuadStrip <V, E, F> >();
var stack = new Stack <E>();
int currTag = faces.NextTag;
for (int i = 0; i < faces.Count; i++)
{
var f = faces[i];
if (f.IsUnused || f.Tag == currTag || !f.IsDegree(4))
{
continue; // skip if unused, visited, or non-quads
}
stack.Push((flip) ? f.First.Next : f.First);
foreach (var strip in GetQuadStrips <V, E, F>(stack, currTag))
{
yield return(strip);
}
}
}
/// <summary>
/// Returns a quad strip that includes the given halfedge.
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="hedge"></param>
/// <returns></returns>
public static QuadStrip <V, E, F> GetQuadStrip <V, E, F>(HeMesh <V, E, F> mesh, E hedge)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
mesh.Halfedges.OwnsCheck(hedge);
return(GetQuadStrip <V, E, F>(hedge, mesh.Faces.NextTag));
}
/// <summary>
/// Applies a single iteration of Catmull-Clark subdivision to the given mesh.
/// If using pre-allocated external buffers to store vertex attributes, the number of vertices after subdivision equals the sum of the number of vertices, edges, and faces in the initial mesh.
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="position"></param>
public static void QuadSplit <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
QuadSplitGeometry(mesh, position);
QuadSplitTopology(mesh);
}
/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="position"></param>
public static void Loop <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
// TODO implement
throw new NotImplementedException();
}
/// <summary>
/// Applies a single iteration of Catmull-Clark subdivision to the given mesh.
/// If using external buffers to store vertex attributes, the number of vertices after subdivision equals the sum of the number of vertices, edges, and faces in the initial mesh.
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="position"></param>
/// <param name="boundaryType"></param>
public static void CatmullClark <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position, SmoothBoundaryType boundaryType)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
// impl ref
// http://rosettacode.org/wiki/Catmull%E2%80%93Clark_subdivision_surface
// http://w3.impa.br/~lcruz/courses/cma/surfaces.html
CatmullClarkGeometry(mesh, position, boundaryType);
QuadSplitTopology(mesh);
}
/*
* /// <summary>
* /// Applies a single iteration of Catmull-Clark subdivision to the given mesh.
* /// http://rosettacode.org/wiki/Catmull%E2%80%93Clark_subdivision_surface
* /// http://w3.impa.br/~lcruz/courses/cma/surfaces.html
* /// </summary>
* /// <typeparam name="V"></typeparam>
* /// <typeparam name="E"></typeparam>
* /// <typeparam name="F"></typeparam>
* /// <param name="mesh"></param>
* /// <param name="position"></param>
* /// <param name="boundaryType"></param>
* public static void CatmullClark<V, E, F>(HeMesh<V, E, F> mesh, Property<V, Vec3d> position, SmoothBoundaryType boundaryType, bool parallel)
* where V : HeMeshBase<V, E, F>.Vertex
* where E : HeMeshBase<V, E, F>.Halfedge
* where F : HeMeshBase<V, E, F>.Face
* {
* CatmullClarkGeometry(mesh, position, boundaryType, parallel);
* QuadSplitTopology(mesh);
* }
*
*
* /// <summary>
* ///
* /// </summary>
* private static void CatmullClarkGeometry<V, E, F>(HeMesh<V, E, F> mesh, Property<V, Vec3d> position, SmoothBoundaryType boundaryType, bool parallel)
* where V : HeMeshBase<V, E, F>.Vertex
* where E : HeMeshBase<V, E, F>.Halfedge
* where F : HeMeshBase<V, E, F>.Face
* {
* var verts = mesh.Vertices;
* var edges = mesh.Edges;
* var faces = mesh.Faces;
*
* int fv0 = verts.Count; // index of first face vertex
* int ev0 = verts.Count + faces.Count;
*
* // add all new vertices
* mesh.AddVertices(faces.Count);
* mesh.AddVertices(edges.Count);
*
* // set attributes of face vertices
* Action<Tuple<int, int>> setFaceVerts = range =>
* {
* for (int i = range.Item1; i < range.Item2; i++)
* {
* var f = faces[i];
*
* if (!f.IsUnused)
* position.Set(verts[i + fv0], f.Vertices.Mean(position.Get));
* }
* };
*
* // set attributes of edge vertices
* Action<Tuple<int, int>> setEdgeVerts = range =>
* {
* for (int i = range.Item1; i < range.Item2; i++)
* {
* var he0 = edges[i];
* if (he0.IsUnused) continue;
*
* if (he0.IsBoundary)
* {
* position.Set(verts[i + ev0], he0.Lerp(position.Get, 0.5));
* continue;
* }
*
* var he1 = he0.Twin;
* var p0 = position.Get(he0.Start);
* var p1 = position.Get(he1.Start);
* var p2 = position.Get(verts[he0.Face.Index + fv0]);
* var p3 = position.Get(verts[he1.Face.Index + fv0]);
* position.Set(verts[i + ev0], (p0 + p1 + p2 + p3) * 0.25);
* }
* };
*
* // set attributes of old vertices
* //CatmullClarkSmooth(mesh, position, boundaryType);
* Action<Tuple<int, int>> setOldVerts = range =>
* {
* for (int i = range.Item1; i < range.Item2; i++)
* {
* var v = verts[i];
* if (v.IsUnused) continue;
*
* if (v.IsBoundary)
* {
* var he0 = v.FirstOut;
* var he1 = he0.PrevInFace;
* var p0 = position.Get(verts[(he0.Index >> 1) + ev0]);
* var p1 = position.Get(verts[(he1.Index >> 1) + ev0]);
* position.Set(v, position.Get(v) * 0.5 + (p0 + p1) * 0.25);
* }
* else
* {
* Vec3d fsum = new Vec3d();
* Vec3d esum = new Vec3d();
* int n = 0;
*
* foreach (var he in v.OutgoingHalfedges)
* {
* fsum += position.Get(verts[he.Face.Index + fv0]);
* esum += position.Get(verts[(he.Index >> 1) + ev0]);
* n++;
* }
*
* double t = 1.0 / n;
* position.Set(v, (position.Get(v) * (n - 3) + fsum * t + 2 * esum * t) * t);
* }
* }
* };
*
*
* if (parallel)
* {
* Parallel.ForEach(Partitioner.Create(0, faces.Count), setFaceVerts);
* Parallel.ForEach(Partitioner.Create(0, edges.Count), setEdgeVerts);
* Parallel.ForEach(Partitioner.Create(0, verts.Count), setOldVerts);
* }
* else
* {
* setFaceVerts(Tuple.Create(0, faces.Count));
* setEdgeVerts(Tuple.Create(0, edges.Count));
* setOldVerts(Tuple.Create(0, verts.Count));
* }
* }
*/
#endregion
#region Misc
/// <summary>
/// If using pre-allocated external buffers to store vertex attributes, the number of vertices after subdivision equals the sum of the number of vertices and faces in the initial mesh.
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="position"></param>
/// <param name="skipBoundary"></param>
public static void Diagonalize <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position, bool skipBoundary)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
var edges = mesh.Edges;
var faces = mesh.Faces;
int ne = edges.Count;
int nf = faces.Count;
// stellate faces
for (int i = 0; i < nf; i++)
{
var f = faces[i];
if (f.IsUnused)
{
continue;
}
var v = mesh.AddVertex();
position.Set(v, f.GetBarycenter(position.Get));
mesh.PokeFaceImpl(f.First, v);
}
// merge faces
if (skipBoundary)
{
for (int i = 0; i < ne; i++)
{
var he = edges[i];
if (he.IsUnused || he.IsBoundary)
{
continue;
}
mesh.MergeFaces(he);
}
}
else
{
for (int i = 0; i < ne; i++)
{
var he = edges[i];
if (he.IsUnused)
{
continue;
}
mesh.MergeFaces(he);
}
}
}
/// <summary>
///
/// </summary>
private static void CatmullClarkSmoothCornerFixed <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
var verts = mesh.Vertices;
int ev0 = verts.Count - mesh.Edges.Count; // index of first edge vertex
int fv0 = ev0 - mesh.Faces.Count; // index of first face vertex
// set old vertices
for (int i = 0; i < fv0; i++)
{
var v = verts[i];
if (v.IsUnused)
{
continue;
}
if (v.IsBoundary)
{
var he0 = v.First;
if (he0.IsAtDegree2)
{
continue; // skip corner verts
}
var he1 = he0.Previous;
var p0 = position.Get(verts[(he0.Index >> 1) + ev0]);
var p1 = position.Get(verts[(he1.Index >> 1) + ev0]);
position.Set(v, position.Get(v) * 0.5 + (p0 + p1) * 0.25);
}
else
{
Vector3d fsum = new Vector3d();
Vector3d esum = new Vector3d();
int n = 0;
foreach (var he in v.OutgoingHalfedges)
{
fsum += position.Get(verts[he.Face.Index + fv0]);
esum += position.Get(verts[(he.Index >> 1) + ev0]);
n++;
}
double t = 1.0 / n;
position.Set(v, (position.Get(v) * (n - 3) + fsum * t + 2 * esum * t) * t);
}
}
}
/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
/// <param name="position"></param>
/// <param name="boundaryType"></param>
private static void CatmullClarkGeometry <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position, SmoothBoundaryType boundaryType)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
var verts = mesh.Vertices;
int fv0 = verts.Count; // index of first face vertex
// create face vertices
foreach (var f in mesh.Faces)
{
var v = mesh.AddVertex();
if (!f.IsUnused)
{
position.Set(v, f.Vertices.Mean(position.Get));
}
}
// create edge vertices
foreach (var he0 in mesh.Edges)
{
var v = mesh.AddVertex();
if (he0.IsUnused)
{
continue;
}
if (he0.IsBoundary)
{
var p = (position.Get(he0.Start) + position.Get(he0.End)) * 0.5;
position.Set(v, p);
continue;
}
var he1 = he0.Twin;
var p0 = position.Get(he0.Start);
var p1 = position.Get(he1.Start);
var p2 = position.Get(verts[he0.Face.Index + fv0]);
var p3 = position.Get(verts[he1.Face.Index + fv0]);
position.Set(v, (p0 + p1 + p2 + p3) * 0.25);
}
// smooth old vertices
CatmullClarkSmooth(mesh, position, boundaryType);
}
/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="mesh"></param>
private static void QuadSplitTopology <V, E, F>(HeMesh <V, E, F> mesh)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
var verts = mesh.Vertices;
var hedges = mesh.Halfedges;
var faces = mesh.Faces;
int ne = hedges.Count >> 1;
int nf = faces.Count;
int ev0 = verts.Count - ne; // index of first edge vertex
int fv0 = ev0 - nf; // index of first face vertex (also the number of vertices in the initial mesh)
// split edges
for (int i = 0; i < ne; i++)
{
var he = hedges[i << 1];
if (he.IsUnused)
{
continue;
}
var ev = verts[i + ev0];
mesh.SplitEdgeImpl(he, ev);
}
// split faces
for (int i = 0; i < nf; i++)
{
var f = faces[i];
if (f.IsUnused)
{
continue;
}
var he = f.First;
if (he.Start.Index >= fv0)
{
he = he.Previous; // ensure halfedge starts from an old vertex
}
mesh.QuadSplitFace(he, verts[i + fv0]);
}
}
/// <summary>
///
/// </summary>
private static void CatmullClarkSmooth <V, E, F>(HeMesh <V, E, F> mesh, Property <V, Vector3d> position, SmoothBoundaryType boundaryType)
where V : HeMesh <V, E, F> .Vertex
where E : HeMesh <V, E, F> .Halfedge
where F : HeMesh <V, E, F> .Face
{
switch (boundaryType)
{
case SmoothBoundaryType.Fixed:
CatmullClarkSmoothFixed(mesh, position);
return;
case SmoothBoundaryType.CornerFixed:
CatmullClarkSmoothCornerFixed(mesh, position);
return;
case SmoothBoundaryType.Free:
CatmullClarkSmoothFree(mesh, position);
return;
}
throw new NotSupportedException();
}
/// <summary>
///
/// </summary>
/// <param name="mesh"></param>
/// <param name="start"></param>
/// <param name="getPosition"></param>
/// <param name="setUnrolledPosition"></param>
/// <param name="getUnrollFactor"></param>
public static void Unroll(HeMesh <V, E, F> mesh, F start, Func <V, Vector3d> getPosition, Action <V, Vector3d> setUnrolledPosition, Func <E, double> getUnrollFactor = null)
{
const string errorMessage = "Face cycle detected. The given mesh cannot be unrolled.";
start.UnusedCheck();
mesh.Faces.OwnsCheck(start);
// stack of edges with corresponding transforms
var queue = new Queue <(E, Orient3d)>();
var tag = mesh.Faces.NextTag;
// current unroll transform
var unroll = Orient3d.Identity;
// enqueue twin of each halfedge in the first face
foreach (var he in start.Halfedges)
{
var v = he.Start;
setUnrolledPosition(v, getPosition(v));
TryEnqueue(he.Twin);
}
// breadth-first walk and transform
while (queue.Count > 0)
{
(var he0, var m0) = queue.Dequeue();
var m1 = getUnrollFactor == null?
GetHalfedgeTransform(he0, getPosition) :
GetHalfedgeTransform(he0, getPosition, getUnrollFactor(he0));
unroll = m0.Apply(ref m1);
var he1 = he0.Next;
// enqueue first hedge
TryEnqueue(he1.Twin);
he1 = he1.Next;
// transform and enqueue remaining hedges
do
{
var v = he1.Start;
setUnrolledPosition(v, unroll.Apply(getPosition(v)));
TryEnqueue(he1.Twin);
he1 = he1.Next;
} while (he1 != he0);
}
void TryEnqueue(E hedge)
{
var f = hedge.Face;
if (f == null)
{
return;
}
if (f.Tag == tag)
{
throw new ArgumentException(errorMessage);
}
queue.Enqueue((hedge, unroll));
f.Tag = tag;
}
}
/// <summary>
///
/// </summary>
/// <param name="mesh"></param>
public void AppendFaceTopology(HeMesh <HeMesh3d.Vertex, HeMesh3d.Halfedge, HeMesh3d.Face> mesh)
{
AppendFaceTopology(mesh, Set, Set);
}