/// <summary>
/// Creates a new edge such that eNew == eOrg.Lnext and eNew.Dst is a newly created vertex.
/// eOrg and eNew will have the same left face.
/// </summary>
public MeshUtils.Edge AddEdgeVertex(MeshUtils.Edge eOrg)
{
var eNew = MeshUtils.MakeEdge(eOrg);
var eNewSym = eNew._Sym;
// Connect the new edge appropriately
MeshUtils.Splice(eNew, eOrg._Lnext);
// Set vertex and face information
eNew._Org = eOrg._Dst;
MeshUtils.MakeVertex(new MeshUtils.Vertex(), eNewSym, eNew._Org);
eNew._Lface = eNewSym._Lface = eOrg._Lface;
return(eNew);
}
/// <summary>
/// Splits eOrg into two edges eOrg and eNew such that eNew == eOrg.Lnext.
/// The new vertex is eOrg.Dst == eNew.Org.
/// eOrg and eNew will have the same left face.
/// </summary>
public MeshUtils.Edge SplitEdge(MeshUtils.Edge eOrg)
{
var eTmp = AddEdgeVertex(eOrg);
var eNew = eTmp._Sym;
// Disconnect eOrg from eOrg->Dst and connect it to eNew->Org
MeshUtils.Splice(eOrg._Sym, eOrg._Sym._Oprev);
MeshUtils.Splice(eOrg._Sym, eNew);
// Set the vertex and face information
eOrg._Dst = eNew._Org;
eNew._Dst._anEdge = eNew._Sym; // may have pointed to eOrg->Sym
eNew._Rface = eOrg._Rface;
eNew._winding = eOrg._winding; // copy old winding information
eNew._Sym._winding = eOrg._Sym._winding;
return(eNew);
}
/// <summary>
/// Splice is the basic operation for changing the
/// mesh connectivity and topology. It changes the mesh so that
/// eOrg->Onext = OLD( eDst->Onext )
/// eDst->Onext = OLD( eOrg->Onext )
/// where OLD(...) means the value before the meshSplice operation.
///
/// This can have two effects on the vertex structure:
/// - if eOrg->Org != eDst->Org, the two vertices are merged together
/// - if eOrg->Org == eDst->Org, the origin is split into two vertices
/// In both cases, eDst->Org is changed and eOrg->Org is untouched.
///
/// Similarly (and independently) for the face structure,
/// - if eOrg->Lface == eDst->Lface, one loop is split into two
/// - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
/// In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
///
/// Some special cases:
/// If eDst == eOrg, the operation has no effect.
/// If eDst == eOrg->Lnext, the new face will have a single edge.
/// If eDst == eOrg->Lprev, the old face will have a single edge.
/// If eDst == eOrg->Onext, the new vertex will have a single edge.
/// If eDst == eOrg->Oprev, the old vertex will have a single edge.
/// </summary>
public void Splice(MeshUtils.Edge eOrg, MeshUtils.Edge eDst)
{
if (eOrg == eDst)
{
return;
}
bool joiningVertices = false;
if (eDst._Org != eOrg._Org)
{
// We are merging two disjoint vertices -- destroy eDst->Org
joiningVertices = true;
MeshUtils.KillVertex(eDst._Org, eOrg._Org);
}
bool joiningLoops = false;
if (eDst._Lface != eOrg._Lface)
{
// We are connecting two disjoint loops -- destroy eDst->Lface
joiningLoops = true;
MeshUtils.KillFace(eDst._Lface, eOrg._Lface);
}
// Change the edge structure
MeshUtils.Splice(eDst, eOrg);
if (!joiningVertices)
{
// We split one vertex into two -- the new vertex is eDst->Org.
// Make sure the old vertex points to a valid half-edge.
MeshUtils.MakeVertex(new MeshUtils.Vertex(), eDst, eOrg._Org);
eOrg._Org._anEdge = eOrg;
}
if (!joiningLoops)
{
// We split one loop into two -- the new loop is eDst->Lface.
// Make sure the old face points to a valid half-edge.
MeshUtils.MakeFace(new MeshUtils.Face(), eDst, eOrg._Lface);
eOrg._Lface._anEdge = eOrg;
}
}
/// <summary>
/// Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
/// evaluates the t-coord of the edge uw at the s-coord of the vertex v.
/// Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
/// If uw is vertical (and thus passes thru v), the result is zero.
///
/// The calculation is extremely accurate and stable, even when v
/// is very close to u or w. In particular if we set v->t = 0 and
/// let r be the negated result (this evaluates (uw)(v->s)), then
/// r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
/// </summary>
public static float EdgeEval(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
Debug.Assert(VertLeq(u, v) && VertLeq(v, w));
float gapL = v._s - u._s;
float gapR = w._s - v._s;
if (gapL + gapR > 0.0f)
{
if (gapL < gapR)
{
return (v._t - u._t) + (u._t - w._t) * (gapL / (gapL + gapR));
} else
{
return (v._t - w._t) + (w._t - u._t) * (gapR / (gapL + gapR));
}
}
/* vertical line */
return 0.0f;
}
static void Swap(ref MeshUtils.Vertex a, ref MeshUtils.Vertex b)
{
var tmp = a;
a = b;
b = tmp;
}
/// <summary>
/// Given edges (o1,d1) and (o2,d2), compute their point of intersection.
/// The computed point is guaranteed to lie in the intersection of the
/// bounding rectangles defined by each edge.
/// </summary>
public static void EdgeIntersect(MeshUtils.Vertex o1, MeshUtils.Vertex d1, MeshUtils.Vertex o2, MeshUtils.Vertex d2, MeshUtils.Vertex v)
{
float z1, z2;
// This is certainly not the most efficient way to find the intersection
// of two line segments, but it is very numerically stable.
//
// Strategy: find the two middle vertices in the VertLeq ordering,
// and interpolate the intersection s-value from these. Then repeat
// using the TransLeq ordering to find the intersection t-value.
if (!VertLeq(o1, d1))
{
Swap(ref o1, ref d1);
}
if (!VertLeq(o2, d2))
{
Swap(ref o2, ref d2);
}
if (!VertLeq(o1, o2))
{
Swap(ref o1, ref o2);
Swap(ref d1, ref d2);
}
if (!VertLeq(o2, d1))
{
// Technically, no intersection -- do our best
v._s = (o2._s + d1._s) / 2.0f;
} else if (VertLeq(d1, d2))
{
// Interpolate between o2 and d1
z1 = EdgeEval(o1, o2, d1);
z2 = EdgeEval(o2, d1, d2);
if (z1 + z2 < 0.0f)
{
z1 = -z1;
z2 = -z2;
}
v._s = Interpolate(z1, o2._s, z2, d1._s);
} else
{
// Interpolate between o2 and d2
z1 = EdgeSign(o1, o2, d1);
z2 = -EdgeSign(o1, d2, d1);
if (z1 + z2 < 0.0f)
{
z1 = -z1;
z2 = -z2;
}
v._s = Interpolate(z1, o2._s, z2, d2._s);
}
// Now repeat the process for t
if (!TransLeq(o1, d1))
{
Swap(ref o1, ref d1);
}
if (!TransLeq(o2, d2))
{
Swap(ref o2, ref d2);
}
if (!TransLeq(o1, o2))
{
Swap(ref o1, ref o2);
Swap(ref d1, ref d2);
}
if (!TransLeq(o2, d1))
{
// Technically, no intersection -- do our best
v._t = (o2._t + d1._t) / 2.0f;
} else if (TransLeq(d1, d2))
{
// Interpolate between o2 and d1
z1 = TransEval(o1, o2, d1);
z2 = TransEval(o2, d1, d2);
if (z1 + z2 < 0.0f)
{
z1 = -z1;
z2 = -z2;
}
v._t = Interpolate(z1, o2._t, z2, d1._t);
} else
{
// Interpolate between o2 and d2
z1 = TransSign(o1, o2, d1);
z2 = -TransSign(o1, d2, d1);
if (z1 + z2 < 0.0f)
{
z1 = -z1;
z2 = -z2;
}
v._t = Interpolate(z1, o2._t, z2, d2._t);
}
}
/// <summary>
/// Purpose: connect a "left" vertex (one where both edges go right)
/// to the processed portion of the mesh. Let R be the active region
/// containing vEvent, and let U and L be the upper and lower edge
/// chains of R. There are two possibilities:
///
/// - the normal case: split R into two regions, by connecting vEvent to
/// the rightmost vertex of U or L lying to the left of the sweep line
///
/// - the degenerate case: if vEvent is close enough to U or L, we
/// merge vEvent into that edge chain. The subcases are:
/// - merging with the rightmost vertex of U or L
/// - merging with the active edge of U or L
/// - merging with an already-processed portion of U or L
/// </summary>
private void ConnectLeftVertex(MeshUtils.Vertex vEvent)
{
var tmp = new ActiveRegion();
// Get a pointer to the active region containing vEvent
tmp._eUp = vEvent._anEdge._Sym;
var regUp = _dict.Find(tmp).Key;
var regLo = RegionBelow(regUp);
if (regLo == null)
{
// This may happen if the input polygon is coplanar.
return;
}
var eUp = regUp._eUp;
var eLo = regLo._eUp;
// Try merging with U or L first
if (Geom.EdgeSign(eUp._Dst, vEvent, eUp._Org) == 0.0f)
{
ConnectLeftDegenerate(regUp, vEvent);
return;
}
// Connect vEvent to rightmost processed vertex of either chain.
// e._Dst is the vertex that we will connect to vEvent.
var reg = Geom.VertLeq(eLo._Dst, eUp._Dst) ? regUp : regLo;
if (regUp._inside || reg._fixUpperEdge)
{
MeshUtils.Edge eNew;
if (reg == regUp)
{
eNew = _mesh.Connect(vEvent._anEdge._Sym, eUp._Lnext);
} else
{
eNew = _mesh.Connect(eLo._Dnext, vEvent._anEdge)._Sym;
}
if (reg._fixUpperEdge)
{
FixUpperEdge(reg, eNew);
} else
{
ComputeWinding(AddRegionBelow(regUp, eNew));
}
SweepEvent(vEvent);
} else
{
// The new vertex is in a region which does not belong to the polygon.
// We don't need to connect this vertex to the rest of the mesh.
AddRightEdges(regUp, vEvent._anEdge, vEvent._anEdge, null, true);
}
}
/// <summary>
/// Splice is the basic operation for changing the
/// mesh connectivity and topology. It changes the mesh so that
/// eOrg->Onext = OLD( eDst->Onext )
/// eDst->Onext = OLD( eOrg->Onext )
/// where OLD(...) means the value before the meshSplice operation.
///
/// This can have two effects on the vertex structure:
/// - if eOrg->Org != eDst->Org, the two vertices are merged together
/// - if eOrg->Org == eDst->Org, the origin is split into two vertices
/// In both cases, eDst->Org is changed and eOrg->Org is untouched.
///
/// Similarly (and independently) for the face structure,
/// - if eOrg->Lface == eDst->Lface, one loop is split into two
/// - if eOrg->Lface != eDst->Lface, two distinct loops are joined into one
/// In both cases, eDst->Lface is changed and eOrg->Lface is unaffected.
///
/// Some special cases:
/// If eDst == eOrg, the operation has no effect.
/// If eDst == eOrg->Lnext, the new face will have a single edge.
/// If eDst == eOrg->Lprev, the old face will have a single edge.
/// If eDst == eOrg->Onext, the new vertex will have a single edge.
/// If eDst == eOrg->Oprev, the old vertex will have a single edge.
/// </summary>
public void Splice(MeshUtils.Edge eOrg, MeshUtils.Edge eDst)
{
if (eOrg == eDst)
{
return;
}
bool joiningVertices = false;
if (eDst._Org != eOrg._Org)
{
// We are merging two disjoint vertices -- destroy eDst->Org
joiningVertices = true;
MeshUtils.KillVertex(eDst._Org, eOrg._Org);
}
bool joiningLoops = false;
if (eDst._Lface != eOrg._Lface)
{
// We are connecting two disjoint loops -- destroy eDst->Lface
joiningLoops = true;
MeshUtils.KillFace(eDst._Lface, eOrg._Lface);
}
// Change the edge structure
MeshUtils.Splice(eDst, eOrg);
if (!joiningVertices)
{
// We split one vertex into two -- the new vertex is eDst->Org.
// Make sure the old vertex points to a valid half-edge.
MeshUtils.MakeVertex(new MeshUtils.Vertex(), eDst, eOrg._Org);
eOrg._Org._anEdge = eOrg;
}
if (!joiningLoops)
{
// We split one loop into two -- the new loop is eDst->Lface.
// Make sure the old face points to a valid half-edge.
MeshUtils.MakeFace(new MeshUtils.Face(), eDst, eOrg._Lface);
eOrg._Lface._anEdge = eOrg;
}
}
/// <summary>
/// Find some weights which describe how the intersection vertex is
/// a linear combination of "org" and "dest". Each of the two edges
/// which generated "isect" is allocated 50% of the weight; each edge
/// splits the weight between its org and dst according to the
/// relative distance to "isect".
/// </summary>
private void VertexWeights(MeshUtils.Vertex isect, MeshUtils.Vertex org, MeshUtils.Vertex dst, out float w0, out float w1)
{
var t1 = Geom.VertL1dist(org, isect);
var t2 = Geom.VertL1dist(dst, isect);
w0 = 0.5f * t2 / (t1 + t2);
w1 = 0.5f * t1 / (t1 + t2);
isect._coords.X += w0 * org._coords.X + w1 * dst._coords.X;
isect._coords.Y += w0 * org._coords.Y + w1 * dst._coords.Y;
isect._coords.Z += w0 * org._coords.Z + w1 * dst._coords.Z;
}
/// <summary>
/// Purpose: connect a "right" vertex vEvent (one where all edges go left)
/// to the unprocessed portion of the mesh. Since there are no right-going
/// edges, two regions (one above vEvent and one below) are being merged
/// into one. "regUp" is the upper of these two regions.
///
/// There are two reasons for doing this (adding a right-going edge):
/// - if the two regions being merged are "inside", we must add an edge
/// to keep them separated (the combined region would not be monotone).
/// - in any case, we must leave some record of vEvent in the dictionary,
/// so that we can merge vEvent with features that we have not seen yet.
/// For example, maybe there is a vertical edge which passes just to
/// the right of vEvent; we would like to splice vEvent into this edge.
///
/// However, we don't want to connect vEvent to just any vertex. We don''t
/// want the new edge to cross any other edges; otherwise we will create
/// intersection vertices even when the input data had no self-intersections.
/// (This is a bad thing; if the user's input data has no intersections,
/// we don't want to generate any false intersections ourselves.)
///
/// Our eventual goal is to connect vEvent to the leftmost unprocessed
/// vertex of the combined region (the union of regUp and regLo).
/// But because of unseen vertices with all right-going edges, and also
/// new vertices which may be created by edge intersections, we don''t
/// know where that leftmost unprocessed vertex is. In the meantime, we
/// connect vEvent to the closest vertex of either chain, and mark the region
/// as "fixUpperEdge". This flag says to delete and reconnect this edge
/// to the next processed vertex on the boundary of the combined region.
/// Quite possibly the vertex we connected to will turn out to be the
/// closest one, in which case we won''t need to make any changes.
/// </summary>
private void ConnectRightVertex(ActiveRegion regUp, MeshUtils.Edge eBottomLeft)
{
var eTopLeft = eBottomLeft._Onext;
var regLo = RegionBelow(regUp);
var eUp = regUp._eUp;
var eLo = regLo._eUp;
bool degenerate = false;
if (eUp._Dst != eLo._Dst)
{
CheckForIntersect(regUp);
}
// Possible new degeneracies: upper or lower edge of regUp may pass
// through vEvent, or may coincide with new intersection vertex
if (Geom.VertEq(eUp._Org, _event))
{
_mesh.Splice(eTopLeft._Oprev, eUp);
regUp = TopLeftRegion(regUp);
eTopLeft = RegionBelow(regUp)._eUp;
FinishLeftRegions(RegionBelow(regUp), regLo);
degenerate = true;
}
if (Geom.VertEq(eLo._Org, _event))
{
_mesh.Splice(eBottomLeft, eLo._Oprev);
eBottomLeft = FinishLeftRegions(regLo, null);
degenerate = true;
}
if (degenerate)
{
AddRightEdges(regUp, eBottomLeft._Onext, eTopLeft, eTopLeft, true);
return;
}
// Non-degenerate situation -- need to add a temporary, fixable edge.
// Connect to the closer of eLo.Org, eUp.Org.
MeshUtils.Edge eNew;
if (Geom.VertLeq(eLo._Org, eUp._Org))
{
eNew = eLo._Oprev;
} else
{
eNew = eUp;
}
eNew = _mesh.Connect(eBottomLeft._Lprev, eNew);
// Prevent cleanup, otherwise eNew might disappear before we've even
// had a chance to mark it as a temporary edge.
AddRightEdges(regUp, eNew, eNew._Onext, eNew._Onext, false);
eNew._Sym._activeRegion._fixUpperEdge = true;
WalkDirtyRegions(regUp);
}
/// <summary>
/// Replace an upper edge which needs fixing (see ConnectRightVertex).
/// </summary>
private void FixUpperEdge(ActiveRegion reg, MeshUtils.Edge newEdge)
{
Debug.Assert(reg._fixUpperEdge);
_mesh.Delete(reg._eUp);
reg._fixUpperEdge = false;
reg._eUp = newEdge;
newEdge._activeRegion = reg;
}
/// <summary>
/// Purpose: insert right-going edges into the edge dictionary, and update
/// winding numbers and mesh connectivity appropriately. All right-going
/// edges share a common origin vOrg. Edges are inserted CCW starting at
/// eFirst; the last edge inserted is eLast.Oprev. If vOrg has any
/// left-going edges already processed, then eTopLeft must be the edge
/// such that an imaginary upward vertical segment from vOrg would be
/// contained between eTopLeft.Oprev and eTopLeft; otherwise eTopLeft
/// should be null.
/// </summary>
private void AddRightEdges(ActiveRegion regUp, MeshUtils.Edge eFirst, MeshUtils.Edge eLast, MeshUtils.Edge eTopLeft, bool cleanUp)
{
bool firstTime = true;
var e = eFirst;
do
{
Debug.Assert(Geom.VertLeq(e._Org, e._Dst));
AddRegionBelow(regUp, e._Sym);
e = e._Onext;
} while (e != eLast);
// Walk *all* right-going edges from e.Org, in the dictionary order,
// updating the winding numbers of each region, and re-linking the mesh
// edges to match the dictionary ordering (if necessary).
if (eTopLeft == null)
{
eTopLeft = RegionBelow(regUp)._eUp._Rprev;
}
ActiveRegion regPrev = regUp, reg;
var ePrev = eTopLeft;
while (true)
{
reg = RegionBelow(regPrev);
e = reg._eUp._Sym;
if (e._Org != ePrev._Org)
break;
if (e._Onext != ePrev)
{
// Unlink e from its current position, and relink below ePrev
_mesh.Splice(e._Oprev, e);
_mesh.Splice(ePrev._Oprev, e);
}
// Compute the winding number and "inside" flag for the new regions
reg._windingNumber = regPrev._windingNumber - e._winding;
reg._inside = Geom.IsWindingInside(_windingRule, reg._windingNumber);
// Check for two outgoing edges with same slope -- process these
// before any intersection tests (see example in tessComputeInterior).
regPrev._dirty = true;
if (!firstTime && CheckForRightSplice(regPrev))
{
Geom.AddWinding(e, ePrev);
DeleteRegion(regPrev);
_mesh.Delete(ePrev);
}
firstTime = false;
regPrev = reg;
ePrev = e;
}
regPrev._dirty = true;
Debug.Assert(regPrev._windingNumber - e._winding == reg._windingNumber);
if (cleanUp)
{
// Check for intersections between newly adjacent edges.
WalkDirtyRegions(regPrev);
}
}
public static bool VertCCW(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
return (u._s * (v._t - w._t) + v._s * (w._t - u._t) + w._s * (u._t - v._t)) >= 0.0f;
}
public static bool VertLeq(MeshUtils.Vertex lhs, MeshUtils.Vertex rhs)
{
return (lhs._s < rhs._s) || (lhs._s == rhs._s && lhs._t <= rhs._t);
}
/// <summary>
/// Removes the edge eDel. There are several cases:
/// if (eDel->Lface != eDel->Rface), we join two loops into one; the loop
/// eDel->Lface is deleted. Otherwise, we are splitting one loop into two;
/// the newly created loop will contain eDel->Dst. If the deletion of eDel
/// would create isolated vertices, those are deleted as well.
/// </summary>
public void Delete(MeshUtils.Edge eDel)
{
var eDelSym = eDel._Sym;
// First step: disconnect the origin vertex eDel->Org. We make all
// changes to get a consistent mesh in this "intermediate" state.
bool joiningLoops = false;
if (eDel._Lface != eDel._Rface)
{
// We are joining two loops into one -- remove the left face
joiningLoops = true;
MeshUtils.KillFace(eDel._Lface, eDel._Rface);
}
if (eDel._Onext == eDel)
{
MeshUtils.KillVertex(eDel._Org, null);
} else
{
// Make sure that eDel->Org and eDel->Rface point to valid half-edges
eDel._Rface._anEdge = eDel._Oprev;
eDel._Org._anEdge = eDel._Onext;
MeshUtils.Splice(eDel, eDel._Oprev);
if (!joiningLoops)
{
// We are splitting one loop into two -- create a new loop for eDel.
MeshUtils.MakeFace(new MeshUtils.Face(), eDel, eDel._Lface);
}
}
// Claim: the mesh is now in a consistent state, except that eDel->Org
// may have been deleted. Now we disconnect eDel->Dst.
if (eDelSym._Onext == eDelSym)
{
MeshUtils.KillVertex(eDelSym._Org, null);
MeshUtils.KillFace(eDelSym._Lface, null);
} else
{
// Make sure that eDel->Dst and eDel->Lface point to valid half-edges
eDel._Lface._anEdge = eDelSym._Oprev;
eDelSym._Org._anEdge = eDelSym._Onext;
MeshUtils.Splice(eDelSym, eDelSym._Oprev);
}
// Any isolated vertices or faces have already been freed.
MeshUtils.KillEdge(eDel);
}
/// <summary>
/// Creates a new edge such that eNew == eOrg.Lnext and eNew.Dst is a newly created vertex.
/// eOrg and eNew will have the same left face.
/// </summary>
public MeshUtils.Edge AddEdgeVertex(MeshUtils.Edge eOrg)
{
var eNew = MeshUtils.MakeEdge(eOrg);
var eNewSym = eNew._Sym;
// Connect the new edge appropriately
MeshUtils.Splice(eNew, eOrg._Lnext);
// Set vertex and face information
eNew._Org = eOrg._Dst;
MeshUtils.MakeVertex(new MeshUtils.Vertex(), eNewSym, eNew._Org);
eNew._Lface = eNewSym._Lface = eOrg._Lface;
return eNew;
}
/// <summary>
/// Destroys a face and removes it from the global face list. All edges of
/// fZap will have a NULL pointer as their left face. Any edges which
/// also have a NULL pointer as their right face are deleted entirely
/// (along with any isolated vertices this produces).
/// An entire mesh can be deleted by zapping its faces, one at a time,
/// in any order. Zapped faces cannot be used in further mesh operations!
/// </summary>
public void ZapFace(MeshUtils.Face fZap)
{
var eStart = fZap._anEdge;
// walk around face, deleting edges whose right face is also NULL
var eNext = eStart._Lnext;
MeshUtils.Edge e, eSym;
do
{
e = eNext;
eNext = e._Lnext;
e._Lface = null;
if (e._Rface == null)
{
// delete the edge -- see TESSmeshDelete above
if (e._Onext == e)
{
MeshUtils.KillVertex(e._Org, null);
} else
{
// Make sure that e._Org points to a valid half-edge
e._Org._anEdge = e._Onext;
MeshUtils.Splice(e, e._Oprev);
}
eSym = e._Sym;
if (eSym._Onext == eSym)
{
MeshUtils.KillVertex(eSym._Org, null);
} else
{
// Make sure that eSym._Org points to a valid half-edge
eSym._Org._anEdge = eSym._Onext;
MeshUtils.Splice(eSym, eSym._Oprev);
}
MeshUtils.KillEdge(e);
}
} while (e != eStart);
/* delete from circular doubly-linked list */
var fPrev = fZap._prev;
var fNext = fZap._next;
fNext._prev = fPrev;
fPrev._next = fNext;
}
/// <summary>
/// Creates a new edge from eOrg->Dst to eDst->Org, and returns the corresponding half-edge eNew.
/// If eOrg->Lface == eDst->Lface, this splits one loop into two,
/// and the newly created loop is eNew->Lface. Otherwise, two disjoint
/// loops are merged into one, and the loop eDst->Lface is destroyed.
///
/// If (eOrg == eDst), the new face will have only two edges.
/// If (eOrg->Lnext == eDst), the old face is reduced to a single edge.
/// If (eOrg->Lnext->Lnext == eDst), the old face is reduced to two edges.
/// </summary>
public MeshUtils.Edge Connect(MeshUtils.Edge eOrg, MeshUtils.Edge eDst)
{
var eNew = MeshUtils.MakeEdge(eOrg);
var eNewSym = eNew._Sym;
bool joiningLoops = false;
if (eDst._Lface != eOrg._Lface)
{
// We are connecting two disjoint loops -- destroy eDst->Lface
joiningLoops = true;
MeshUtils.KillFace(eDst._Lface, eOrg._Lface);
}
// Connect the new edge appropriately
MeshUtils.Splice(eNew, eOrg._Lnext);
MeshUtils.Splice(eNewSym, eDst);
// Set the vertex and face information
eNew._Org = eOrg._Dst;
eNewSym._Org = eDst._Org;
eNew._Lface = eNewSym._Lface = eOrg._Lface;
// Make sure the old face points to a valid half-edge
eOrg._Lface._anEdge = eNewSym;
if (!joiningLoops)
{
MeshUtils.MakeFace(new MeshUtils.Face(), eNew, eOrg._Lface);
}
return eNew;
}
/// <summary>
/// Splits eOrg into two edges eOrg and eNew such that eNew == eOrg.Lnext.
/// The new vertex is eOrg.Dst == eNew.Org.
/// eOrg and eNew will have the same left face.
/// </summary>
public MeshUtils.Edge SplitEdge(MeshUtils.Edge eOrg)
{
var eTmp = AddEdgeVertex(eOrg);
var eNew = eTmp._Sym;
// Disconnect eOrg from eOrg->Dst and connect it to eNew->Org
MeshUtils.Splice(eOrg._Sym, eOrg._Sym._Oprev);
MeshUtils.Splice(eOrg._Sym, eNew);
// Set the vertex and face information
eOrg._Dst = eNew._Org;
eNew._Dst._anEdge = eNew._Sym; // may have pointed to eOrg->Sym
eNew._Rface = eOrg._Rface;
eNew._winding = eOrg._winding; // copy old winding information
eNew._Sym._winding = eOrg._Sym._winding;
return eNew;
}
public static bool VertEq(MeshUtils.Vertex lhs, MeshUtils.Vertex rhs)
{
return lhs._s == rhs._s && lhs._t == rhs._t;
}
/// <summary>
/// Returns a number whose sign matches EdgeEval(u,v,w) but which
/// is cheaper to evaluate. Returns > 0, == 0 , or < 0
/// as v is above, on, or below the edge uw.
/// </summary>
public static float EdgeSign(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
Debug.Assert(VertLeq(u, v) && VertLeq(v, w));
float gapL = v._s - u._s;
float gapR = w._s - v._s;
if (gapL + gapR > 0.0f)
{
return (v._t - w._t) * gapL + (v._t - u._t) * gapR;
}
/* vertical line */
return 0.0f;
}
public static bool TransLeq(MeshUtils.Vertex lhs, MeshUtils.Vertex rhs)
{
return (lhs._t < rhs._t) || (lhs._t == rhs._t && lhs._s <= rhs._s);
}
public static float TransSign(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
Debug.Assert(TransLeq(u, v) && TransLeq(v, w));
float gapL = v._t - u._t;
float gapR = w._t - v._t;
if (gapL + gapR > 0.0f)
{
return (v._s - w._s) * gapL + (v._s - u._s) * gapR;
}
/* vertical line */
return 0.0f;
}
/// <summary>
/// Add a new active region to the sweep line, *somewhere* below "regAbove"
/// (according to where the new edge belongs in the sweep-line dictionary).
/// The upper edge of the new region will be "eNewUp".
/// Winding number and "inside" flag are not updated.
/// </summary>
private ActiveRegion AddRegionBelow(ActiveRegion regAbove, MeshUtils.Edge eNewUp)
{
var regNew = new ActiveRegion();
regNew._eUp = eNewUp;
regNew._nodeUp = _dict.InsertBefore(regAbove._nodeUp, regNew);
regNew._fixUpperEdge = false;
regNew._sentinel = false;
regNew._dirty = false;
eNewUp._activeRegion = regNew;
return regNew;
}
public static bool EdgeGoesLeft(MeshUtils.Edge e)
{
return VertLeq(e._Dst, e._Org);
}
/// <summary>
/// Two vertices with idential coordinates are combined into one.
/// e1.Org is kept, while e2.Org is discarded.
/// </summary>
private void SpliceMergeVertices(MeshUtils.Edge e1, MeshUtils.Edge e2)
{
_mesh.Splice(e1, e2);
}
public static bool EdgeGoesRight(MeshUtils.Edge e)
{
return VertLeq(e._Org, e._Dst);
}
/// <summary>
/// We've computed a new intersection point, now we need a "data" pointer
/// from the user so that we can refer to this new vertex in the
/// rendering callbacks.
/// </summary>
private void GetIntersectData(MeshUtils.Vertex isect, MeshUtils.Vertex orgUp, MeshUtils.Vertex dstUp, MeshUtils.Vertex orgLo, MeshUtils.Vertex dstLo)
{
isect._coords = Vec3.Zero;
float w0, w1, w2, w3;
VertexWeights(isect, orgUp, dstUp, out w0, out w1);
VertexWeights(isect, orgLo, dstLo, out w2, out w3);
if (_combineCallback != null)
{
isect._data = _combineCallback(
isect._coords,
new object[]
{
orgUp._data,
dstUp._data,
orgLo._data,
dstLo._data
},
new float[] { w0, w1, w2, w3 }
);
}
}
public static float VertL1dist(MeshUtils.Vertex u, MeshUtils.Vertex v)
{
return Math.Abs(u._s - v._s) + Math.Abs(u._t - v._t);
}
/// <summary>
/// The event vertex lies exacty on an already-processed edge or vertex.
/// Adding the new vertex involves splicing it into the already-processed
/// part of the mesh.
/// </summary>
private void ConnectLeftDegenerate(ActiveRegion regUp, MeshUtils.Vertex vEvent)
{
var e = regUp._eUp;
if (Geom.VertEq(e._Org, vEvent))
{
// e.Org is an unprocessed vertex - just combine them, and wait
// for e.Org to be pulled from the queue
// C# : in the C version, there is a flag but it was never implemented
// the vertices are before beginning the tesselation
throw new InvalidOperationException("Vertices should have been merged before");
}
if (!Geom.VertEq(e._Dst, vEvent))
{
// General case -- splice vEvent into edge e which passes through it
_mesh.SplitEdge(e._Sym);
if (regUp._fixUpperEdge)
{
// This edge was fixable -- delete unused portion of original edge
_mesh.Delete(e._Onext);
regUp._fixUpperEdge = false;
}
_mesh.Splice(vEvent._anEdge, e);
SweepEvent(vEvent); // recurse
return;
}
// See above
throw new InvalidOperationException("Vertices should have been merged before");
}
public static void AddWinding(MeshUtils.Edge eDst, MeshUtils.Edge eSrc)
{
eDst._winding += eSrc._winding;
eDst._Sym._winding += eSrc._Sym._winding;
}
/// <summary>
/// Does everything necessary when the sweep line crosses a vertex.
/// Updates the mesh and the edge dictionary.
/// </summary>
private void SweepEvent(MeshUtils.Vertex vEvent)
{
_event = vEvent;
// Check if this vertex is the right endpoint of an edge that is
// already in the dictionary. In this case we don't need to waste
// time searching for the location to insert new edges.
var e = vEvent._anEdge;
while (e._activeRegion == null)
{
e = e._Onext;
if (e == vEvent._anEdge)
{
// All edges go right -- not incident to any processed edges
ConnectLeftVertex(vEvent);
return;
}
}
// Processing consists of two phases: first we "finish" all the
// active regions where both the upper and lower edges terminate
// at vEvent (ie. vEvent is closing off these regions).
// We mark these faces "inside" or "outside" the polygon according
// to their winding number, and delete the edges from the dictionary.
// This takes care of all the left-going edges from vEvent.
var regUp = TopLeftRegion(e._activeRegion);
var reg = RegionBelow(regUp);
var eTopLeft = reg._eUp;
var eBottomLeft = FinishLeftRegions(reg, null);
// Next we process all the right-going edges from vEvent. This
// involves adding the edges to the dictionary, and creating the
// associated "active regions" which record information about the
// regions between adjacent dictionary edges.
if (eBottomLeft._Onext == eTopLeft)
{
// No right-going edges -- add a temporary "fixable" edge
ConnectRightVertex(regUp, eBottomLeft);
} else
{
AddRightEdges(regUp, eBottomLeft._Onext, eTopLeft, eTopLeft, true);
}
}
private int GetNeighbourFace(MeshUtils.Edge edge)
{
if (edge._Rface == null)
return MeshUtils.Undef;
if (!edge._Rface._inside)
return MeshUtils.Undef;
return edge._Rface._n;
}
