/*
** SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
** Copyright (C) 2011 Silicon Graphics, Inc.
** All Rights Reserved.
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**
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**
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** INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
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** OR OTHER DEALINGS IN THE SOFTWARE.
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*/
/*
** Original Author: Eric Veach, July 1994.
** libtess2: Mikko Mononen, http://code.google.com/p/libtess2/.
** LibTessDotNet: Remi Gillig, https://github.com/speps/LibTessDotNet
*/
using System;
using System.Diagnostics;
namespace UnityEngine.Rendering.Universal
{
using Real = System.Single;
namespace LibTessDotNet
{
internal partial class Tess
{
internal class ActiveRegion
{
internal MeshUtils.Edge _eUp;
internal Dict<ActiveRegion>.Node _nodeUp;
internal int _windingNumber;
internal bool _inside, _sentinel, _dirty, _fixUpperEdge;
}
private ActiveRegion RegionBelow(ActiveRegion reg)
{
return reg._nodeUp._prev._key;
}
private ActiveRegion RegionAbove(ActiveRegion reg)
{
return reg._nodeUp._next._key;
}
/// <summary>
/// Both edges must be directed from right to left (this is the canonical
/// direction for the upper edge of each region).
///
/// The strategy is to evaluate a "t" value for each edge at the
/// current sweep line position, given by tess->event. The calculations
/// are designed to be very stable, but of course they are not perfect.
///
/// Special case: if both edge destinations are at the sweep event,
/// we sort the edges by slope (they would otherwise compare equally).
/// </summary>
private bool EdgeLeq(ActiveRegion reg1, ActiveRegion reg2)
{
var e1 = reg1._eUp;
var e2 = reg2._eUp;
if (e1._Dst == _event)
{
if (e2._Dst == _event)
{
// Two edges right of the sweep line which meet at the sweep event.
// Sort them by slope.
if (Geom.VertLeq(e1._Org, e2._Org))
{
return Geom.EdgeSign(e2._Dst, e1._Org, e2._Org) <= 0.0f;
}
return Geom.EdgeSign(e1._Dst, e2._Org, e1._Org) >= 0.0f;
}
return Geom.EdgeSign(e2._Dst, _event, e2._Org) <= 0.0f;
}
if (e2._Dst == _event)
{
return Geom.EdgeSign(e1._Dst, _event, e1._Org) >= 0.0f;
}
// General case - compute signed distance *from* e1, e2 to event
var t1 = Geom.EdgeEval(e1._Dst, _event, e1._Org);
var t2 = Geom.EdgeEval(e2._Dst, _event, e2._Org);
return (t1 >= t2);
}
private void DeleteRegion(ActiveRegion reg)
{
if (reg._fixUpperEdge)
{
// It was created with zero winding number, so it better be
// deleted with zero winding number (ie. it better not get merged
// with a real edge).
Debug.Assert(reg._eUp._winding == 0);
}
reg._eUp._activeRegion = null;
_dict.Remove(reg._nodeUp);
}
/// <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;
}
private ActiveRegion TopLeftRegion(ActiveRegion reg)
{
var org = reg._eUp._Org;
// Find the region above the uppermost edge with the same origin
do
{
reg = RegionAbove(reg);
}
while (reg._eUp._Org == org);
// If the edge above was a temporary edge introduced by ConnectRightVertex,
// now is the time to fix it.
if (reg._fixUpperEdge)
{
var e = _mesh.Connect(RegionBelow(reg)._eUp._Sym, reg._eUp._Lnext);
FixUpperEdge(reg, e);
reg = RegionAbove(reg);
}
return reg;
}
private ActiveRegion TopRightRegion(ActiveRegion reg)
{
var dst = reg._eUp._Dst;
// Find the region above the uppermost edge with the same destination
do
{
reg = RegionAbove(reg);
}
while (reg._eUp._Dst == dst);
return reg;
}
/// <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;
}
private void ComputeWinding(ActiveRegion reg)
{
reg._windingNumber = RegionAbove(reg)._windingNumber + reg._eUp._winding;
reg._inside = Geom.IsWindingInside(_windingRule, reg._windingNumber);
}
/// <summary>
/// Delete a region from the sweep line. This happens when the upper
/// and lower chains of a region meet (at a vertex on the sweep line).
/// The "inside" flag is copied to the appropriate mesh face (we could
/// not do this before -- since the structure of the mesh is always
/// changing, this face may not have even existed until now).
/// </summary>
private void FinishRegion(ActiveRegion reg)
{
var e = reg._eUp;
var f = e._Lface;
f._inside = reg._inside;
f._anEdge = e;
DeleteRegion(reg);
}
/// <summary>
/// We are given a vertex with one or more left-going edges. All affected
/// edges should be in the edge dictionary. Starting at regFirst->eUp,
/// we walk down deleting all regions where both edges have the same
/// origin vOrg. At the same time we copy the "inside" flag from the
/// active region to the face, since at this point each face will belong
/// to at most one region (this was not necessarily true until this point
/// in the sweep). The walk stops at the region above regLast; if regLast
/// is null we walk as far as possible. At the same time we relink the
/// mesh if necessary, so that the ordering of edges around vOrg is the
/// same as in the dictionary.
/// </summary>
private MeshUtils.Edge FinishLeftRegions(ActiveRegion regFirst, ActiveRegion regLast)
{
var regPrev = regFirst;
var ePrev = regFirst._eUp;
while (regPrev != regLast)
{
regPrev._fixUpperEdge = false; // placement was OK
var reg = RegionBelow(regPrev);
var e = reg._eUp;
if (e._Org != ePrev._Org)
{
if (!reg._fixUpperEdge)
{
// Remove the last left-going edge. Even though there are no further
// edges in the dictionary with this origin, there may be further
// such edges in the mesh (if we are adding left edges to a vertex
// that has already been processed). Thus it is important to call
// FinishRegion rather than just DeleteRegion.
FinishRegion(regPrev);
break;
}
// If the edge below was a temporary edge introduced by
// ConnectRightVertex, now is the time to fix it.
e = _mesh.Connect(ePrev._Lprev, e._Sym);
FixUpperEdge(reg, e);
}
// Relink edges so that ePrev.Onext == e
if (ePrev._Onext != e)
{
_mesh.Splice(e._Oprev, e);
_mesh.Splice(ePrev, e);
}
FinishRegion(regPrev); // may change reg.eUp
ePrev = reg._eUp;
regPrev = reg;
}
return ePrev;
}
/// <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);
}
}
/// <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);
}
/// <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 Real w0, out Real w1)
{
var t1 = Geom.VertL1dist(org, isect);
var t2 = Geom.VertL1dist(dst, isect);
w0 = (t2 / (t1 + t2)) / 2.0f;
w1 = (t1 / (t1 + t2)) / 2.0f;
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>
/// 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;
Real 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 Real[] { w0, w1, w2, w3 }
);
}
}
/// <summary>
/// Check the upper and lower edge of "regUp", to make sure that the
/// eUp->Org is above eLo, or eLo->Org is below eUp (depending on which
/// origin is leftmost).
///
/// The main purpose is to splice right-going edges with the same
/// dest vertex and nearly identical slopes (ie. we can't distinguish
/// the slopes numerically). However the splicing can also help us
/// to recover from numerical errors. For example, suppose at one
/// point we checked eUp and eLo, and decided that eUp->Org is barely
/// above eLo. Then later, we split eLo into two edges (eg. from
/// a splice operation like this one). This can change the result of
/// our test so that now eUp->Org is incident to eLo, or barely below it.
/// We must correct this condition to maintain the dictionary invariants.
///
/// One possibility is to check these edges for intersection again
/// (ie. CheckForIntersect). This is what we do if possible. However
/// CheckForIntersect requires that tess->event lies between eUp and eLo,
/// so that it has something to fall back on when the intersection
/// calculation gives us an unusable answer. So, for those cases where
/// we can't check for intersection, this routine fixes the problem
/// by just splicing the offending vertex into the other edge.
/// This is a guaranteed solution, no matter how degenerate things get.
/// Basically this is a combinatorial solution to a numerical problem.
/// </summary>
private bool CheckForRightSplice(ActiveRegion regUp)
{
var regLo = RegionBelow(regUp);
var eUp = regUp._eUp;
var eLo = regLo._eUp;
if (Geom.VertLeq(eUp._Org, eLo._Org))
{
if (Geom.EdgeSign(eLo._Dst, eUp._Org, eLo._Org) > 0.0f)
{
return false;
}
// eUp.Org appears to be below eLo
if (!Geom.VertEq(eUp._Org, eLo._Org))
{
// Splice eUp._Org into eLo
_mesh.SplitEdge(eLo._Sym);
_mesh.Splice(eUp, eLo._Oprev);
regUp._dirty = regLo._dirty = true;
}
else if (eUp._Org != eLo._Org)
{
// merge the two vertices, discarding eUp.Org
_pq.Remove(eUp._Org._pqHandle);
SpliceMergeVertices(eLo._Oprev, eUp);
}
}
else
{
if (Geom.EdgeSign(eUp._Dst, eLo._Org, eUp._Org) < 0.0f)
{
return false;
}
// eLo.Org appears to be above eUp, so splice eLo.Org into eUp
RegionAbove(regUp)._dirty = regUp._dirty = true;
_mesh.SplitEdge(eUp._Sym);
_mesh.Splice(eLo._Oprev, eUp);
}
return true;
}
/// <summary>
/// Check the upper and lower edge of "regUp", to make sure that the
/// eUp->Dst is above eLo, or eLo->Dst is below eUp (depending on which
/// destination is rightmost).
///
/// Theoretically, this should always be true. However, splitting an edge
/// into two pieces can change the results of previous tests. For example,
/// suppose at one point we checked eUp and eLo, and decided that eUp->Dst
/// is barely above eLo. Then later, we split eLo into two edges (eg. from
/// a splice operation like this one). This can change the result of
/// the test so that now eUp->Dst is incident to eLo, or barely below it.
/// We must correct this condition to maintain the dictionary invariants
/// (otherwise new edges might get inserted in the wrong place in the
/// dictionary, and bad stuff will happen).
///
/// We fix the problem by just splicing the offending vertex into the
/// other edge.
/// </summary>
private bool CheckForLeftSplice(ActiveRegion regUp)
{
var regLo = RegionBelow(regUp);
var eUp = regUp._eUp;
var eLo = regLo._eUp;
Debug.Assert(!Geom.VertEq(eUp._Dst, eLo._Dst));
if (Geom.VertLeq(eUp._Dst, eLo._Dst))
{
if (Geom.EdgeSign(eUp._Dst, eLo._Dst, eUp._Org) < 0.0f)
{
return false;
}
// eLo.Dst is above eUp, so splice eLo.Dst into eUp
RegionAbove(regUp)._dirty = regUp._dirty = true;
var e = _mesh.SplitEdge(eUp);
_mesh.Splice(eLo._Sym, e);
e._Lface._inside = regUp._inside;
}
else
{
if (Geom.EdgeSign(eLo._Dst, eUp._Dst, eLo._Org) > 0.0f)
{
return false;
}
// eUp.Dst is below eLo, so splice eUp.Dst into eLo
regUp._dirty = regLo._dirty = true;
var e = _mesh.SplitEdge(eLo);
_mesh.Splice(eUp._Lnext, eLo._Sym);
e._Rface._inside = regUp._inside;
}
return true;
}
/// <summary>
/// Check the upper and lower edges of the given region to see if
/// they intersect. If so, create the intersection and add it
/// to the data structures.
///
/// Returns TRUE if adding the new intersection resulted in a recursive
/// call to AddRightEdges(); in this case all "dirty" regions have been
/// checked for intersections, and possibly regUp has been deleted.
/// </summary>
private bool CheckForIntersect(ActiveRegion regUp)
{
var regLo = RegionBelow(regUp);
var eUp = regUp._eUp;
var eLo = regLo._eUp;
var orgUp = eUp._Org;
var orgLo = eLo._Org;
var dstUp = eUp._Dst;
var dstLo = eLo._Dst;
Debug.Assert(!Geom.VertEq(dstLo, dstUp));
Debug.Assert(Geom.EdgeSign(dstUp, _event, orgUp) <= 0.0f);
Debug.Assert(Geom.EdgeSign(dstLo, _event, orgLo) >= 0.0f);
Debug.Assert(orgUp != _event && orgLo != _event);
Debug.Assert(!regUp._fixUpperEdge && !regLo._fixUpperEdge);
if (orgUp == orgLo)
{
// right endpoints are the same
return false;
}
var tMinUp = Math.Min(orgUp._t, dstUp._t);
var tMaxLo = Math.Max(orgLo._t, dstLo._t);
if (tMinUp > tMaxLo)
{
// t ranges do not overlap
return false;
}
if (Geom.VertLeq(orgUp, orgLo))
{
if (Geom.EdgeSign(dstLo, orgUp, orgLo) > 0.0f)
{
return false;
}
}
else
{
if (Geom.EdgeSign(dstUp, orgLo, orgUp) < 0.0f)
{
return false;
}
}
// At this point the edges intersect, at least marginally
var isect = MeshUtils.Vertex.Create();
Geom.EdgeIntersect(dstUp, orgUp, dstLo, orgLo, isect);
// The following properties are guaranteed:
Debug.Assert(Math.Min(orgUp._t, dstUp._t) <= isect._t);
Debug.Assert(isect._t <= Math.Max(orgLo._t, dstLo._t));
Debug.Assert(Math.Min(dstLo._s, dstUp._s) <= isect._s);
Debug.Assert(isect._s <= Math.Max(orgLo._s, orgUp._s));
if (Geom.VertLeq(isect, _event))
{
// The intersection point lies slightly to the left of the sweep line,
// so move it until it''s slightly to the right of the sweep line.
// (If we had perfect numerical precision, this would never happen
// in the first place). The easiest and safest thing to do is
// replace the intersection by tess._event.
isect._s = _event._s;
isect._t = _event._t;
}
// Similarly, if the computed intersection lies to the right of the
// rightmost origin (which should rarely happen), it can cause
// unbelievable inefficiency on sufficiently degenerate inputs.
// (If you have the test program, try running test54.d with the
// "X zoom" option turned on).
var orgMin = Geom.VertLeq(orgUp, orgLo) ? orgUp : orgLo;
if (Geom.VertLeq(orgMin, isect))
{
isect._s = orgMin._s;
isect._t = orgMin._t;
}
if (Geom.VertEq(isect, orgUp) || Geom.VertEq(isect, orgLo))
{
// Easy case -- intersection at one of the right endpoints
CheckForRightSplice(regUp);
return false;
}
if ((!Geom.VertEq(dstUp, _event)
&& Geom.EdgeSign(dstUp, _event, isect) >= 0.0f)
|| (!Geom.VertEq(dstLo, _event)
&& Geom.EdgeSign(dstLo, _event, isect) <= 0.0f))
{
// Very unusual -- the new upper or lower edge would pass on the
// wrong side of the sweep event, or through it. This can happen
// due to very small numerical errors in the intersection calculation.
if (dstLo == _event)
{
// Splice dstLo into eUp, and process the new region(s)
_mesh.SplitEdge(eUp._Sym);
_mesh.Splice(eLo._Sym, eUp);
regUp = TopLeftRegion(regUp);
eUp = RegionBelow(regUp)._eUp;
FinishLeftRegions(RegionBelow(regUp), regLo);
AddRightEdges(regUp, eUp._Oprev, eUp, eUp, true);
return true;
}
if (dstUp == _event)
{
/* Splice dstUp into eLo, and process the new region(s) */
_mesh.SplitEdge(eLo._Sym);
_mesh.Splice(eUp._Lnext, eLo._Oprev);
regLo = regUp;
regUp = TopRightRegion(regUp);
var e = RegionBelow(regUp)._eUp._Rprev;
regLo._eUp = eLo._Oprev;
eLo = FinishLeftRegions(regLo, null);
AddRightEdges(regUp, eLo._Onext, eUp._Rprev, e, true);
return true;
}
// Special case: called from ConnectRightVertex. If either
// edge passes on the wrong side of tess._event, split it
// (and wait for ConnectRightVertex to splice it appropriately).
if (Geom.EdgeSign(dstUp, _event, isect) >= 0.0f)
{
RegionAbove(regUp)._dirty = regUp._dirty = true;
_mesh.SplitEdge(eUp._Sym);
eUp._Org._s = _event._s;
eUp._Org._t = _event._t;
}
if (Geom.EdgeSign(dstLo, _event, isect) <= 0.0f)
{
regUp._dirty = regLo._dirty = true;
_mesh.SplitEdge(eLo._Sym);
eLo._Org._s = _event._s;
eLo._Org._t = _event._t;
}
// leave the rest for ConnectRightVertex
return false;
}
// General case -- split both edges, splice into new vertex.
// When we do the splice operation, the order of the arguments is
// arbitrary as far as correctness goes. However, when the operation
// creates a new face, the work done is proportional to the size of
// the new face. We expect the faces in the processed part of
// the mesh (ie. eUp._Lface) to be smaller than the faces in the
// unprocessed original contours (which will be eLo._Oprev._Lface).
_mesh.SplitEdge(eUp._Sym);
_mesh.SplitEdge(eLo._Sym);
_mesh.Splice(eLo._Oprev, eUp);
eUp._Org._s = isect._s;
eUp._Org._t = isect._t;
eUp._Org._pqHandle = _pq.Insert(eUp._Org);
if (eUp._Org._pqHandle._handle == PQHandle.Invalid)
{
throw new InvalidOperationException("PQHandle should not be invalid");
}
GetIntersectData(eUp._Org, orgUp, dstUp, orgLo, dstLo);
RegionAbove(regUp)._dirty = regUp._dirty = regLo._dirty = true;
return false;
}
/// <summary>
/// When the upper or lower edge of any region changes, the region is
/// marked "dirty". This routine walks through all the dirty regions
/// and makes sure that the dictionary invariants are satisfied
/// (see the comments at the beginning of this file). Of course
/// new dirty regions can be created as we make changes to restore
/// the invariants.
/// </summary>
private void WalkDirtyRegions(ActiveRegion regUp)
{
var regLo = RegionBelow(regUp);
MeshUtils.Edge eUp, eLo;
while (true)
{
// Find the lowest dirty region (we walk from the bottom up).
while (regLo._dirty)
{
regUp = regLo;
regLo = RegionBelow(regLo);
}
if (!regUp._dirty)
{
regLo = regUp;
regUp = RegionAbove(regUp);
if (regUp == null || !regUp._dirty)
{
// We've walked all the dirty regions
return;
}
}
regUp._dirty = false;
eUp = regUp._eUp;
eLo = regLo._eUp;
if (eUp._Dst != eLo._Dst)
{
// Check that the edge ordering is obeyed at the Dst vertices.
if (CheckForLeftSplice(regUp))
{
// If the upper or lower edge was marked fixUpperEdge, then
// we no longer need it (since these edges are needed only for
// vertices which otherwise have no right-going edges).
if (regLo._fixUpperEdge)
{
DeleteRegion(regLo);
_mesh.Delete(eLo);
regLo = RegionBelow(regUp);
eLo = regLo._eUp;
}
else if (regUp._fixUpperEdge)
{
DeleteRegion(regUp);
_mesh.Delete(eUp);
regUp = RegionAbove(regLo);
eUp = regUp._eUp;
}
}
}
if (eUp._Org != eLo._Org)
{
if (eUp._Dst != eLo._Dst
&& !regUp._fixUpperEdge && !regLo._fixUpperEdge
&& (eUp._Dst == _event || eLo._Dst == _event))
{
// When all else fails in CheckForIntersect(), it uses tess._event
// as the intersection location. To make this possible, it requires
// that tess._event lie between the upper and lower edges, and also
// that neither of these is marked fixUpperEdge (since in the worst
// case it might splice one of these edges into tess.event, and
// violate the invariant that fixable edges are the only right-going
// edge from their associated vertex).
if (CheckForIntersect(regUp))
{
// WalkDirtyRegions() was called recursively; we're done
return;
}
}
else
{
// Even though we can't use CheckForIntersect(), the Org vertices
// may violate the dictionary edge ordering. Check and correct this.
CheckForRightSplice(regUp);
}
}
if (eUp._Org == eLo._Org && eUp._Dst == eLo._Dst)
{
// A degenerate loop consisting of only two edges -- delete it.
Geom.AddWinding(eLo, eUp);
DeleteRegion(regUp);
_mesh.Delete(eUp);
regUp = RegionAbove(regLo);
}
}
}
/// <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>
/// 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 tessellation
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");
}
/// <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>
/// 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);
}
}
/// <summary>
/// Make the sentinel coordinates big enough that they will never be
/// merged with real input features.
///
/// We add two sentinel edges above and below all other edges,
/// to avoid special cases at the top and bottom.
/// </summary>
private void AddSentinel(Real smin, Real smax, Real t)
{
var e = _mesh.MakeEdge();
e._Org._s = smax;
e._Org._t = t;
e._Dst._s = smin;
e._Dst._t = t;
_event = e._Dst; // initialize it
var reg = new ActiveRegion();
reg._eUp = e;
reg._windingNumber = 0;
reg._inside = false;
reg._fixUpperEdge = false;
reg._sentinel = true;
reg._dirty = false;
reg._nodeUp = _dict.Insert(reg);
}
/// <summary>
/// We maintain an ordering of edge intersections with the sweep line.
/// This order is maintained in a dynamic dictionary.
/// </summary>
private void InitEdgeDict()
{
_dict = new Dict<ActiveRegion>(EdgeLeq);
AddSentinel(-SentinelCoord, SentinelCoord, -SentinelCoord);
AddSentinel(-SentinelCoord, SentinelCoord, +SentinelCoord);
}
private void DoneEdgeDict()
{
int fixedEdges = 0;
ActiveRegion reg;
while ((reg = _dict.Min().Key) != null)
{
// At the end of all processing, the dictionary should contain
// only the two sentinel edges, plus at most one "fixable" edge
// created by ConnectRightVertex().
if (!reg._sentinel)
{
Debug.Assert(reg._fixUpperEdge);
Debug.Assert(++fixedEdges == 1);
}
Debug.Assert(reg._windingNumber == 0);
DeleteRegion(reg);
}
_dict = null;
}
/// <summary>
/// Remove zero-length edges, and contours with fewer than 3 vertices.
/// </summary>
private void RemoveDegenerateEdges()
{
MeshUtils.Edge eHead = _mesh._eHead, e, eNext, eLnext;
for (e = eHead._next; e != eHead; e = eNext)
{
eNext = e._next;
eLnext = e._Lnext;
if (Geom.VertEq(e._Org, e._Dst) && e._Lnext._Lnext != e)
{
// Zero-length edge, contour has at least 3 edges
SpliceMergeVertices(eLnext, e); // deletes e.Org
_mesh.Delete(e); // e is a self-loop
e = eLnext;
eLnext = e._Lnext;
}
if (eLnext._Lnext == e)
{
// Degenerate contour (one or two edges)
if (eLnext != e)
{
if (eLnext == eNext || eLnext == eNext._Sym)
{
eNext = eNext._next;
}
_mesh.Delete(eLnext);
}
if (e == eNext || e == eNext._Sym)
{
eNext = eNext._next;
}
_mesh.Delete(e);
}
}
}
/// <summary>
/// Insert all vertices into the priority queue which determines the
/// order in which vertices cross the sweep line.
/// </summary>
private void InitPriorityQ()
{
MeshUtils.Vertex vHead = _mesh._vHead, v;
int vertexCount = 0;
for (v = vHead._next; v != vHead; v = v._next)
{
vertexCount++;
}
// Make sure there is enough space for sentinels.
vertexCount += 8;
_pq = new PriorityQueue<MeshUtils.Vertex>(vertexCount, Geom.VertLeq);
vHead = _mesh._vHead;
for (v = vHead._next; v != vHead; v = v._next)
{
v._pqHandle = _pq.Insert(v);
if (v._pqHandle._handle == PQHandle.Invalid)
{
throw new InvalidOperationException("PQHandle should not be invalid");
}
}
_pq.Init();
}
private void DonePriorityQ()
{
_pq = null;
}
/// <summary>
/// Delete any degenerate faces with only two edges. WalkDirtyRegions()
/// will catch almost all of these, but it won't catch degenerate faces
/// produced by splice operations on already-processed edges.
/// The two places this can happen are in FinishLeftRegions(), when
/// we splice in a "temporary" edge produced by ConnectRightVertex(),
/// and in CheckForLeftSplice(), where we splice already-processed
/// edges to ensure that our dictionary invariants are not violated
/// by numerical errors.
///
/// In both these cases it is *very* dangerous to delete the offending
/// edge at the time, since one of the routines further up the stack
/// will sometimes be keeping a pointer to that edge.
/// </summary>
private void RemoveDegenerateFaces()
{
MeshUtils.Face f, fNext;
MeshUtils.Edge e;
for (f = _mesh._fHead._next; f != _mesh._fHead; f = fNext)
{
fNext = f._next;
e = f._anEdge;
Debug.Assert(e._Lnext != e);
if (e._Lnext._Lnext == e)
{
// A face with only two edges
Geom.AddWinding(e._Onext, e);
_mesh.Delete(e);
}
}
}
/// <summary>
/// ComputeInterior computes the planar arrangement specified
/// by the given contours, and further subdivides this arrangement
/// into regions. Each region is marked "inside" if it belongs
/// to the polygon, according to the rule given by windingRule.
/// Each interior region is guaranteed to be monotone.
/// </summary>
protected void ComputeInterior()
{
// Each vertex defines an event for our sweep line. Start by inserting
// all the vertices in a priority queue. Events are processed in
// lexicographic order, ie.
//
// e1 < e2 iff e1.x < e2.x || (e1.x == e2.x && e1.y < e2.y)
RemoveDegenerateEdges();
InitPriorityQ();
RemoveDegenerateFaces();
InitEdgeDict();
MeshUtils.Vertex v, vNext;
while ((v = _pq.ExtractMin()) != null)
{
while (true)
{
vNext = _pq.Minimum();
if (vNext == null || !Geom.VertEq(vNext, v))
{
break;
}
// Merge together all vertices at exactly the same location.
// This is more efficient than processing them one at a time,
// simplifies the code (see ConnectLeftDegenerate), and is also
// important for correct handling of certain degenerate cases.
// For example, suppose there are two identical edges A and B
// that belong to different contours (so without this code they would
// be processed by separate sweep events). Suppose another edge C
// crosses A and B from above. When A is processed, we split it
// at its intersection point with C. However this also splits C,
// so when we insert B we may compute a slightly different
// intersection point. This might leave two edges with a small
// gap between them. This kind of error is especially obvious
// when using boundary extraction (BoundaryOnly).
vNext = _pq.ExtractMin();
SpliceMergeVertices(v._anEdge, vNext._anEdge);
}
SweepEvent(v);
}
DoneEdgeDict();
DonePriorityQ();
RemoveDegenerateFaces();
_mesh.Check();
}
}
}
}