private void ComputeNormal(ref Vec3 norm)
{
var v = _mesh._vHead._next;
var minVal = new Real[3] { v._coords.X, v._coords.Y, v._coords.Z };
var minVert = new MeshUtils.Vertex[3] { v, v, v };
var maxVal = new Real[3] { v._coords.X, v._coords.Y, v._coords.Z };
var maxVert = new MeshUtils.Vertex[3] { v, v, v };
for (; v != _mesh._vHead; v = v._next)
{
if (v._coords.X < minVal[0]) { minVal[0] = v._coords.X; minVert[0] = v; }
if (v._coords.Y < minVal[1]) { minVal[1] = v._coords.Y; minVert[1] = v; }
if (v._coords.Z < minVal[2]) { minVal[2] = v._coords.Z; minVert[2] = v; }
if (v._coords.X > maxVal[0]) { maxVal[0] = v._coords.X; maxVert[0] = v; }
if (v._coords.Y > maxVal[1]) { maxVal[1] = v._coords.Y; maxVert[1] = v; }
if (v._coords.Z > maxVal[2]) { maxVal[2] = v._coords.Z; maxVert[2] = v; }
}
// Find two vertices separated by at least 1/sqrt(3) of the maximum
// distance between any two vertices
int i = 0;
if (maxVal[1] - minVal[1] > maxVal[0] - minVal[0]) { i = 1; }
if (maxVal[2] - minVal[2] > maxVal[i] - minVal[i]) { i = 2; }
if (minVal[i] >= maxVal[i])
{
// All vertices are the same -- normal doesn't matter
norm = new Vec3 { X = 0, Y = 0, Z = 1 };
return;
}
// Look for a third vertex which forms the triangle with maximum area
// (Length of normal == twice the triangle area)
Real maxLen2 = 0, tLen2;
var v1 = minVert[i];
var v2 = maxVert[i];
Vec3 d1, d2, tNorm;
Vec3.Sub(ref v1._coords, ref v2._coords, out d1);
for (v = _mesh._vHead._next; v != _mesh._vHead; v = v._next)
{
Vec3.Sub(ref v._coords, ref v2._coords, out d2);
tNorm.X = d1.Y * d2.Z - d1.Z * d2.Y;
tNorm.Y = d1.Z * d2.X - d1.X * d2.Z;
tNorm.Z = d1.X * d2.Y - d1.Y * d2.X;
tLen2 = tNorm.X*tNorm.X + tNorm.Y*tNorm.Y + tNorm.Z*tNorm.Z;
if (tLen2 > maxLen2)
{
maxLen2 = tLen2;
norm = tNorm;
}
}
if (maxLen2 <= 0.0f)
{
// All points lie on a single line -- any decent normal will do
norm = Vec3.Zero;
i = Vec3.LongAxis(ref d1);
norm[i] = 1;
}
}
static void Swap(ref MeshUtils.Vertex a, ref MeshUtils.Vertex b)
{
var tmp = a;
a = b;
b = tmp;
}
private ActiveRegion TopLeftRegion(ActiveRegion reg)
{
MeshUtils.Vertex org = reg._eUp._Org;
// Find the region above the uppermost edge with the same origin
do
{
reg = RegionAbove(reg);
} while (reg._eUp._Org == org);
switch (reg._fixUpperEdge)
{
// If the edge above was a temporary edge introduced by ConnectRightVertex,
// now is the time to fix it.
case true:
{
MeshUtils.Edge e = Mesh.Connect(_pool, RegionBelow(reg)._eUp._Sym, reg._eUp._Lnext);
FixUpperEdge(reg, e);
reg = RegionAbove(reg);
break;
}
}
return(reg);
}
private void CheckOrientation()
{
// When we compute the normal automatically, we choose the orientation
// so that the sum of the signed areas of all contours is non-negative.
double area = 0.0f;
for (MeshUtils.Face f = _mesh._fHead._next; f != _mesh._fHead; f = f._next)
{
switch (f._anEdge._winding)
{
case <= 0:
continue;
default:
area += MeshUtils.FaceArea(f);
break;
}
}
switch (area)
{
case < 0.0f:
{
// Reverse the orientation by flipping all the t-coordinates
for (MeshUtils.Vertex v = _mesh._vHead._next; v != _mesh._vHead; v = v._next)
{
v._t = -v._t;
}
Vec3.Neg(ref _tUnit);
break;
}
}
}
public void Check()
{
MeshUtils.Edge e;
MeshUtils.Face fPrev = _fHead, f;
for (fPrev = _fHead; (f = fPrev._next) != _fHead; fPrev = f)
{
e = f._anEdge;
do
{
Debug.Assert(e._Sym != e);
Debug.Assert(e._Sym._Sym == e);
Debug.Assert(e._Lnext._Onext._Sym == e);
Debug.Assert(e._Onext._Sym._Lnext == e);
Debug.Assert(e._Lface == f);
e = e._Lnext;
} while (e != f._anEdge);
}
Debug.Assert(f._prev == fPrev && f._anEdge == null);
MeshUtils.Vertex vPrev = _vHead, v;
for (vPrev = _vHead; (v = vPrev._next) != _vHead; vPrev = v)
{
Debug.Assert(v._prev == vPrev);
e = v._anEdge;
do
{
Debug.Assert(e._Sym != e);
Debug.Assert(e._Sym._Sym == e);
Debug.Assert(e._Lnext._Onext._Sym == e);
Debug.Assert(e._Onext._Sym._Lnext == e);
Debug.Assert(e._Org == v);
e = e._Onext;
} while (e != v._anEdge);
}
Debug.Assert(v._prev == vPrev && v._anEdge == null);
MeshUtils.Edge ePrev = _eHead;
for (ePrev = _eHead; (e = ePrev._next) != _eHead; ePrev = e)
{
Debug.Assert(e._Sym._next == ePrev._Sym);
Debug.Assert(e._Sym != e);
Debug.Assert(e._Sym._Sym == e);
Debug.Assert(e._Org != null);
Debug.Assert(e._Dst != null);
Debug.Assert(e._Lnext._Onext._Sym == e);
Debug.Assert(e._Onext._Sym._Lnext == e);
}
Debug.Assert(e._Sym._next == ePrev._Sym &&
e._Sym == _eHeadSym &&
e._Sym._Sym == e &&
e._Org == null && e._Dst == null &&
e._Lface == null && e._Rface == null);
}
/// <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 static void VertexWeights(MeshUtils.Vertex isect, MeshUtils.Vertex org, MeshUtils.Vertex dst, out double w0, out double w1)
{
double t1 = Geom.VertL1dist(org, isect);
double 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;
}
private ActiveRegion TopRightRegion(ActiveRegion reg)
{
MeshUtils.Vertex 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>
/// 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 Real EdgeSign(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
Debug.Assert(VertLeq(u, v) && VertLeq(v, w));
var gapL = v._s - u._s;
var 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;
}
public override void Reset()
{
MeshUtils.Face f = _fHead._next;
while (true)
{
MeshUtils.Face fNext = f._next;
f.Free();
if (f == _fHead)
{
break;
}
f = fNext;
}
MeshUtils.Vertex v = _vHead._next;
while (true)
{
MeshUtils.Vertex vNext = v._next;
v.Free();
if (v == _vHead)
{
break;
}
v = vNext;
}
for (int i = 0; i < _allEdgePairs.Count; i++)
{
MeshUtils.EdgePair pair = _allEdgePairs[i];
MeshUtils.Edge e = pair._e;
if (!e.IsReturnedToPool()) // (can be Free in KillEdge)
{
e.Free();
}
MeshUtils.Edge eSym = pair._eSym;
if (!eSym.IsReturnedToPool()) // (can be Free in KillEdge)
{
eSym.Free();
}
pair.Free();
}
_allEdgePairs.Clear();
_vHead = null;
_fHead = null;
_eHead = _eHeadSym = null;
}
public static Real TransSign(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
Debug.Assert(TransLeq(u, v) && TransLeq(v, w));
var gapL = v._t - u._t;
var 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;
}
/// <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;
VertexWeights(isect, orgUp, dstUp, out double w0, out double w1);
VertexWeights(isect, orgLo, dstLo, out double w2, out double w3);
if (_combineCallback != null)
{
isect._data = _combineCallback(
isect._coords,
new [] { orgUp._data, dstUp._data, orgLo._data, dstLo._data },
new [] { w0, w1, w2, w3 }
);
}
}
public override void OnFree()
{
for (MeshUtils.Face f = _fHead._next, fNext = _fHead; f != _fHead; f = fNext)
{
fNext = f._next;
f.Free();
}
for (MeshUtils.Vertex v = _vHead._next, vNext = _vHead; v != _vHead; v = vNext)
{
vNext = v._next;
v.Free();
}
for (MeshUtils.Edge e = _eHead._next, eNext = _eHead; e != _eHead; e = eNext)
{
eNext = e._next;
e.Free();
}
}
public void MergeConvexFaces(IPool pool, int maxVertsPerFace)
{
for (MeshUtils.Face f = _fHead._next; f != _fHead; f = f._next)
{
switch (f._inside)
{
// Skip faces which are outside the result
case false:
continue;
}
MeshUtils.Edge eCur = f._anEdge;
MeshUtils.Vertex vStart = eCur._Org;
while (true)
{
MeshUtils.Edge eNext = eCur._Lnext;
MeshUtils.Edge eSym = eCur._Sym;
if (eSym is { _Lface._inside: true })
/// <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 Real EdgeEval(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
Debug.Assert(VertLeq(u, v) && VertLeq(v, w));
var gapL = v._s - u._s;
var 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;
}
public static Real TransEval(MeshUtils.Vertex u, MeshUtils.Vertex v, MeshUtils.Vertex w)
{
Debug.Assert(TransLeq(u, v) && TransLeq(v, w));
var gapL = v._t - u._t;
var gapR = w._t - v._t;
if (gapL + gapR > 0.0f)
{
if (gapL < gapR)
{
return((v._s - u._s) + (u._s - w._s) * (gapL / (gapL + gapR)));
}
else
{
return((v._s - w._s) + (w._s - u._s) * (gapR / (gapL + gapR)));
}
}
/* vertical line */
return(0);
}
public void Reset(IPool pool)
{
for (MeshUtils.Face f = _fHead, fNext = _fHead; f._next != null; f = fNext)
{
fNext = f._next;
pool.Return(f);
}
for (MeshUtils.Vertex v = _vHead, vNext = _vHead; v._next != null; v = vNext)
{
vNext = v._next;
pool.Return(v);
}
for (MeshUtils.Edge e = _eHead, eNext = _eHead; e._next != null; e = eNext)
{
eNext = e._next;
pool.Return(e._Sym);
pool.Return(e);
}
_vHead = null;
_fHead = null;
_eHead = _eHeadSym = null;
}
public void Init(IPool pool)
{
var v = _vHead = pool.Get <MeshUtils.Vertex>();
var f = _fHead = pool.Get <MeshUtils.Face>();
var pair = MeshUtils.EdgePair.Create(pool);
var e = _eHead = pair._e;
var eSym = _eHeadSym = pair._eSym;
v._next = v._prev = v;
v._anEdge = null;
f._next = f._prev = f;
f._anEdge = null;
f._trail = null;
f._marked = false;
f._inside = false;
e._next = e;
e._Sym = eSym;
e._Onext = null;
e._Lnext = null;
e._Org = null;
e._Lface = null;
e._winding = 0;
e._activeRegion = null;
eSym._next = eSym;
eSym._Sym = e;
eSym._Onext = null;
eSym._Lnext = null;
eSym._Org = null;
eSym._Lface = null;
eSym._winding = 0;
eSym._activeRegion = null;
}
// ReSharper restore InconsistentNaming
public Mesh()
{
var v = _vHead = new MeshUtils.Vertex();
var f = _fHead = new MeshUtils.Face();
var pair = MeshUtils.EdgePair.Create();
var e = _eHead = pair._e;
var eSym = _eHeadSym = pair._eSym;
v._next = v._prev = v;
v._anEdge = null;
f._next = f._prev = f;
f._anEdge = null;
f._trail = null;
f._marked = false;
f._inside = false;
e._next = e;
e._Sym = eSym;
e._Onext = null;
e._Lnext = null;
e._Org = null;
e._Lface = null;
e._winding = 0;
e._activeRegion = null;
eSym._next = eSym;
eSym._Sym = e;
eSym._Onext = null;
eSym._Lnext = null;
eSym._Org = null;
eSym._Lface = null;
eSym._winding = 0;
eSym._activeRegion = null;
}
private void ProjectPolygon()
{
Vec3 norm = _normal;
bool computedNormal = false;
switch (norm.X)
{
case 0.0f when norm.Y == 0.0f && norm.Z == 0.0f:
ComputeNormal(ref norm);
_normal = norm;
computedNormal = true;
break;
}
int i = Vec3.LongAxis(ref norm);
_sUnit[i] = 0;
_sUnit[(i + 1) % 3] = SUnitX;
_sUnit[(i + 2) % 3] = SUnitY;
_tUnit[i] = 0;
_tUnit[(i + 1) % 3] = norm[i] > 0.0f ? -SUnitY : SUnitY;
_tUnit[(i + 2) % 3] = norm[i] > 0.0f ? SUnitX : -SUnitX;
// Project the vertices onto the sweep plane
for (MeshUtils.Vertex v = _mesh._vHead._next; v != _mesh._vHead; v = v._next)
{
Vec3.Dot(ref v._coords, ref _sUnit, out v._s);
Vec3.Dot(ref v._coords, ref _tUnit, out v._t);
}
switch (computedNormal)
{
case true:
CheckOrientation();
break;
}
// Compute ST bounds.
bool first = true;
for (MeshUtils.Vertex v = _mesh._vHead._next; v != _mesh._vHead; v = v._next)
{
switch (first)
{
case true:
_bminX = _bmaxX = v._s;
_bminY = _bmaxY = v._t;
first = false;
break;
default:
{
if (v._s < _bminX)
{
_bminX = v._s;
}
if (v._s > _bmaxX)
{
_bmaxX = v._s;
}
if (v._t < _bminY)
{
_bminY = v._t;
}
if (v._t > _bmaxY)
{
_bmaxY = v._t;
}
break;
}
}
}
}
/// <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 = new MeshUtils.Vertex();
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;
}
private void ComputeNormal(ref Vec3 norm)
{
MeshUtils.Vertex v = _mesh._vHead._next;
double[] minVal = { v._coords.X, v._coords.Y, v._coords.Z };
MeshUtils.Vertex[] minVert = { v, v, v };
double[] maxVal = { v._coords.X, v._coords.Y, v._coords.Z };
MeshUtils.Vertex[] maxVert = { v, v, v };
for (; v != _mesh._vHead; v = v._next)
{
if (v._coords.X < minVal[0])
{
minVal[0] = v._coords.X; minVert[0] = v;
}
if (v._coords.Y < minVal[1])
{
minVal[1] = v._coords.Y; minVert[1] = v;
}
if (v._coords.Z < minVal[2])
{
minVal[2] = v._coords.Z; minVert[2] = v;
}
if (v._coords.X > maxVal[0])
{
maxVal[0] = v._coords.X; maxVert[0] = v;
}
if (v._coords.Y > maxVal[1])
{
maxVal[1] = v._coords.Y; maxVert[1] = v;
}
if (!(v._coords.Z > maxVal[2]))
{
continue;
}
maxVal[2] = v._coords.Z; maxVert[2] = v;
}
// Find two vertices separated by at least 1/sqrt(3) of the maximum
// distance between any two vertices
int i = 0;
if (maxVal[1] - minVal[1] > maxVal[0] - minVal[0])
{
i = 1;
}
if (maxVal[2] - minVal[2] > maxVal[i] - minVal[i])
{
i = 2;
}
if (minVal[i] >= maxVal[i])
{
// All vertices are the same -- normal doesn't matter
norm = new Vec3(0, 0, 1);
return;
}
// Look for a third vertex which forms the triangle with maximum area
// (Length of normal == twice the triangle area)
double maxLen2 = 0;
MeshUtils.Vertex v1 = minVert[i];
MeshUtils.Vertex v2 = maxVert[i];
Vec3.Sub(ref v1._coords, ref v2._coords, out Vec3 d1);
for (v = _mesh._vHead._next; v != _mesh._vHead; v = v._next)
{
Vec3.Sub(ref v._coords, ref v2._coords, out Vec3 d2);
Vec3 tNorm;
tNorm.X = d1.Y * d2.Z - d1.Z * d2.Y;
tNorm.Y = d1.Z * d2.X - d1.X * d2.Z;
tNorm.Z = d1.X * d2.Y - d1.Y * d2.X;
double tLen2 = tNorm.X * tNorm.X + tNorm.Y * tNorm.Y + tNorm.Z * tNorm.Z;
if (!(tLen2 > maxLen2))
{
continue;
}
maxLen2 = tLen2;
norm = tNorm;
}
switch (maxLen2)
{
case <= 0.0f:
// All points lie on a single line -- any decent normal will do
norm = Vec3.Zero;
i = Vec3.LongAxis(ref d1);
norm[i] = 1;
break;
}
}
/// <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)
{
ActiveRegion regLo = RegionBelow(regUp);
MeshUtils.Edge eUp = regUp._eUp;
MeshUtils.Edge eLo = regLo._eUp;
MeshUtils.Vertex orgUp = eUp._Org;
MeshUtils.Vertex orgLo = eLo._Org;
MeshUtils.Vertex dstUp = eUp._Dst;
MeshUtils.Vertex 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);
}
double tMinUp = Math.Min(orgUp._t, dstUp._t);
double 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
MeshUtils.Vertex isect = _pool.Get <MeshUtils.Vertex>();
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).
MeshUtils.Vertex 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);
_pool.Return(isect);
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(_pool, eUp._Sym);
Mesh.Splice(_pool, eLo._Sym, eUp);
regUp = TopLeftRegion(regUp);
eUp = RegionBelow(regUp)._eUp;
FinishLeftRegions(RegionBelow(regUp), regLo);
AddRightEdges(regUp, eUp._Oprev, eUp, eUp, true);
_pool.Return(isect);
return(true);
}
if (dstUp == _event)
{
/* Splice dstUp into eLo, and process the new region(s) */
_mesh.SplitEdge(_pool, eLo._Sym);
Mesh.Splice(_pool, eUp._Lnext, eLo._Oprev);
regLo = regUp;
regUp = TopRightRegion(regUp);
MeshUtils.Edge e = RegionBelow(regUp)._eUp._Rprev;
regLo._eUp = eLo._Oprev;
eLo = FinishLeftRegions(regLo, null);
AddRightEdges(regUp, eLo._Onext, eUp._Rprev, e, true);
_pool.Return(isect);
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(_pool, 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(_pool, eLo._Sym);
eLo._Org._s = _event._s;
eLo._Org._t = _event._t;
}
// leave the rest for ConnectRightVertex
_pool.Return(isect);
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(_pool, eUp._Sym);
_mesh.SplitEdge(_pool, eLo._Sym);
Mesh.Splice(_pool, eLo._Oprev, eUp);
eUp._Org._s = isect._s;
eUp._Org._t = isect._t;
_pool.Return(isect);
isect = null;
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);
}
public static bool VertLeq(MeshUtils.Vertex lhs, MeshUtils.Vertex rhs)
{
return (lhs._s < rhs._s) || (lhs._s == rhs._s && lhs._t <= rhs._t);
}
public static bool VertEq(MeshUtils.Vertex lhs, MeshUtils.Vertex rhs)
{
return lhs._s == rhs._s && lhs._t == rhs._t;
}
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;
}
/// <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)
{
// 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
var z1 = EdgeEval(o1, o2, d1);
var 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
var z1 = EdgeSign(o1, o2, d1);
var 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
var z1 = TransEval(o1, o2, d1);
var 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
var z1 = TransSign(o1, o2, d1);
var z2 = -TransSign(o1, d2, d1);
if (z1 + z2 < 0.0f)
{
z1 = -z1;
z2 = -z2;
}
v._t = Interpolate(z1, o2._t, z2, d2._t);
}
}
public static Real VertL1dist(MeshUtils.Vertex u, MeshUtils.Vertex v)
{
return Math.Abs(u._s - v._s) + Math.Abs(u._t - v._t);
}
public override void Reset()
{
_vHead = null;
_fHead = null;
_eHead = _eHeadSym = null;
}
public static bool TransLeq(MeshUtils.Vertex lhs, MeshUtils.Vertex rhs)
{
return (lhs._t < rhs._t) || (lhs._t == rhs._t && lhs._s <= rhs._s);
}