static void Swap(ref MeshUtils.Vertex a, ref MeshUtils.Vertex b)
{
var tmp = a;
a = b;
b = tmp;
}
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);
}
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>
/// 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);
}
/// <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);
}
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;
}
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;
}
/// <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;
}
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)
{
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);
}
}
public static float VertL1dist(MeshUtils.Vertex u, MeshUtils.Vertex v)
{
return(Math.Abs(u._s - v._s) + Math.Abs(u._t - v._t));
}
public static bool TransLeq(MeshUtils.Vertex lhs, MeshUtils.Vertex rhs)
{
return((lhs._t < rhs._t) || (lhs._t == rhs._t && lhs._s <= rhs._s));
}
private void ComputeNormal(ref Vec3 norm)
{
var v = _mesh._vHead._next;
var minVal = new float[3] {
v._coords.X, v._coords.Y, v._coords.Z
};
var minVert = new MeshUtils.Vertex[3] {
v, v, v
};
var maxVal = new float[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 = 0.0f, Y = 0.0f, Z = 1.0f
};
return;
}
// Look for a third vertex which forms the triangle with maximum area
// (Length of normal == twice the triangle area)
float maxLen2 = 0.0f, 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] = 1.0f;
}
}
private void ComputeNormal(ref Vec3 norm)
{
var v = _mesh._vHead._next;
var minVal = new float[3] { v._coords.X, v._coords.Y, v._coords.Z };
var minVert = new MeshUtils.Vertex[3] { v, v, v };
var maxVal = new float[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 = 0.0f, Y = 0.0f, Z = 1.0f };
return;
}
// Look for a third vertex which forms the triangle with maximum area
// (Length of normal == twice the triangle area)
float maxLen2 = 0.0f, 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] = 1.0f;
}
}