/// <summary>
/// Divide a triangle at the given vertex located on a side
/// without performing any edge swaps.
/// </summary>
/// <param name="t">The triangle to divide</param>
/// <param name="loc">The location of the vertex on the triangle</param>
/// <param name="v">The vertex on the side</param>
private Triangle[] DivideTriangleOnEdgeNoSwap(Triangle t, PointOnTriangle loc, Vertex v)
{
Triangle t1 = null;
Triangle t2 = null;
if (loc == PointOnTriangle.OnS12)
{
// divide edge 12
t1 = new Triangle(t.V1, v, t.V3);
t2 = new Triangle(v, t.V2, t.V3);
t1.SetMeshParams(t.S12.Opposite, t2.S31, t.S31.Opposite);
t2.SetMeshParams(t.S12.Opposite, t.S23.Opposite, t1.S23);
}
else if (loc == PointOnTriangle.OnS23)
{
// divide edge 23
t1 = new Triangle(t.V2, v, t.V1);
t2 = new Triangle(v, t.V3, t.V1);
t1.SetMeshParams(t.S23.Opposite, t2.S31, t.S12.Opposite);
t2.SetMeshParams(t.S23.Opposite, t.S31.Opposite, t1.S23);
}
else if (loc == PointOnTriangle.OnS31)
{
// divide edge 31
t1 = new Triangle(t.V3, v, t.V2);
t2 = new Triangle(v, t.V1, t.V2);
t1.SetMeshParams(t.S31.Opposite, t2.S31, t.S23.Opposite);
t2.SetMeshParams(t.S31.Opposite, t.S12.Opposite, t1.S23);
}
return(new Triangle[] { t1, t2 });
}
/// <summary>
/// Divide two triangles at the given vertex located on
/// their shared edge into four new triangles performing local
/// edge swaps as necessary to keep the mesh delaunay.
/// </summary>
/// <param name="tt1">First triangle to divide</param>
/// <param name="loc1">The location of the vertex on the first triangle</param>
/// <param name="tt2">Second triangle to divide</param>
/// <param name="loc2">The location of the vertex on the second triangle</param>
/// <param name="v">The vertex on the shared side</param>
private void DivideTrianglesOnSharedEdge(Triangle tt1, PointOnTriangle loc1, Triangle tt2, PointOnTriangle loc2, Vertex v)
{
OnDividingTriangle(new DividingTriangleEventArgs(v, new Triangle[] { tt1, tt2 }));
Halfedge e1 = (loc1 == PointOnTriangle.OnS12 ? tt1.S12 : (loc1 == PointOnTriangle.OnS23 ? tt1.S23 : tt1.S31));
Halfedge e2 = (loc2 == PointOnTriangle.OnS12 ? tt2.S12 : (loc2 == PointOnTriangle.OnS23 ? tt2.S23 : tt2.S31));
// Divide into four triangles
Triangle[] tn1 = DivideTriangleOnEdgeNoSwap(tt1, loc1, v);
Triangle[] tn2 = DivideTriangleOnEdgeNoSwap(tt2, loc2, v);
Triangle t1 = tn1[0];
Triangle t2 = tn1[1];
Triangle t3 = tn2[0];
Triangle t4 = tn2[1];
t1.SetMeshParams(t4.S12, t2.S31, null);
t2.SetMeshParams(t3.S12, null, t1.S23);
t3.SetMeshParams(t2.S12, t4.S31, null);
t4.SetMeshParams(t1.S12, null, t3.S23);
tt1.IsRemoved = true;
tt2.IsRemoved = true;
Triangles.SetRootTriangle(t1);
OnDividedTriangle(new DividedTriangleEventArgs(v, new Triangle[] { tt1, tt2 }, new Triangle[] { t1, t2, t3, t4 }));
// edge flip
SwapTest(t1.S31, v);
SwapTest(t2.S23, v);
SwapTest(t3.S31, v);
SwapTest(t4.S23, v);
}
/// <summary>
/// Divides a triangles at the given vertex located on
/// its edge into two new triangles performing local
/// edge swaps as necessary to keep the mesh delaunay.
/// </summary>
/// <param name="tt">First triangle to divide</param>
/// <param name="loc">The location of the vertex on the first triangle</param>
/// <param name="tt2">Second triangle to divide</param>
/// <param name="loc2">The location of the vertex on the second triangle</param>
/// <param name="v">The vertex on the shared side</param>
private void DivideTriangleOnEdge(Triangle tt, PointOnTriangle loc, Vertex v)
{
OnDividingTriangle(new DividingTriangleEventArgs(v, new Triangle[] { tt }));
// Divide into two triangles
Triangle[] tn1 = DivideTriangleOnEdgeNoSwap(tt, loc, v);
Triangle t1 = tn1[0];
Triangle t2 = tn1[1];
t1.SetMeshParams(null, t2.S31, null);
t2.SetMeshParams(null, null, t1.S23);
tt.IsRemoved = true;
Triangles.SetRootTriangle(t1);
OnDividedTriangle(new DividedTriangleEventArgs(v, new Triangle[] { tt }, new Triangle[] { t1, t2 }));
}
/// <summary>
/// Find the triangle(s) containing the given point. The search starts from an arbitrary
/// triangle and homes in on the vertex by visiting triangles closest to the vertex.
/// If the vertex is on and edge seperating two triangles, both are returned.
/// </summary>
/// <param name="v">The vertex to search for</param>
/// <returns>The triangles(s) containing the vertex</returns>
internal FindTriangle[] FindContaining(Vertex v)
{
Triangle current = root;
while (true)
{
PointOnTriangle loc = PointOnTriangle.None;
Halfedge closestEdge = null;
PointShapeRelation rel = current.Contains(v, out loc, out closestEdge);
if (rel == PointShapeRelation.Inside)
{
// Inside triangle, return.
return(new FindTriangle[] { new FindTriangle(current, rel, loc) });
}
else if (rel == PointShapeRelation.Outside)
{
// Outside triangle, continue searching from the neighbour closest to the point
Halfedge opp = closestEdge.Opposite;
if (opp == null)
{
throw new InvalidOperationException("No triangle contains this vertex.");
}
current = opp.Parent;
}
else
{
// On an edge, return the triangle and its neighbour (if there is one)
Halfedge opp = closestEdge.Opposite;
if (opp == null)
{
return(new FindTriangle[] { new FindTriangle(current, rel, loc) });
}
else
{
Triangle other = opp.Parent;
PointOnTriangle otherLoc = PointOnTriangle.None;
PointShapeRelation otherRel = other.Contains(v, out otherLoc);
return(new FindTriangle[] { new FindTriangle(current, rel, loc), new FindTriangle(other, otherRel, otherLoc) });
}
}
}
}
/// <summary>
/// Determines whether the triangle contains the given vertex.
/// </summary>
/// <param name="v">The vertex to check</param>
/// <param name="location">On return, contains where on the triangle the vertex lies</param>
/// <param name="closestEdge">On return, contains the edge closest to the input vertex</param>
/// <returns>The relative location of the vertex</returns>
public PointShapeRelation Contains(Vertex v, out PointOnTriangle location, out Halfedge closestEdge)
{
double a12 = new Matrix3(
V1.X, V1.Y, 1,
V2.X, V2.Y, 1,
v.X, v.Y, 1).Determinant;
double a23 = new Matrix3(
V2.X, V2.Y, 1,
V3.X, V3.Y, 1,
v.X, v.Y, 1).Determinant;
double a31 = new Matrix3(
V3.X, V3.Y, 1,
V1.X, V1.Y, 1,
v.X, v.Y, 1).Determinant;
if (Utility.AlmostZero(a12))
{
if (Utility.AlmostZero(a23))
{
location = PointOnTriangle.OnV2;
}
else if (Utility.AlmostZero(a31))
{
location = PointOnTriangle.OnV1;
}
else
{
location = PointOnTriangle.OnS12;
}
closestEdge = S12;
return(PointShapeRelation.On);
}
else if (Utility.AlmostZero(a23))
{
if (Utility.AlmostZero(a31))
{
location = PointOnTriangle.OnV3;
}
else if (Utility.AlmostZero(a12))
{
location = PointOnTriangle.OnV2;
}
else
{
location = PointOnTriangle.OnS23;
}
closestEdge = S23;
return(PointShapeRelation.On);
}
else if (Utility.AlmostZero(a31))
{
if (Utility.AlmostZero(a12))
{
location = PointOnTriangle.OnV1;
}
else if (Utility.AlmostZero(a23))
{
location = PointOnTriangle.OnV3;
}
else
{
location = PointOnTriangle.OnS31;
}
closestEdge = S31;
return(PointShapeRelation.On);
}
else if (a12 < 0 || a23 < 0 || a31 < 0)
{
if (a12 < 0)
{
closestEdge = S12;
}
else if (a23 < 0)
{
closestEdge = S23;
}
else
{
closestEdge = S31;
}
location = PointOnTriangle.None;
return(PointShapeRelation.Outside);
}
else
{
double d12 = a12 / S12.Length;
double d23 = a23 / S23.Length;
double d31 = a31 / S31.Length;
if (d12 < d23 && d12 < d31)
{
closestEdge = S12;
}
else if (d23 < d12 && d23 < d31)
{
closestEdge = S23;
}
else
{
closestEdge = S31;
}
location = PointOnTriangle.None;
return(PointShapeRelation.Inside);
}
}
/// <summary>
/// Determines whether the triangle contains the given vertex.
/// </summary>
/// <param name="v">The vertex to check</param>
/// <param name="location">On return, contains where on the triangle the vertex lies</param>
/// <returns>The relative location of the vertex</returns>
public PointShapeRelation Contains(Vertex v, out PointOnTriangle location)
{
double a12 = new Matrix3(
V1.X, V1.Y, 1,
V2.X, V2.Y, 1,
v.X, v.Y, 1).Determinant;
double a23 = new Matrix3(
V2.X, V2.Y, 1,
V3.X, V3.Y, 1,
v.X, v.Y, 1).Determinant;
double a31 = new Matrix3(
V3.X, V3.Y, 1,
V1.X, V1.Y, 1,
v.X, v.Y, 1).Determinant;
if (Utility.AlmostZero(a12))
{
if (Utility.AlmostZero(a23))
{
location = PointOnTriangle.OnV2;
}
else if (Utility.AlmostZero(a31))
{
location = PointOnTriangle.OnV1;
}
else
{
location = PointOnTriangle.OnS12;
}
return(PointShapeRelation.On);
}
else if (Utility.AlmostZero(a23))
{
if (Utility.AlmostZero(a31))
{
location = PointOnTriangle.OnV3;
}
else if (Utility.AlmostZero(a12))
{
location = PointOnTriangle.OnV2;
}
else
{
location = PointOnTriangle.OnS23;
}
return(PointShapeRelation.On);
}
else if (Utility.AlmostZero(a31))
{
if (Utility.AlmostZero(a12))
{
location = PointOnTriangle.OnV1;
}
else if (Utility.AlmostZero(a23))
{
location = PointOnTriangle.OnV3;
}
else
{
location = PointOnTriangle.OnS31;
}
return(PointShapeRelation.On);
}
else if (a12 < 0 || a23 < 0 || a31 < 0)
{
location = PointOnTriangle.None;
return(PointShapeRelation.Outside);
}
else
{
location = PointOnTriangle.None;
return(PointShapeRelation.Inside);
}
}
public FindTriangle(Triangle tri, PointShapeRelation rel, PointOnTriangle loc)
{
Triangle = tri;
Relation = rel;
Location = loc;
}
