// Calculate the distance between two SimplePoints
private static double Distance3d(SimplePoint3d p1, SimplePoint3d p2)
{
double result = 0;
result = Math.Sqrt(Math.Pow((p2.x - p1.x), 2) + Math.Pow((p2.y - p1.y), 2));
return(result);
}
private static void CalculateCircumcircle3d(SimplePoint3d p1, SimplePoint3d p2, SimplePoint3d p3, out SimplePoint3d circumCentre, out double radius)
{
// Calculate the length of each side of the triangle
double a = Distance3d(p2, p3); // side a is opposite point 1
double b = Distance3d(p1, p3); // side b is opposite point 2
double c = Distance3d(p1, p2); // side c is opposite point 3
// Calculate the radius of the circumcircle
double area = Math.Abs((double)(p1.x * (p2.y - p3.y) + p2.x * (p3.y - p1.y) + p3.x * (p1.y - p2.y)) / 2);
radius = a * b * c / (4 * area);
// Define area coordinates to calculate the circumcentre
double pp1 = Math.Pow(a, 2) * (Math.Pow(b, 2) + Math.Pow(c, 2) - Math.Pow(a, 2));
double pp2 = Math.Pow(b, 2) * (Math.Pow(c, 2) + Math.Pow(a, 2) - Math.Pow(b, 2));
double pp3 = Math.Pow(c, 2) * (Math.Pow(a, 2) + Math.Pow(b, 2) - Math.Pow(c, 2));
// Normalise
double t1 = pp1 / (pp1 + pp2 + pp3);
double t2 = pp2 / (pp1 + pp2 + pp3);
double t3 = pp3 / (pp1 + pp2 + pp3);
// Convert to Cartesian
double x = t1 * p1.x + t2 * p2.x + t3 * p3.x;
double y = t1 * p1.y + t2 * p2.y + t3 * p3.y;
circumCentre = new SimplePoint3d(x, y, 0);
}
public SimpleTriangle3d(int a, int b, int c, SimplePoint3d circumcentre, double radius)
{
this.a = a;
this.b = b;
this.c = c;
this.circumcentre = circumcentre;
this.radius = radius;
}
// Construct a triangle from 3 vertices
private static SqlGeometry Triangle3dFromPoints(SimplePoint3d p1, SimplePoint3d p2, SimplePoint3d p3, int srid)
{
SqlGeometryBuilder TriangleBuilder = new SqlGeometryBuilder();
TriangleBuilder.SetSrid(srid);
TriangleBuilder.BeginGeometry(OpenGisGeometryType.Polygon);
TriangleBuilder.BeginFigure(p1.x, p1.y, p1.z, null);
TriangleBuilder.AddLine(p2.x, p2.y, p2.z, null);
TriangleBuilder.AddLine(p3.x, p3.y, p3.z, null);
TriangleBuilder.AddLine(p1.x, p1.y, p1.z, null);
TriangleBuilder.EndFigure();
TriangleBuilder.EndGeometry();
return(TriangleBuilder.ConstructedGeometry);
}
// Implement IComparable CompareTo method to enable sorting
int IComparable.CompareTo(object obj)
{
SimplePoint3d other = (SimplePoint3d)obj;
if (this.x > other.x)
{
return(1);
}
else if (this.x < other.x)
{
return(-1);
}
else
{
return(0);
}
}
public static void GeometryTriangulate3d(SqlGeometry MultiPoint)
{
// Retrieve the SRID
int srid = (int)MultiPoint.STSrid;
// Check valid input
if (!(MultiPoint.STGeometryType() == "MULTIPOINT" && MultiPoint.STNumPoints() > 3))
{
throw new ArgumentException("Input must be a MultiPoint containing at least three points");
}
// Initialise a list of vertices
List <SimplePoint3d> Vertices = new List <SimplePoint3d>();
// Add all the original supplied points
for (int i = 1; i <= MultiPoint.STNumPoints(); i++)
{
SqlGeometry p = MultiPoint.STPointN(i);
SimplePoint3d Point = new SimplePoint3d((double)p.STX, (double)p.STY, p.HasZ ? (double)p.Z : 0);
// MultiPoints can contain the same point twice, but this messes up Delauney
if (!Vertices.Contains(Point))
{
Vertices.Add(Point);
}
}
// Important - count the number of points in the array, NOT using STNumPoints of the supplied geometry, as some duplicate points
// may have been removed
int numPoints = Vertices.Count;
// Important! Sort the list so that points sweep from left - right
Vertices.Sort();
// Calculate the "supertriangle" that encompasses the pointset
SqlGeometry Envelope = MultiPoint.STEnvelope();
// Width
double dx = (double)(Envelope.STPointN(2).STX - Envelope.STPointN(1).STX);
// Height
double dy = (double)(Envelope.STPointN(4).STY - Envelope.STPointN(1).STY);
// Maximum dimension
double dmax = (dx > dy) ? dx : dy;
// Centre
double avgx = (double)Envelope.STCentroid().STX;
double avgy = (double)Envelope.STCentroid().STY;
// Create the points at corners of the supertriangle
SimplePoint3d a = new SimplePoint3d(avgx - 2 * dmax, avgy - dmax, 0);
SimplePoint3d b = new SimplePoint3d(avgx + 2 * dmax, avgy - dmax, 0);
SimplePoint3d c = new SimplePoint3d(avgx, avgy + 2 * dmax, 0);
// Add the supertriangle vertices to the end of the vertex array
Vertices.Add(a);
Vertices.Add(b);
Vertices.Add(c);
double radius;
SimplePoint3d circumcentre;
CalculateCircumcircle3d(a, b, c, out circumcentre, out radius);
// Create a triangle from the vertices
SimpleTriangle3d SuperTriangle = new SimpleTriangle3d(numPoints, numPoints + 1, numPoints + 2, circumcentre, radius);
// Add the supertriangle to the list of triangles
List <SimpleTriangle3d> Triangles = new List <SimpleTriangle3d>();
Triangles.Add(SuperTriangle);
List <SimpleTriangle3d> CompletedTriangles = new List <SimpleTriangle3d>();
// Loop through each point
for (int i = 0; i < numPoints; i++)
{
// Initialise the edge buffer
List <int[]> Edges = new List <int[]>();
// Loop through each triangle
for (int j = Triangles.Count - 1; j >= 0; j--)
{
// If the point lies within the circumcircle of this triangle
if (Distance3d(Triangles[j].circumcentre, Vertices[i]) < Triangles[j].radius)
{
// Add the triangle edges to the edge buffer
Edges.Add(new int[] { Triangles[j].a, Triangles[j].b });
Edges.Add(new int[] { Triangles[j].b, Triangles[j].c });
Edges.Add(new int[] { Triangles[j].c, Triangles[j].a });
// Remove this triangle from the list
Triangles.RemoveAt(j);
}
// If this triangle is complete
else if (Vertices[i].x > Triangles[j].circumcentre.x + Triangles[j].radius)
{
{
CompletedTriangles.Add(Triangles[j]);
}
Triangles.RemoveAt(j);
}
}
// Remove duplicate edges
for (int j = Edges.Count - 1; j > 0; j--)
{
for (int k = j - 1; k >= 0; k--)
{
// Compare if this edge match in either direction
if (Edges[j][0].Equals(Edges[k][1]) && Edges[j][1].Equals(Edges[k][0]))
{
// Remove both duplicates
Edges.RemoveAt(j);
Edges.RemoveAt(k);
// We've removed an item from lower down the list than where j is now, so update j
j--;
break;
}
}
}
// Create new triangles for the current point
for (int j = 0; j < Edges.Count; j++)
{
CalculateCircumcircle3d(Vertices[Edges[j][0]], Vertices[Edges[j][1]], Vertices[i], out circumcentre, out radius);
SimpleTriangle3d T = new SimpleTriangle3d(Edges[j][0], Edges[j][1], i, circumcentre, radius);
Triangles.Add(T);
}
}
// We've finished triangulation. Move any remaining triangles onto the completed list
CompletedTriangles.AddRange(Triangles);
// Define the metadata of the results column
SqlMetaData metadata = new SqlMetaData("Triangle", SqlDbType.Udt, typeof(SqlGeometry));
// Create a record based on this metadata
SqlDataRecord record = new SqlDataRecord(metadata);
// Send the results back to the client
SqlContext.Pipe.SendResultsStart(record);
foreach (SimpleTriangle3d Tri in CompletedTriangles)
{
// Check that this is a triangle formed only from vertices in the original multipoint
// i.e. not from the vertices of the supertriangle.
if (Tri.a < numPoints && Tri.b < numPoints && Tri.c < numPoints)
{
SqlGeometry triangle = Triangle3dFromPoints(Vertices[Tri.a], Vertices[Tri.b], Vertices[Tri.c], srid);
record.SetValue(0, triangle);
SqlContext.Pipe.SendResultsRow(record);
}
}
SqlContext.Pipe.SendResultsEnd();
}
