Triangle GetAdjacent(DelaunayPoint start, DelaunayPoint end)
{
double t = 0;
double s = SegmentsIntersect(m_v[0], m_v[1], start, end, t);
if (t >= 0 && t <= 1 && s >= 0 && s <= 1)
{
return(adjacentFace[0]);
}
s = SegmentsIntersect(m_v[1], m_v[2], start, end, t);
if (t >= 0 && t <= 1 && s >= 0 && s <= 1)
{
return(adjacentFace[1]);
}
s = SegmentsIntersect(m_v[2], m_v[0], start, end, t);
if (t >= 0 && t <= 1 && s >= 0 && s <= 1)
{
return(adjacentFace[2]);
}
return(null);
}
float SegmentsIntersect(DelaunayPoint a, DelaunayPoint b, DelaunayPoint c, DelaunayPoint d, double t)
{
//what if denominator is zero??
double diff0 = (c.Y - a.Y) * MULTIPLIER;
double diff1 = (d.X - c.X) * MULTIPLIER;
double diff2 = (a.X - c.X) * MULTIPLIER;
double diff3 = (d.Y - c.Y) * MULTIPLIER;
double diff4 = (b.Y - a.Y) * MULTIPLIER;
double diff5 = (b.X - a.X) * MULTIPLIER;
t = (diff0 * diff1 + diff2 * diff3) / (diff4 * diff1 - diff5 * diff3);
double s = (-diff2 * diff4 - diff0 * diff5) / (diff3 * diff5 - diff1 * diff4);
if (Math.Abs(t) <= VERY_SMALL_DIST)
{
t = 0;
}
if (Math.Abs(s) <= VERY_SMALL_DIST)
{
s = 0;
}
return((float)s);
}
bool IsClose(DelaunayPoint p, double maxDistance)
{
if (m_norm == 0)
{
ComputePlaneParams();
}
double dist = Math.Abs((m_a * p.X + m_b * p.Y + m_c * p.Z + m_d) / m_norm);
return(dist <= maxDistance);
}
private void ForceClockwise()
{
if (DelaunayGeometry.CrossProduct(m_v[0], m_v[1], m_v[2]) >= 0)
{
// a positive value indicates counter clockwise
// Swapping the first 2 points should be enough
DelaunayPoint tmp = m_v[0];
m_v[0] = m_v[1];
m_v[1] = tmp;
}
}
bool LocateInternalUsingTriangleList(IEnumerable <Triangle> triangles, DelaunayPoint p)
{
foreach (Triangle triangle in triangles)
{
if (LocateInternal(triangle, p) != null)
{
return(true);
}
}
return(false);
}
bool LocateInternal(DelaunayPoint p)
{
if (m_currentTriangle != null)
{
Triangle newTriangle = LocateInternal(m_currentTriangle, p);
if (newTriangle != null)
{
return(true);
}
}
return(false);
}
public Triangle(DelaunayPoint v1, DelaunayPoint v2, DelaunayPoint v3)
{
m_v = new DelaunayPoint[] { v1, v2, v3 };
ForceClockwise();
adjacentFace = new Triangle[3];
centroidX = (float)(v1.X + v2.X + v3.X) / 3.0f;
centroidY = (float)(v1.Y + v2.Y + v3.Y) / 3.0f;
m_extent = new Extent2D(m_v[0], m_v[1], m_v[2]);
}
public bool Contains(DelaunayPoint p)
{
// Only bother to check if the point is within the initial extents of the Triangle_t
if (m_extent.Contains(p.X, p.Y, true))
{
return (
(DelaunayGeometry.CrossProduct(m_v[0], p, m_v[1]) >= 0.0) &&
(DelaunayGeometry.CrossProduct(m_v[1], p, m_v[2]) >= 0.0) &&
(DelaunayGeometry.CrossProduct(m_v[2], p, m_v[0]) >= 0.0));
}
return false;
}
public Triangle(DelaunayPoint v1, DelaunayPoint v2, DelaunayPoint v3)
{
m_v = new DelaunayPoint[] { v1, v2, v3 };
ForceClockwise();
adjacentFace = new Triangle[3];
centroidX = (float)(v1.X + v2.X + v3.X) / 3.0f;
centroidY = (float)(v1.Y + v2.Y + v3.Y) / 3.0f;
m_extent = new Extent2D(m_v[0], m_v[1], m_v[2]);
}
public bool Contains(DelaunayPoint p)
{
// Only bother to check if the point is within the initial extents of the Triangle_t
if (m_extent.Contains(p.X, p.Y, true))
{
return(
(DelaunayGeometry.CrossProduct(m_v[0], p, m_v[1]) >= 0.0) &&
(DelaunayGeometry.CrossProduct(m_v[1], p, m_v[2]) >= 0.0) &&
(DelaunayGeometry.CrossProduct(m_v[2], p, m_v[0]) >= 0.0));
}
return(false);
}
public bool IsCoincidentWithVertex(DelaunayPoint p)
{
double distA = (m_v[0].X - p.X) * (m_v[0].X - p.X) + (m_v[0].Y - p.Y) * (m_v[0].Y - p.Y);
double distB = (m_v[1].X - p.X) * (m_v[1].X - p.X) + (m_v[1].Y - p.Y) * (m_v[1].Y - p.Y);
double distC = (m_v[2].X - p.X) * (m_v[2].X - p.X) + (m_v[2].Y - p.Y) * (m_v[2].Y - p.Y);
if ((distA <= VERY_SMALL_DIST) || (distB <= VERY_SMALL_DIST) || (distC <= VERY_SMALL_DIST))
{
return(true);
}
return(false);
}
bool LocateInternalBruteForce(DelaunayPoint p)
{
m_currentTriangle = null;
foreach (Triangle triangle in m_newTriangles)
{
if (triangle.Contains(p))
{
m_currentTriangle = triangle;
return(true);
}
}
return(false);
}
////use this only for direction and nothing else
public static float CrossProduct(DelaunayPoint p, DelaunayPoint a, DelaunayPoint b)
{
// FUTURE: Migrate this into a more appropriate place.
//use the multiplier for making sure we handle small numbers correctly
double diffax = (double)a.X - p.X;
double diffay = (double)a.Y - p.Y;
double diffbx = (double)b.X - p.X;
double diffby = (double)b.Y - p.Y;
double cross = (diffax * diffby - diffbx * diffay);
if (cross >= 1.0e-12 || cross <= -1.0e-12)
return (float)cross;
return 0.0f;
}
public bool UpdateTriangle(DelaunayPoint p)
{
if (m_currentTriangle == null)
{
return(false);
}
if (m_currentTriangle.IsCoincidentWithVertex(p))
{
return(false);
}
Update(p);
return(true);
}
public static Extent2D Circumcircle(DelaunayPoint v1, DelaunayPoint v2, DelaunayPoint v3, double cx, double cy)
{
const double ERROR_BOUND = 0.005;
//http://mathworld.wolfram.com/Circumcircle.html
double x1 = v1.X;
double x2 = v2.X;
double x3 = v3.X;
double y1 = v1.Y;
double y2 = v2.Y;
double y3 = v3.Y;
double x1Sq = x1 * x1;
double x2Sq = x2 * x2;
double x3Sq = x3 * x3;
double y1Sq = y1 * y1;
double y2Sq = y2 * y2;
double y3Sq = y3 * y3;
double a = (x1 - x2) * (y2 - y3) - (y1 - y2) * (x2 - x3);
double bx = -((x1Sq + y1Sq - x2Sq - y2Sq) * (y2 - y3) - (x2Sq + y2Sq - x3Sq - y3Sq) * (y1 - y2));
double by = ((x1Sq + y1Sq - x2Sq - y2Sq) * (x2 - x3) - (x2Sq + y2Sq - x3Sq - y3Sq) * (x1 - x2));
double c = -((x1Sq + y1Sq) * (x2 * y3 - x3 * y2) - (x2Sq + y2Sq) * (x1 * y3 - x3 * y1) + (x3Sq + y3Sq) * (x1 * y2 - x2 * y1));
Extent2D extent = null;
if (a == 0.0f)
{
extent = new Extent2D(cx - ERROR_BOUND, cx + ERROR_BOUND, cy - ERROR_BOUND, cy + ERROR_BOUND);
}
else
{
double x0 = -bx / (2.0f * a);
double y0 = -by / (2.0f * a);
double numerator = bx * bx + by * by - 4.0f * a * c;
double rad = 0;
if (numerator >= 0)
{
rad = Math.Sqrt(numerator) / (2.0f * Math.Abs(a));
}
extent = new Extent2D(x0 - rad - ERROR_BOUND, x0 + rad + ERROR_BOUND, y0 - rad - ERROR_BOUND, y0 + rad + ERROR_BOUND);
}
return(extent);
}
// Returns true if the point is contained in the triangle otherwise returns false
// if false then ref is the next triangle
public bool Contains(DelaunayPoint p, ref Triangle next)
{
//unrolled the dot product logic for optimization
// a refers to point m_v[0]
// b refers to point m_v[1]
// c refers to point m_v[1]
// p is the point
double diffax = (m_v[0].X - p.X);
double diffay = (m_v[0].Y - p.Y);
double diffcx = (m_v[2].X - p.X);
double diffcy = (m_v[2].Y - p.Y);
double aXc = (diffax * diffcy - diffcx * diffay);
if (aXc < 0.0) // if negative point is outside of edge a,c
{
next = adjacentFace[2];
return(false);
}
else
{
double diffbx = (m_v[1].X - p.X);
double diffby = (m_v[1].Y - p.Y);
double cXb = (diffcx * diffby - diffbx * diffcy);
if (cXb < 0.0) // if
{
next = adjacentFace[1];
return(false);
}
else
{
double bXa = (diffbx * diffay - diffax * diffby);
if (bXa < 0.0)
{
next = adjacentFace[0];
return(false);
}
}
}
return(true);
}
////use this only for direction and nothing else
public static float CrossProduct(DelaunayPoint p, DelaunayPoint a, DelaunayPoint b)
{
// FUTURE: Migrate this into a more appropriate place.
//use the multiplier for making sure we handle small numbers correctly
double diffax = (double)a.X - p.X;
double diffay = (double)a.Y - p.Y;
double diffbx = (double)b.X - p.X;
double diffby = (double)b.Y - p.Y;
double cross = (diffax * diffby - diffbx * diffay);
if (cross >= 1.0e-12 || cross <= -1.0e-12)
{
return((float)cross);
}
return(0.0f);
}
public static Extent2D Circumcircle(DelaunayPoint v1, DelaunayPoint v2, DelaunayPoint v3, double cx, double cy)
{
const double ERROR_BOUND = 0.005;
//http://mathworld.wolfram.com/Circumcircle.html
double x1 = v1.X;
double x2 = v2.X;
double x3 = v3.X;
double y1 = v1.Y;
double y2 = v2.Y;
double y3 = v3.Y;
double x1Sq = x1 * x1;
double x2Sq = x2 * x2;
double x3Sq = x3 * x3;
double y1Sq = y1 * y1;
double y2Sq = y2 * y2;
double y3Sq = y3 * y3;
double a = (x1 - x2) * (y2 - y3) - (y1 - y2) * (x2 - x3);
double bx = -((x1Sq + y1Sq - x2Sq - y2Sq) * (y2 - y3) - (x2Sq + y2Sq - x3Sq - y3Sq) * (y1 - y2));
double by = ((x1Sq + y1Sq - x2Sq - y2Sq) * (x2 - x3) - (x2Sq + y2Sq - x3Sq - y3Sq) * (x1 - x2));
double c = -((x1Sq + y1Sq) * (x2 * y3 - x3 * y2) - (x2Sq + y2Sq) * (x1 * y3 - x3 * y1) + (x3Sq + y3Sq) * (x1 * y2 - x2 * y1));
Extent2D extent = null;
if (a == 0.0f)
{
extent = new Extent2D(cx - ERROR_BOUND, cx + ERROR_BOUND, cy - ERROR_BOUND, cy + ERROR_BOUND);
}
else
{
double x0 = -bx / (2.0f * a);
double y0 = -by / (2.0f * a);
double numerator = bx * bx + by * by - 4.0f * a * c;
double rad = 0;
if (numerator >= 0)
rad = Math.Sqrt(numerator) / (2.0f * Math.Abs(a));
extent = new Extent2D(x0 - rad - ERROR_BOUND, x0 + rad + ERROR_BOUND, y0 - rad - ERROR_BOUND, y0 + rad + ERROR_BOUND);
}
return extent;
}
public bool CircumCircleContains(DelaunayPoint p)
{
// http://www.cs.cmu.edu/~quake/robust.html
double a1 = (double)m_v[0].X - p.X;
double a2 = (double)m_v[0].Y - p.Y;
double a3 = a1*a1 + a2*a2;
double b1 = (double)m_v[1].X - p.X;
double b2 = (double)m_v[1].Y - p.Y;
double b3 = b1*b1 + b2*b2;
double c1 = (double)m_v[2].X - p.X;
double c2 = (double)m_v[2].Y - p.Y;
double c3 = c1*c1 + c2*c2;
double det = a1 * (b2 * c3 - b3 * c2) - a2 * (b1 * c3 - b3 * c1) + a3 * (b1 * c2 - b2 * c1);
return !(det >= double.Epsilon);
}
public bool Locate(DelaunayPoint p)
{
// Attempt to walk to the triangle.
if (LocateInternal(p))
{
return(true);
}
else
{
//// Attempt to walk to the triangle using the cell's boundary triangles.
//if(LocateInternalUsingTriangleList(cell->BoundaryTriangles(), p))
//{
// return true;
//}
// Last ditch effort to find the triangle looking through memory -- O(n)
return(LocateInternalBruteForce(p));
}
}
public bool Locate(DelaunayPoint p)
{
// Attempt to walk to the triangle.
if(LocateInternal(p))
{
return true;
}
else
{
//// Attempt to walk to the triangle using the cell's boundary triangles.
//if(LocateInternalUsingTriangleList(cell->BoundaryTriangles(), p))
//{
// return true;
//}
// Last ditch effort to find the triangle looking through memory -- O(n)
return LocateInternalBruteForce(p);
}
}
public bool CircumCircleContains(DelaunayPoint p)
{
// http://www.cs.cmu.edu/~quake/robust.html
double a1 = (double)m_v[0].X - p.X;
double a2 = (double)m_v[0].Y - p.Y;
double a3 = a1 * a1 + a2 * a2;
double b1 = (double)m_v[1].X - p.X;
double b2 = (double)m_v[1].Y - p.Y;
double b3 = b1 * b1 + b2 * b2;
double c1 = (double)m_v[2].X - p.X;
double c2 = (double)m_v[2].Y - p.Y;
double c3 = c1 * c1 + c2 * c2;
double det = a1 * (b2 * c3 - b3 * c2) - a2 * (b1 * c3 - b3 * c1) + a3 * (b1 * c2 - b2 * c1);
return(!(det >= double.Epsilon));
}
void FreeTriangle(Triangle t, bool flush)
{
if (t == null)
{
//should never come here, maybe the last ones
return;
}
//make sure we arent deleting the m_currentTriangle
if (m_currentTriangle == t)
{
m_currentTriangle = null;
}
// TODO: Encapsulate this later if triangles reference edges/vertices via shared_ptr.
DelaunayPoint v1 = t.m_v[0];
DelaunayPoint v2 = t.m_v[1];
DelaunayPoint v3 = t.m_v[2];
if (flush)
{
bool isSuperTriangleVertex = false;
for (int i = 0; i < 3; i++)
{
DelaunayPoint v = t.m_v[i];
if (v == m_superA || v == m_superB || v == m_superC)
{
isSuperTriangleVertex = true;
break;
}
}
if (!isSuperTriangleVertex)
{
m_outputTriangles.Add(v1.Index);
m_outputTriangles.Add(v2.Index);
m_outputTriangles.Add(v3.Index);
}
}
//m_trianglesMemoryManager.dealloc(*t);
}
Triangle LocateInternal(Triangle startTriangle, DelaunayPoint end)
{
int step = 0;
//first check if the point is in the current Triangle_t
while ((startTriangle != null) && !startTriangle.Contains(end, ref startTriangle) && (++step) <= NUM_STEPS_TO_LOCATE)
{
}
if (step > NUM_STEPS_TO_LOCATE)
{
startTriangle = null;
}
if (startTriangle == null)
{
return(null);
}
m_currentTriangle = startTriangle;
return(m_currentTriangle);
}
public void Initialize(Extent3D extent, int numPointsToProcess)
{
double SQRT3 = Math.Sqrt(3);
//create one big Triangle_t aka. supertriangle
//Make the bounding box slightly bigger,
//actually no need for this if coming from streaming delaunay side
m_extent = extent;
// compute the supertriangle vertices, clockwise order, check the math
m_superA = new DelaunayPoint(extent.MinX - extent.RangeY * SQRT3 / 3.0f, extent.MinY, extent.MinZ, numPointsToProcess);
m_superB = new DelaunayPoint(extent.MidpointX, extent.MaxY + extent.RangeX * SQRT3 * 0.5f, extent.MinZ, numPointsToProcess + 1);
m_superC = new DelaunayPoint(extent.MaxX + extent.RangeY * SQRT3 / 3.0f, extent.MinY, extent.MinZ, numPointsToProcess + 2);
//create the super Triangle_t
m_delaunayGraph = new Triangle(m_superA, m_superB, m_superC);
//keep track of the current Triangle_t
m_currentTriangle = m_delaunayGraph;
m_newTriangles = new List<Triangle>();
m_outputTriangles = new List<int>();
}
public void Initialize(Extent3D extent, int numPointsToProcess)
{
double SQRT3 = Math.Sqrt(3);
//create one big Triangle_t aka. supertriangle
//Make the bounding box slightly bigger,
//actually no need for this if coming from streaming delaunay side
m_extent = extent;
// compute the supertriangle vertices, clockwise order, check the math
m_superA = new DelaunayPoint(extent.MinX - extent.RangeY * SQRT3 / 3.0f, extent.MinY, extent.MinZ, numPointsToProcess);
m_superB = new DelaunayPoint(extent.MidpointX, extent.MaxY + extent.RangeX * SQRT3 * 0.5f, extent.MinZ, numPointsToProcess + 1);
m_superC = new DelaunayPoint(extent.MaxX + extent.RangeY * SQRT3 / 3.0f, extent.MinY, extent.MinZ, numPointsToProcess + 2);
//create the super Triangle_t
m_delaunayGraph = new Triangle(m_superA, m_superB, m_superC);
//keep track of the current Triangle_t
m_currentTriangle = m_delaunayGraph;
m_newTriangles = new List <Triangle>();
m_outputTriangles = new List <int>();
}
bool LocateInternalBruteForce(DelaunayPoint p)
{
m_currentTriangle = null;
foreach (Triangle triangle in m_newTriangles)
{
if (triangle.Contains(p))
{
m_currentTriangle = triangle;
return true;
}
}
return false;
}
Triangle LocateInternal(Triangle startTriangle, DelaunayPoint end)
{
int step = 0;
//first check if the point is in the current Triangle_t
while((startTriangle != null) && !startTriangle.Contains(end, ref startTriangle) && (++step) <= NUM_STEPS_TO_LOCATE)
{
}
if(step > NUM_STEPS_TO_LOCATE)
startTriangle = null;
if(startTriangle == null)
return null;
m_currentTriangle = startTriangle;
return m_currentTriangle;
}
bool LocateInternal(DelaunayPoint p)
{
if(m_currentTriangle != null)
{
Triangle newTriangle = LocateInternal(m_currentTriangle, p);
if(newTriangle != null)
return true;
}
return false;
}
public bool UpdateTriangle(DelaunayPoint p)
{
if (m_currentTriangle == null)
return false;
if (m_currentTriangle.IsCoincidentWithVertex(p))
return false;
Update(p);
return true;
}
bool IsClose(DelaunayPoint p, double maxDistance)
{
if (m_norm == 0)
ComputePlaneParams();
double dist = Math.Abs((m_a * p.X + m_b * p.Y + m_c * p.Z + m_d) / m_norm);
return (dist <= maxDistance);
}
// Returns true if the point is contained in the triangle otherwise returns false
// if false then ref is the next triangle
public bool Contains(DelaunayPoint p, ref Triangle next)
{
//unrolled the dot product logic for optimization
// a refers to point m_v[0]
// b refers to point m_v[1]
// c refers to point m_v[1]
// p is the point
double diffax = (m_v[0].X - p.X);
double diffay = (m_v[0].Y - p.Y);
double diffcx = (m_v[2].X - p.X);
double diffcy = (m_v[2].Y - p.Y);
double aXc = (diffax * diffcy - diffcx * diffay);
if(aXc < 0.0) // if negative point is outside of edge a,c
{
next = adjacentFace[2];
return false;
}
else
{
double diffbx = (m_v[1].X - p.X);
double diffby = (m_v[1].Y - p.Y);
double cXb = (diffcx * diffby - diffbx * diffcy);
if(cXb < 0.0) // if
{
next = adjacentFace[1];
return false;
}
else
{
double bXa = (diffbx * diffay - diffax * diffby);
if(bXa < 0.0)
{
next = adjacentFace[0];
return false;
}
}
}
return true;
}
bool Overlaps(Extent2D extent)
{
// Check simplist case - triangle inside extent.
if (extent.Contains(m_extent))
{
return(true);
}
// Use right-hand rule for each triangle segment against all points of extent rectangle.
DelaunayPoint p1 = new DelaunayPoint(extent.MinX, extent.MinY, 0.0f, 0);
DelaunayPoint p2 = new DelaunayPoint(extent.MaxX, extent.MinY, 0.0f, 0);
DelaunayPoint p3 = new DelaunayPoint(extent.MaxX, extent.MaxY, 0.0f, 0);
DelaunayPoint p4 = new DelaunayPoint(extent.MinX, extent.MaxY, 0.0f, 0);
int ar = 0;
if (DelaunayGeometry.CrossProduct(m_v[0], p1, m_v[1]) >= 0.0f)
{
++ar;
}
if (DelaunayGeometry.CrossProduct(m_v[0], p2, m_v[1]) >= 0.0f)
{
++ar;
}
if (DelaunayGeometry.CrossProduct(m_v[0], p3, m_v[1]) >= 0.0f)
{
++ar;
}
if (DelaunayGeometry.CrossProduct(m_v[0], p4, m_v[1]) >= 0.0f)
{
++ar;
}
int br = 0;
if (DelaunayGeometry.CrossProduct(m_v[1], p1, m_v[2]) >= 0.0f)
{
++br;
}
if (DelaunayGeometry.CrossProduct(m_v[1], p2, m_v[2]) >= 0.0f)
{
++br;
}
if (DelaunayGeometry.CrossProduct(m_v[1], p3, m_v[2]) >= 0.0f)
{
++br;
}
if (DelaunayGeometry.CrossProduct(m_v[1], p4, m_v[2]) >= 0.0f)
{
++br;
}
int cr = 0;
if (DelaunayGeometry.CrossProduct(m_v[2], p1, m_v[0]) >= 0.0f)
{
++cr;
}
if (DelaunayGeometry.CrossProduct(m_v[2], p2, m_v[0]) >= 0.0f)
{
++cr;
}
if (DelaunayGeometry.CrossProduct(m_v[2], p3, m_v[0]) >= 0.0f)
{
++cr;
}
if (DelaunayGeometry.CrossProduct(m_v[2], p4, m_v[0]) >= 0.0f)
{
++cr;
}
// There will be some sort intersection of triangle with rectangle if at least one point of
// the rectangle is on, or to the right (not zero) of every segment of the triangle.
if (ar != 0 && br != 0 && cr != 0)
{
return(true);
}
return(false);
}
void Update(DelaunayPoint p)
{
List <Triangle> removeList = new List <Triangle>();
List <Triangle> visitedList = new List <Triangle>();
// Go in dfs order and keep adding triangles to it until the vertices of Triangle dont fall in the circumcircle
m_currentTriangle.remove = true;
m_currentTriangle.visited = true;
removeList.Add(m_currentTriangle);
for (int start = 0; start != removeList.Count; ++start)
{
// All triangles with circumcircle containing the point will need to be removed.
Triangle remTriangle = removeList[start];
for (int k = 0; k < 3; k++)
{
Triangle adjacentTriangle = remTriangle.adjacentFace[k];
if (adjacentTriangle != null && !adjacentTriangle.visited)
{
adjacentTriangle.visited = true;
if (adjacentTriangle.CircumCircleContains(p))
{
adjacentTriangle.remove = true;
removeList.Add(adjacentTriangle); //holds a list of removeable Triangle_t
}
else
{
visitedList.Add(adjacentTriangle);
}
}
}
}
if (visitedList.Count > 0)
{
for (int i = 0; i < visitedList.Count; i++)
{
visitedList[i].visited = false;
}
}
visitedList.Clear();
// For every n triangles we are going to remove we should be able to add n+2 new ones
int numNewTriangles = 0;
for (int i = 0; i != removeList.Count; i++)
{
Triangle remTriangle = removeList[i];
for (int j = 0; j != 3; j++)
{
// Create a Triangle for each side that isnt to be removed.
if (remTriangle.adjacentFace[j] == null)
{
numNewTriangles++;
}
else if (!remTriangle.adjacentFace[j].remove)
{
numNewTriangles++;
}
}
}
// Paranoia check.
if (numNewTriangles - 2 != removeList.Count)
{
// Don't expect to hit this, but checking anyways just in case of rounding errors.
for (int i = 0; i != removeList.Count; i++)
{
removeList[i].visited = false;
removeList[i].remove = false;
}
return;
}
// Create new triangles.
List <Triangle> newList = new List <Triangle>();
int[] vertIndex = new int[] { 1, 2, 0 };
for (int i = 0; i != removeList.Count; i++)
{
Triangle remTriangle = removeList[i];
for (int j = 0; j < 3; j++)
{
//create a Triangle for each side that isnt to be removed
Triangle adjacent = remTriangle.adjacentFace[j];
if (adjacent == null)
{
Triangle t = new Triangle(remTriangle.m_v[j], remTriangle.m_v[vertIndex[j]], p);
newList.Add(t);
}
else if (!adjacent.remove)
{
Triangle t = new Triangle(remTriangle.m_v[j], remTriangle.m_v[vertIndex[j]], p);
// Stitch shared edge of new triangle into existing network.
t.adjacentFace[0] = adjacent;
for (int e = 0; e != 3; e++)
{
if (adjacent.adjacentFace[e] == remTriangle)
{
adjacent.adjacentFace[e] = t;
}
}
newList.Add(t);
}
}
}
// Stitch up the new triangles with each-other. Simplified case because vertex[2] for all shared triangles is the same, and is
// in fact parameter point 'p'.
m_currentTriangle = null;
for (int i = 0; i != newList.Count; i++)
{
Triangle t = newList[i];
m_currentTriangle = t;
// Iterate over other un-stitched edges looking for a match.
for (int j = i + 1; (j != newList.Count) && ((t.adjacentFace[1] == null) || (t.adjacentFace[2] == null)); j++)
{
Triangle q = newList[j];
if (t.adjacentFace[1] == null)
{
if (t.m_v[1] == q.m_v[0])
{
t.adjacentFace[1] = q;
q.adjacentFace[2] = t;
}
}
if (t.adjacentFace[2] == null)
{
if (t.m_v[0] == q.m_v[1])
{
t.adjacentFace[2] = q;
q.adjacentFace[1] = t;
}
}
}
}
// Free triangles that were to be removed.
for (int i = 0; i != removeList.Count; i++)
{
Triangle cur = removeList[i];
m_newTriangles.Remove(cur);
FreeTriangle(cur, false);
}
// Add new triangles for later consideration & processing.
for (int i = 0; i != newList.Count; ++i)
{
m_newTriangles.Add(newList[i]);
}
}
bool LocateInternalUsingTriangleList(IEnumerable<Triangle> triangles, DelaunayPoint p)
{
foreach(Triangle triangle in triangles)
{
if (LocateInternal(triangle, p) != null)
return true;
}
return false;
}
float SegmentsIntersect(DelaunayPoint a, DelaunayPoint b, DelaunayPoint c, DelaunayPoint d, double t)
{
//what if denominator is zero??
double diff0 = (c.Y - a.Y) * MULTIPLIER;
double diff1 = (d.X - c.X) * MULTIPLIER;
double diff2 = (a.X - c.X) * MULTIPLIER;
double diff3 = (d.Y - c.Y) * MULTIPLIER;
double diff4 = (b.Y - a.Y) * MULTIPLIER;
double diff5 = (b.X - a.X) * MULTIPLIER;
t = (diff0 * diff1 + diff2 * diff3) / (diff4 * diff1 - diff5 * diff3);
double s = (-diff2 * diff4 - diff0 * diff5) /(diff3 * diff5 - diff1 * diff4);
if(Math.Abs(t) <= VERY_SMALL_DIST)
t = 0;
if(Math.Abs(s) <= VERY_SMALL_DIST)
s = 0;
return (float)s;
}
void Update(DelaunayPoint p)
{
List<Triangle> removeList = new List<Triangle>();
List<Triangle> visitedList = new List<Triangle>();
// Go in dfs order and keep adding triangles to it until the vertices of Triangle dont fall in the circumcircle
m_currentTriangle.remove = true;
m_currentTriangle.visited = true;
removeList.Add(m_currentTriangle);
for (int start = 0; start != removeList.Count; ++start)
{
// All triangles with circumcircle containing the point will need to be removed.
Triangle remTriangle = removeList[start];
for(int k = 0; k < 3; k++)
{
Triangle adjacentTriangle = remTriangle.adjacentFace[k];
if(adjacentTriangle != null && !adjacentTriangle.visited )
{
adjacentTriangle.visited = true;
if(adjacentTriangle.CircumCircleContains(p))
{
adjacentTriangle.remove = true;
removeList.Add(adjacentTriangle); //holds a list of removeable Triangle_t
}
else
{
visitedList.Add(adjacentTriangle);
}
}
}
}
if (visitedList.Count > 0)
{
for(int i = 0; i < visitedList.Count; i++)
visitedList[i].visited = false;
}
visitedList.Clear();
// For every n triangles we are going to remove we should be able to add n+2 new ones
int numNewTriangles = 0;
for(int i = 0; i != removeList.Count; i++)
{
Triangle remTriangle = removeList[i];
for(int j = 0; j != 3; j++)
{
// Create a Triangle for each side that isnt to be removed.
if(remTriangle.adjacentFace[j] == null)
{
numNewTriangles++;
}
else if(!remTriangle.adjacentFace[j].remove)
{
numNewTriangles++;
}
}
}
// Paranoia check.
if(numNewTriangles - 2 != removeList.Count)
{
// Don't expect to hit this, but checking anyways just in case of rounding errors.
for(int i = 0; i != removeList.Count; i++)
{
removeList[i].visited = false;
removeList[i].remove = false;
}
return;
}
// Create new triangles.
List<Triangle> newList = new List<Triangle>();
int[] vertIndex = new int[] { 1, 2, 0 };
for(int i = 0; i != removeList.Count; i++)
{
Triangle remTriangle = removeList[i];
for(int j = 0; j < 3; j++)
{
//create a Triangle for each side that isnt to be removed
Triangle adjacent = remTriangle.adjacentFace[j];
if(adjacent == null)
{
Triangle t = new Triangle(remTriangle.m_v[j], remTriangle.m_v[vertIndex[j]], p);
newList.Add(t);
}
else if(!adjacent.remove)
{
Triangle t = new Triangle(remTriangle.m_v[j], remTriangle.m_v[vertIndex[j]], p);
// Stitch shared edge of new triangle into existing network.
t.adjacentFace[0] = adjacent;
for (int e = 0; e != 3; e++)
{
if (adjacent.adjacentFace[e] == remTriangle)
adjacent.adjacentFace[e] = t;
}
newList.Add(t);
}
}
}
// Stitch up the new triangles with each-other. Simplified case because vertex[2] for all shared triangles is the same, and is
// in fact parameter point 'p'.
m_currentTriangle = null;
for(int i = 0; i != newList.Count; i++)
{
Triangle t = newList[i];
m_currentTriangle = t;
// Iterate over other un-stitched edges looking for a match.
for(int j = i+1; (j != newList.Count) && ((t.adjacentFace[1] == null) || (t.adjacentFace[2] == null)); j++)
{
Triangle q = newList[j];
if (t.adjacentFace[1] == null)
{
if(t.m_v[1] == q.m_v[0])
{
t.adjacentFace[1] = q;
q.adjacentFace[2] = t;
}
}
if (t.adjacentFace[2] == null)
{
if(t.m_v[0] == q.m_v[1])
{
t.adjacentFace[2] = q;
q.adjacentFace[1] = t;
}
}
}
}
// Free triangles that were to be removed.
for(int i = 0; i != removeList.Count; i++)
{
Triangle cur = removeList[i];
m_newTriangles.Remove(cur);
FreeTriangle(cur, false);
}
// Add new triangles for later consideration & processing.
for (int i = 0; i != newList.Count; ++i)
m_newTriangles.Add(newList[i]);
}
bool Overlaps(Extent2D extent)
{
// Check simplist case - triangle inside extent.
if (extent.Contains(m_extent))
return true;
// Use right-hand rule for each triangle segment against all points of extent rectangle.
DelaunayPoint p1 = new DelaunayPoint(extent.MinX, extent.MinY, 0.0f, 0);
DelaunayPoint p2 = new DelaunayPoint(extent.MaxX, extent.MinY, 0.0f, 0);
DelaunayPoint p3 = new DelaunayPoint(extent.MaxX, extent.MaxY, 0.0f, 0);
DelaunayPoint p4 = new DelaunayPoint(extent.MinX, extent.MaxY, 0.0f, 0);
int ar = 0;
if (DelaunayGeometry.CrossProduct(m_v[0], p1, m_v[1]) >= 0.0f)
++ar;
if (DelaunayGeometry.CrossProduct(m_v[0], p2, m_v[1]) >= 0.0f)
++ar;
if (DelaunayGeometry.CrossProduct(m_v[0], p3, m_v[1]) >= 0.0f)
++ar;
if (DelaunayGeometry.CrossProduct(m_v[0], p4, m_v[1]) >= 0.0f)
++ar;
int br = 0;
if (DelaunayGeometry.CrossProduct(m_v[1], p1, m_v[2]) >= 0.0f)
++br;
if (DelaunayGeometry.CrossProduct(m_v[1], p2, m_v[2]) >= 0.0f)
++br;
if (DelaunayGeometry.CrossProduct(m_v[1], p3, m_v[2]) >= 0.0f)
++br;
if (DelaunayGeometry.CrossProduct(m_v[1], p4, m_v[2]) >= 0.0f)
++br;
int cr = 0;
if (DelaunayGeometry.CrossProduct(m_v[2], p1, m_v[0]) >= 0.0f)
++cr;
if (DelaunayGeometry.CrossProduct(m_v[2], p2, m_v[0]) >= 0.0f)
++cr;
if (DelaunayGeometry.CrossProduct(m_v[2], p3, m_v[0]) >= 0.0f)
++cr;
if (DelaunayGeometry.CrossProduct(m_v[2], p4, m_v[0]) >= 0.0f)
++cr;
// There will be some sort intersection of triangle with rectangle if at least one point of
// the rectangle is on, or to the right (not zero) of every segment of the triangle.
if (ar != 0 && br != 0 && cr != 0)
{
return true;
}
return false;
}
public bool IsCoincidentWithVertex(DelaunayPoint p)
{
double distA = (m_v[0].X - p.X) * (m_v[0].X - p.X) + (m_v[0].Y - p.Y) * (m_v[0].Y - p.Y);
double distB = (m_v[1].X - p.X) * (m_v[1].X - p.X) + (m_v[1].Y - p.Y) * (m_v[1].Y - p.Y);
double distC = (m_v[2].X - p.X) * (m_v[2].X - p.X) + (m_v[2].Y - p.Y) * (m_v[2].Y - p.Y);
if((distA <= VERY_SMALL_DIST) || (distB <= VERY_SMALL_DIST) || (distC <= VERY_SMALL_DIST))
return true;
return false;
}
Triangle GetAdjacent(DelaunayPoint start, DelaunayPoint end)
{
double t = 0;
double s = SegmentsIntersect(m_v[0], m_v[1], start, end, t);
if(t >= 0 && t <= 1 && s >= 0 && s <= 1)
{
return adjacentFace[0];
}
s = SegmentsIntersect(m_v[1], m_v[2], start, end, t);
if(t >= 0 && t <= 1 && s >= 0 && s <= 1)
{
return adjacentFace[1];
}
s = SegmentsIntersect(m_v[2], m_v[0], start, end, t);
if(t >= 0 && t <= 1 && s >= 0 && s <= 1)
{
return adjacentFace[2];
}
return null;
}
