static void FinalTriangulation(ref TriangulationStructure returnData, double MaxArea)
{
for (int i = 0; i < returnData.triangles.Count; i++)
{
double currentSquare = getTriangleSquare(returnData.triangles[i], returnData.points);
if (currentSquare > MaxArea)
{
Point p1 = returnData.points[returnData.triangles[i].A];
Point p2 = returnData.points[returnData.triangles[i].B];
Point p3 = returnData.points[returnData.triangles[i].C];
returnData.triangles.Remove(returnData.triangles[i]);
double lengthAB = Point.GetDistance(p1, p2), lengthAC = Point.GetDistance(p1, p3), lengthBC = Point.GetDistance(p2, p3);
int max = Max(lengthAB, lengthAC, lengthBC);
if (max == 0)
{
Point middle = Point.GetMiddlePoint(p1, p2);
if (findPoint(returnData.points, middle) == -1)
{
returnData.points.Add(middle);
}
returnData.triangles.Add(new Triangle(findPoint(returnData.points, p1), findPoint(returnData.points, middle), findPoint(returnData.points, p3)));
returnData.triangles.Add(new Triangle(findPoint(returnData.points, p3), findPoint(returnData.points, middle), findPoint(returnData.points, p2)));
}
else if (max == 1)
{
Point middle = Point.GetMiddlePoint(p1, p3);
if (findPoint(returnData.points, middle) == -1)
{
returnData.points.Add(middle);
}
returnData.triangles.Add(new Triangle(findPoint(returnData.points, p1), findPoint(returnData.points, p2), findPoint(returnData.points, middle)));
returnData.triangles.Add(new Triangle(findPoint(returnData.points, middle), findPoint(returnData.points, p2), findPoint(returnData.points, p3)));
}
else
{
Point middle = Point.GetMiddlePoint(p2, p3);
if (findPoint(returnData.points, middle) == -1)
{
returnData.points.Add(middle);
}
returnData.triangles.Add(new Triangle(findPoint(returnData.points, p1), findPoint(returnData.points, p2), findPoint(returnData.points, middle)));
returnData.triangles.Add(new Triangle(findPoint(returnData.points, p1), findPoint(returnData.points, middle), findPoint(returnData.points, p3)));
}
i--;
}
}
returnData.boundaryPoints = new List <List <List <int> > >();
}
public static TriangulationStructure Triangulate(List <Point> points, double MaxArea)
{
TriangulationStructure res = new TriangulationStructure();
String s = "";
foreach (Point p in points)
{
s += String.Format("{0},{1} ", p.X, p.Y);
}
s = s.Remove(s.Length - 1, 1);
Area area = new Area();
List <Point> tempPoints = new List <Point>();
tempPoints.AddRange(points);
area = Area.convertStrIntoArea(s);
res.points = new List <Point>();
res.triangles = new List <Triangle>();
res.boundaryPoints = new List <List <List <int> > >();
InitialTriangulation(tempPoints, ref res, area, points);
FinalTriangulation(ref res, MaxArea);
SetBoundaryPoints(ref res, points);
return(res);
}
static void SetBoundaryPoints(ref TriangulationStructure returnInfo, List <Point> area)
{
returnInfo.boundaryPoints = new List <List <List <int> > >();
for (int i = 0; i < area.Count - 1; i++)
{
returnInfo.boundaryPoints.Add(new List <List <int> >());
foreach (Triangle tr in returnInfo.triangles)
{
Point p1 = returnInfo.points[tr.A], p2 = returnInfo.points[tr.B], p3 = returnInfo.points[tr.C];
if (Point.IsPointOnTheSegment(area[i], area[i + 1], p1) && Point.IsPointOnTheSegment(area[i], area[i + 1], p2))
{
returnInfo.boundaryPoints.Last().Add(new List <int>()
{
tr.A, tr.B
});
}
else if (Point.IsPointOnTheSegment(area[i], area[i + 1], p1) && Point.IsPointOnTheSegment(area[i], area[i + 1], p3))
{
returnInfo.boundaryPoints.Last().Add(new List <int>()
{
tr.A, tr.C
});
}
else if (Point.IsPointOnTheSegment(area[i], area[i + 1], p2) && Point.IsPointOnTheSegment(area[i], area[i + 1], p3))
{
returnInfo.boundaryPoints.Last().Add(new List <int>()
{
tr.B, tr.C
});
}
}
}
returnInfo.boundaryPoints.Add(new List <List <int> >());
foreach (Triangle tr in returnInfo.triangles)
{
Point p1 = returnInfo.points[tr.A], p2 = returnInfo.points[tr.B], p3 = returnInfo.points[tr.C];
if (Point.IsPointOnTheSegment(area.Last(), area[0], p1) && Point.IsPointOnTheSegment(area.Last(), area[0], p2))
{
returnInfo.boundaryPoints.Last().Add(new List <int>()
{
tr.A, tr.B
});
}
else if (Point.IsPointOnTheSegment(area.Last(), area[0], p1) && Point.IsPointOnTheSegment(area.Last(), area[0], p3))
{
returnInfo.boundaryPoints.Last().Add(new List <int>()
{
tr.A, tr.C
});
}
else if (Point.IsPointOnTheSegment(area.Last(), area[0], p2) && Point.IsPointOnTheSegment(area.Last(), area[0], p3))
{
returnInfo.boundaryPoints.Last().Add(new List <int>()
{
tr.B, tr.C
});
}
}
for (int i = 0; i < area.Count - 1; i++)
{
// List<List<int>> curentBound = returnInfo.boundaryPoints[i];
int begin = findPoint(returnInfo.points, area[i]);
int end = findPoint(returnInfo.points, area[i + 1]);
for (int k = 0; k < returnInfo.boundaryPoints[i].Count; k++)
{
int minIndex = k;
bool direct = true;
for (int j = k; j < returnInfo.boundaryPoints[i].Count; j++)
{
if (returnInfo.boundaryPoints[i][j][0] == begin)
{
minIndex = j;
direct = true;
begin = returnInfo.boundaryPoints[i][j][1];
break;
}
else if (returnInfo.boundaryPoints[i][j][1] == begin)
{
minIndex = j;
direct = false;
begin = returnInfo.boundaryPoints[i][j][0];
break;
}
}
if (direct)
{
List <int> temp = returnInfo.boundaryPoints[i][k];
returnInfo.boundaryPoints[i][k] = returnInfo.boundaryPoints[i][minIndex];
returnInfo.boundaryPoints[i][minIndex] = temp;
}
else
{
returnInfo.boundaryPoints[i][minIndex].Reverse();
List <int> temp = returnInfo.boundaryPoints[i][k];
returnInfo.boundaryPoints[i][k] = returnInfo.boundaryPoints[i][minIndex];
returnInfo.boundaryPoints[i][minIndex] = temp;
}
}
}
// List<List<int>> curentBoundL = returnInfo.boundaryPoints.Last();
int beginL = findPoint(returnInfo.points, area.Last());
int endL = findPoint(returnInfo.points, area[0]);
for (int k = 0; k < returnInfo.boundaryPoints.Last().Count; k++)
{
int minIndexL = k;
bool directL = true;
for (int j = k; j < returnInfo.boundaryPoints.Last().Count; j++)
{
if (returnInfo.boundaryPoints.Last()[j][0] == beginL)
{
minIndexL = j;
directL = true;
beginL = returnInfo.boundaryPoints.Last()[j][1];
break;
}
else if (returnInfo.boundaryPoints.Last()[j][1] == beginL)
{
minIndexL = j;
directL = false;
beginL = returnInfo.boundaryPoints.Last()[j][0];
break;
}
}
if (directL)
{
List <int> temp = returnInfo.boundaryPoints.Last()[k];
returnInfo.boundaryPoints.Last()[k] = returnInfo.boundaryPoints.Last()[minIndexL];
returnInfo.boundaryPoints.Last()[minIndexL] = temp;
}
else
{
returnInfo.boundaryPoints.Last()[minIndexL].Reverse();
List <int> temp = returnInfo.boundaryPoints.Last()[k];
returnInfo.boundaryPoints.Last()[k] = returnInfo.boundaryPoints.Last()[minIndexL];
returnInfo.boundaryPoints.Last()[minIndexL] = temp;
}
}
}
static void InitialTriangulation(List <Point> points, ref TriangulationStructure returnInfo, Area area, List <Point> region)
{
// Triangulation.Triangulation.TriangulationStructure returnInfo = new Triangulation.Triangulation.TriangulationStructure();
List <Point> subPoints = points;
double minimumAngle = 0;
double length1 = 0, length2 = 0;
Point p1 = points.Last();
Point p2 = points[0];
Point p3 = points[1];
length1 = Point.GetDistance(p1, p2);
length2 = Point.GetDistance(p2, p3);
double scalarProduct = Point.GetScalarProduct(p1 - p2, p3 - p2);
minimumAngle = Math.Acos(scalarProduct / length1 / length2);
Point middle = Point.GetMiddlePoint(Point.GetPercentPoint(p2, p1, 1), Point.GetPercentPoint(p2, p3, 1));
if (!ptInPol(area, middle.X, middle.Y))
{
minimumAngle = 2 * Math.PI - minimumAngle;
}
int minIndex = 0;
for (int i = 1; i < points.Count - 1; i++)
{
p1 = points[i - 1];
p2 = points[i];
p3 = points[i + 1];
length1 = Point.GetDistance(p1, p2);
length2 = Point.GetDistance(p2, p3);
scalarProduct = Point.GetScalarProduct(p1 - p2, p3 - p2);
double angle = Math.Acos(scalarProduct / length1 / length2);
middle = Point.GetMiddlePoint(Point.GetPercentPoint(p2, p1, 1), Point.GetPercentPoint(p2, p3, 1));
if (!ptInPol(area, middle.X, middle.Y))
{
angle = 2 * Math.PI - angle;
}
if (angle < minimumAngle)
{
minimumAngle = angle; minIndex = i;
}
}
p1 = points[points.Count() - 2];
p2 = points.Last();
p3 = points[0];
length1 = Point.GetDistance(p1, p2);
length2 = Point.GetDistance(p2, p3);
scalarProduct = Point.GetScalarProduct(p1 - p2, p3 - p2);
double angleL = Math.Acos(scalarProduct / length1 / length2);
middle = Point.GetMiddlePoint(Point.GetPercentPoint(p2, p1, 1), Point.GetPercentPoint(p2, p3, 1));
if (!ptInPol(area, middle.X, middle.Y))
{
angleL = 2 * Math.PI - angleL;
}
if (angleL < minimumAngle)
{
minimumAngle = angleL;
minIndex = points.Count - 1;
}
int k, l, m;
k = l = m = 0;
if (minIndex == 0)
{
k = subPoints.Count - 1;
l = 0;
m = 1;
}
else if (minIndex == points.Count - 1)
{
k = points.Count - 2;
l = points.Count - 1;
m = 0;
}
else
{
k = minIndex - 1;
l = minIndex;
m = minIndex + 1;
}
// returnInfo.points.AddRange(new List<Point>() { points[k], points[l], points[m] });
if (findPoint(returnInfo.points, points[k]) == -1)
{
returnInfo.points.Add(points[k]);
}
if (findPoint(returnInfo.points, points[l]) == -1)
{
returnInfo.points.Add(points[l]);
}
if (findPoint(returnInfo.points, points[m]) == -1)
{
returnInfo.points.Add(points[m]);
}
//int kk = -1, ll = -1, mm = -1;
//for(int i=0; i<region. Count; i++)
//{
// if (points[k] == region[i]) kk = i;
// if (points[l] == region[i]) ll = i;
// if (points[m] == region[i]) mm = i;
//}
//int firstBoundTriangle = -1, secondBoundTriangle = -1;
//List<int> bounds = new List<int>();
returnInfo.triangles.Add(new Triangle(findPoint(returnInfo.points, points[k]), findPoint(returnInfo.points, points[l]), findPoint(returnInfo.points, points[m])));
if (points.Count == 3)
{
return;
}
subPoints.Remove(points[l]);
InitialTriangulation(subPoints, ref returnInfo, area, region);
}
public static TriangulationStructure TriangulateRect(double xx, double yy, int numOfPartision)
{
TriangulationStructure outInfo = new TriangulationStructure();
outInfo.points = new List <Point>();
outInfo.triangles = new List <Triangle>();
double h1 = (xx) / numOfPartision;
double h2 = yy / numOfPartision;
bool isBound = false;
for (int i = 0; i < numOfPartision + 1; i++)
{
double x = i * h1;
if (x == 0 || x == xx)
{
isBound = true;
}
else
{
isBound = false;
}
for (int j = 0; j < numOfPartision + 1; j++)
{
double y = j * h2;
if (isBound == false && (y == 0 || y == yy))
{
isBound = true;
}
outInfo.points.Add(new Point(x, y, isBound));
}
x += h1 / 2.0;
if (x > xx)
{
break;
}
for (int j = 0; j < numOfPartision; j++)
{
double y = j * h2;
y += h2 / 2;
outInfo.points.Add(new Point(x, y));
}
}
for (int i = 0; i < numOfPartision; i++)
{
double x1 = 0 + i * h1;
double x2 = 0 + (i + 1) * h1;
for (int j = 0; j < numOfPartision; j++)
{
double y1 = j * h2;
double y2 = (j + 1) * h2;
Point a11 = new Point(x1, y1), a21 = new Point(x1, y2), a12 = new Point(x2, y1), a22 = new Point(x2, y2), amidle = new Point((x1 + x2) / 2.0, (y1 + y2) / 2.0);
int p11 = findPoint(outInfo.points, a11);
int p12 = findPoint(outInfo.points, a12);
int p21 = findPoint(outInfo.points, a21);
int p22 = findPoint(outInfo.points, a22);
int pmidle = findPoint(outInfo.points, amidle);
outInfo.triangles.Add(new Triangle(p11, p12, pmidle));
outInfo.triangles.Add(new Triangle(p11, pmidle, p21));
outInfo.triangles.Add(new Triangle(pmidle, p12, p22));
outInfo.triangles.Add(new Triangle(p21, pmidle, p22));
}
}
outInfo.boundaryPoints = new List <List <List <int> > >();
outInfo.boundaryPoints.Add(new List <List <int> >());
foreach (var tr in outInfo.triangles)
{
if (outInfo.points[tr.A].Y == 0 && outInfo.points[tr.B].Y == 0)
{
outInfo.boundaryPoints[0].Add(new List <int>()
{
tr.A, tr.B
});
}
if (outInfo.points[tr.B].Y == 0 && outInfo.points[tr.C].Y == 0)
{
outInfo.boundaryPoints[0].Add(new List <int>()
{
tr.B, tr.C
});
}
if (outInfo.points[tr.C].Y == 0 && outInfo.points[tr.A].Y == 0)
{
outInfo.boundaryPoints[0].Add(new List <int>()
{
tr.C, tr.A
});
}
}
outInfo.boundaryPoints.Add(new List <List <int> >());
foreach (var tr in outInfo.triangles)
{
if (outInfo.points[tr.A].X == xx && outInfo.points[tr.B].X == xx)
{
outInfo.boundaryPoints[1].Add(new List <int>()
{
tr.A, tr.B
});
}
if (outInfo.points[tr.B].X == xx && outInfo.points[tr.C].X == xx)
{
outInfo.boundaryPoints[1].Add(new List <int>()
{
tr.B, tr.C
});
}
if (outInfo.points[tr.C].X == xx && outInfo.points[tr.A].X == xx)
{
outInfo.boundaryPoints[1].Add(new List <int>()
{
tr.C, tr.A
});
}
}
outInfo.boundaryPoints.Add(new List <List <int> >());
foreach (var tr in outInfo.triangles)
{
if (outInfo.points[tr.A].Y == yy && outInfo.points[tr.B].Y == yy)
{
outInfo.boundaryPoints[2].Add(new List <int>()
{
tr.A, tr.B
});
}
if (outInfo.points[tr.B].Y == yy && outInfo.points[tr.C].Y == yy)
{
outInfo.boundaryPoints[2].Add(new List <int>()
{
tr.B, tr.C
});
}
if (outInfo.points[tr.C].Y == yy && outInfo.points[tr.A].Y == yy)
{
outInfo.boundaryPoints[2].Add(new List <int>()
{
tr.C, tr.A
});
}
}
outInfo.boundaryPoints[2].Reverse();
outInfo.boundaryPoints.Add(new List <List <int> >());
foreach (var tr in outInfo.triangles)
{
if (outInfo.points[tr.A].X == 0 && outInfo.points[tr.B].X == 0)
{
outInfo.boundaryPoints[3].Add(new List <int>()
{
tr.A, tr.B
});
}
if (outInfo.points[tr.B].X == 0 && outInfo.points[tr.C].X == 0)
{
outInfo.boundaryPoints[3].Add(new List <int>()
{
tr.B, tr.C
});
}
if (outInfo.points[tr.C].X == 0 && outInfo.points[tr.A].X == 0)
{
outInfo.boundaryPoints[3].Add(new List <int>()
{
tr.C, tr.A
});
}
}
outInfo.boundaryPoints[3].Reverse();
return(outInfo);
}