/// <summary>
/// The method calculates the intersection area of triangle a and b both
/// of type XYPolygon.
/// </summary>
/// <param name="triangleA">Triangle of type XYPolygon</param>
/// <param name="triangleB">Triangle of type XYPolygon</param>
/// <returns>
/// Intersection area between the triangles triangleA and triAngleB.
/// </returns>
protected static double TriangleIntersectionArea(XYPolygon triangleA, XYPolygon triangleB)
{
// TODO: Implement new algorithm - it is not very robust.
// Consider an approach similar to the one used by DotSpatial and Java Topology Suite
try
{
if (triangleA.Points.Count != 3 || triangleB.Points.Count != 3)
{
throw new System.Exception("Argument must be a polygon with 3 points");
}
// TODO: implement an epsilon depending on the two triangles at hand.
//XYExtent extentA = XYExtentUtil.GetExtent(triangleA);
//XYExtent extentB = XYExtentUtil.GetExtent(triangleB);
//double scalingLength
// = Math.Max(extentA.XMax - extentA.XMin,
// Math.Max(extentA.YMax - extentA.YMin,
// Math.Max(extentB.XMax - extentB.XMin, extentB.YMax - extentB.YMin)));
//double epsilon = EPSILON * scalingLength;
int i = 1; // Index for "next" node in polygon a.
int j = -1; // Index for "next" node in polygon b.
// -1 indicates that the first has not yet been found.
double area = 0; // Intersection area. Returned.
XYPolygon intersectionPolygon = new XYPolygon(); // Intersection polygon.
XYPoint pFirst = new XYPoint(); // First intersection point between triangles
XYPoint pIntersect = new XYPoint(); // Latest intersection node found
pIntersect.X = triangleA.Points[0].X;
pIntersect.Y = triangleA.Points[0].Y;
Intersect(triangleA, triangleB, ref pIntersect, ref i, ref j, ref intersectionPolygon);
pFirst = pIntersect;
if (j != -1)
{
int jStop = IncrementModula(j, 3);
bool complete = false;
int count = 0;
while (!complete)
{
// coordinates for vectors pointing to next triangleA and triangleB point respectively
double vax = triangleA.Points[i].X - pIntersect.X;
double vay = triangleA.Points[i].Y - pIntersect.Y;
double vbx = triangleB.Points[j].X - pIntersect.X;
double vby = triangleB.Points[j].Y - pIntersect.Y;
// The sideOf tells if the vb vector or the va vector is the one pointing "left"
// If sideOf is positive, vb is pointing left, otherwise va is pointing left
// The "left" vector is the one that is inside the polygon.
double sideOf = vax * vby - vay * vbx;
// Make sure to get out of EPSILON reach from the original point, hence 2*EPSILON
if (sideOf < 0 && IsPointInPolygon(pIntersect.X + 2 * EPSILON * vax, pIntersect.Y + 2 * EPSILON * vay, triangleB))
{
Intersect(triangleA, triangleB, ref pIntersect, ref i, ref j, ref intersectionPolygon);
}
else if (sideOf > 0 && IsPointInPolygon(pIntersect.X + 2 * EPSILON * vbx, pIntersect.Y + 2 * EPSILON * vby, triangleA))
{
Intersect(triangleB, triangleA, ref pIntersect, ref j, ref i, ref intersectionPolygon);
}
// can be true if the point is on the edge of the triangleB
// TODO: Replace with IsPointOnEdge of triangleB
else if (IsPointInPolygonOrOnEdge(pIntersect.X + 2 * EPSILON * vax, pIntersect.Y + 2 * EPSILON * vay, triangleB))
{
Intersect(triangleA, triangleB, ref pIntersect, ref i, ref j, ref intersectionPolygon);
}
// can be true if the point is on the edge of the triangleA
// Should never happen, since above test basically does the same
// TODO: Replace with IsPointOnEdge of triangleA
else if (IsPointInPolygonOrOnEdge(pIntersect.X + 2 * EPSILON * vbx, pIntersect.Y + 2 * EPSILON * vby, triangleA))
{
Intersect(triangleB, triangleA, ref pIntersect, ref j, ref i, ref intersectionPolygon);
}
else // triangleA and triangleB only touches one another but do not intersect
{
area = 0;
return(area);
}
if (intersectionPolygon.Points.Count > 1)
{
complete = (CalculatePointToPointDistance(pIntersect, pFirst) < EPSILON);
}
count++;
if (count > 20)
{
throw new System.Exception("Failed to find intersection polygon");
}
}
area = intersectionPolygon.GetArea();
}
else
{
XYPoint pa = new XYPoint(); // internal point in triangle a
XYPoint pb = new XYPoint(); // internal point in triangle b
pa.X = (triangleA.GetX(0) + triangleA.GetX(1) + triangleA.GetX(2)) / 3;
pa.Y = (triangleA.GetY(0) + triangleA.GetY(1) + triangleA.GetY(2)) / 3;
pb.X = (triangleB.GetX(0) + triangleB.GetX(1) + triangleB.GetX(2)) / 3;
pb.Y = (triangleB.GetY(0) + triangleB.GetY(1) + triangleB.GetY(2)) / 3;
if (IsPointInPolygon(pa, triangleB) || IsPointInPolygon(pb, triangleA)) // triangleA is completely inside triangleB
{
area = Math.Min(triangleA.GetArea(), triangleB.GetArea());
}
else // triangleA and triangleB do dot intersect
{
area = 0;
}
}
return(area);
}
catch (System.Exception e)
{
throw new System.Exception("TriangleIntersectionArea failed", e);
}
}
/// <summary>
/// The method calculates the intersection area of triangle a and b both
/// of type XYPolygon.
/// </summary>
/// <param name="triangleA">Triangle of type XYPolygon</param>
/// <param name="triangleB">Triangle of type XYPolygon</param>
/// <returns>
/// Intersection area between the triangles triangleA and triAngleB.
/// </returns>
protected static double TriangleIntersectionArea(XYPolygon triangleA, XYPolygon triangleB)
{
try
{
if (triangleA.Points.Count != 3 || triangleB.Points.Count != 3)
{
throw new System.Exception("Argument must be a polygon with 3 points");
}
int i = 1; // Index for "next" node in polygon a.
int j = -1; // Index for "next" node in polygon b.
// -1 indicates that the first has not yet been found.
double area = 0; // Intersection area. Returned.
XYPolygon intersectionPolygon = new XYPolygon(); // Intersection polygon.
XYPoint p = new XYPoint(); // Latest intersection node found
p.X = ((XYPoint)triangleA.Points[0]).X;
p.Y = ((XYPoint)triangleA.Points[0]).Y;
Intersect(triangleA, triangleB, ref p, ref i, ref j, ref intersectionPolygon);
if (j != -1)
{
// ERB 8/30/2012: For efficiency, allocate and initialize pFirst inside if block
XYPoint pFirst = new XYPoint(); // First intersection point between triangles
pFirst = p;
int jStop = Increase(j, 2);
bool complete = false;
int count = 0;
while (!complete)
{
// coordinates for vectors pointing to next triangleA and triangleB point respectively
double vax = ((XYPoint)triangleA.Points[i]).X - p.X;
double vay = ((XYPoint)triangleA.Points[i]).Y - p.Y;
double vbx = ((XYPoint)triangleB.Points[j]).X - p.X;
double vby = ((XYPoint)triangleB.Points[j]).Y - p.Y;
if (IsPointInPolygonOrOnEdge(p.X + EPSILON * vax, p.Y + EPSILON * vay, triangleB))
{
Intersect(triangleA, triangleB, ref p, ref i, ref j, ref intersectionPolygon);
}
else if (IsPointInPolygonOrOnEdge(p.X + EPSILON * vbx, p.Y + EPSILON * vby, triangleA))
{
Intersect(triangleB, triangleA, ref p, ref j, ref i, ref intersectionPolygon);
}
else // triangleA and triangleB only touches one another but do not intersect
{
area = 0;
return(area);
}
if (intersectionPolygon.Points.Count > 1)
{
complete = (CalculatePointToPointDistance(p, pFirst) < EPSILON);
}
count++;
if (count > 20)
{
throw new System.Exception("Failed to find intersection polygon");
}
}
area = intersectionPolygon.GetArea();
}
else
{
XYPoint pa = new XYPoint(); // internal point in triangle a
XYPoint pb = new XYPoint(); // internal point in triangle b
pa.X = (triangleA.GetX(0) + triangleA.GetX(1) + triangleA.GetX(2)) / 3;
pa.Y = (triangleA.GetY(0) + triangleA.GetY(1) + triangleA.GetY(2)) / 3;
pb.X = (triangleB.GetX(0) + triangleB.GetX(1) + triangleB.GetX(2)) / 3;
pb.Y = (triangleB.GetY(0) + triangleB.GetY(1) + triangleB.GetY(2)) / 3;
if (IsPointInPolygon(pa, triangleB) || IsPointInPolygon(pb, triangleA)) // triangleA is completely inside triangleB
{
area = Math.Min(triangleA.GetArea(), triangleB.GetArea());
}
else // triangleA and triangleB do dot intersect
{
area = 0;
}
}
return(area);
}
catch (System.Exception e)
{
throw new System.Exception("TriangleIntersectionArea failed", e);
}
}
/// <summary>
/// The method calculates the intersection area of triangle a and b both
/// of type XYPolygon.
/// </summary>
/// <param name="triangleA">Triangle of type XYPolygon</param>
/// <param name="triangleB">Triangle of type XYPolygon</param>
/// <returns>
/// Intersection area between the triangles triangleA and triAngleB.
/// </returns>
protected static double TriangleIntersectionArea(XYPolygon triangleA, XYPolygon triangleB)
{
try
{
if (triangleA.Points.Count != 3 || triangleB.Points.Count != 3)
{
throw new System.Exception("Argument must be a polygon with 3 points");
}
int i = 1; // Index for "next" node in polygon a.
int j = -1; // Index for "next" node in polygon b.
// -1 indicates that the first has not yet been found.
double area = 0; // Intersection area. Returned.
XYPolygon intersectionPolygon = new XYPolygon(); // Intersection polygon.
XYPoint pFirst = new XYPoint(); // First intersection point between triangles
XYPoint p = new XYPoint(); // Latest intersection node found
p.X = ((XYPoint) triangleA.Points[0]).X;
p.Y = ((XYPoint) triangleA.Points[0]).Y;
Intersect(triangleA, triangleB, ref p, ref i, ref j, ref intersectionPolygon);
pFirst = p;
if (j != -1)
{
int jStop = Increase(j, 2);
bool complete = false;
int count = 0;
while (!complete)
{
// coordinates for vectors pointing to next triangleA and triangleB point respectively
double vax= ((XYPoint) triangleA.Points[i]).X - p.X;
double vay= ((XYPoint) triangleA.Points[i]).Y - p.Y;
double vbx= ((XYPoint) triangleB.Points[j]).X - p.X;
double vby= ((XYPoint) triangleB.Points[j]).Y - p.Y;
if(IsPointInPolygonOrOnEdge(p.X + EPSILON*vax, p.Y + EPSILON*vay, triangleB))
{
Intersect(triangleA, triangleB, ref p, ref i, ref j, ref intersectionPolygon);
}
else if(IsPointInPolygonOrOnEdge(p.X + EPSILON*vbx, p.Y + EPSILON*vby, triangleA))
{
Intersect(triangleB, triangleA, ref p, ref j, ref i, ref intersectionPolygon);
}
else // triangleA and triangleB only touches one another but do not intersect
{
area = 0;
return area;
}
if (intersectionPolygon.Points.Count > 1)
{
complete = (CalculatePointToPointDistance(p, pFirst) < EPSILON);
}
count++;
if ( count > 20 )
{
throw new System.Exception("Failed to find intersection polygon");
}
}
area = intersectionPolygon.GetArea();
}
else
{
XYPoint pa = new XYPoint(); // internal point in triangle a
XYPoint pb = new XYPoint(); // internal point in triangle b
pa.X = (triangleA.GetX(0)+triangleA.GetX(1)+triangleA.GetX(2))/3;
pa.Y = (triangleA.GetY(0)+triangleA.GetY(1)+triangleA.GetY(2))/3;
pb.X = (triangleB.GetX(0)+triangleB.GetX(1)+triangleB.GetX(2))/3;
pb.Y = (triangleB.GetY(0)+triangleB.GetY(1)+triangleB.GetY(2))/3;
if (IsPointInPolygon(pa,triangleB) || IsPointInPolygon(pb,triangleA)) // triangleA is completely inside triangleB
{
area = Math.Min(triangleA.GetArea(),triangleB.GetArea());
}
else // triangleA and triangleB do dot intersect
{
area = 0;
}
}
return area;
}
catch (System.Exception e)
{
throw new System.Exception("TriangleIntersectionArea failed",e);
}
}