protected void CalculateFactors(IElementSet elementSet)
{
for (int i = 0; i < elementSet.ElementCount; i++)
{
XYPolygon element = ElementMapper.CreateXYPolygon(elementSet, i);
double area = element.GetArea();
if (_areaExponent == 1)
{
_factors[i] = area;
}
else if (_areaExponent == -1)
{
_factors[i] = 1.0 / area;
}
else
{
_factors[i] = Math.Pow(area, _areaExponent);
}
}
}
public void GetArea()
{
// -- Rectangle --
XYPolygon xypolygon = new XYPolygon();
xypolygon.Points.Add(new XYPoint(1,1));
xypolygon.Points.Add(new XYPoint(9,1));
xypolygon.Points.Add(new XYPoint(9,6));
xypolygon.Points.Add(new XYPoint(1,6));
Assert.AreEqual((double) 40, xypolygon.GetArea());
// -- Triangle --
XYPolygon xypolygon2 = new XYPolygon();
xypolygon2.Points.Add(new XYPoint(1,1));
xypolygon2.Points.Add(new XYPoint(9,1));
xypolygon2.Points.Add(new XYPoint(9,6));
Assert.AreEqual((double) 20, xypolygon2.GetArea());
// -- concave --
XYPolygon xypolygon3 = new XYPolygon();
xypolygon3.Points.Add(new XYPoint(1,1));
xypolygon3.Points.Add(new XYPoint(5,3));
xypolygon3.Points.Add(new XYPoint(9,1));
xypolygon3.Points.Add(new XYPoint(9,6));
xypolygon3.Points.Add(new XYPoint(1,6));
Assert.AreEqual((double) 32, xypolygon3.GetArea());
// -- concave --
XYPolygon xypolygon4 = new XYPolygon();
xypolygon4.Points.Add(new XYPoint(1,1));
xypolygon4.Points.Add(new XYPoint(9,1));
xypolygon4.Points.Add(new XYPoint(5,5));
xypolygon4.Points.Add(new XYPoint(5,3));
xypolygon4.Points.Add(new XYPoint(3,3));
xypolygon4.Points.Add(new XYPoint(3,8));
xypolygon4.Points.Add(new XYPoint(9,8));
xypolygon4.Points.Add(new XYPoint(9,11));
xypolygon4.Points.Add(new XYPoint(1,11));
Assert.AreEqual((double) 50, xypolygon4.GetArea());
}
/// <summary>
/// Calculates the mapping matrix between fromElements and toElements. The mapping method
/// is decided from the combination of methodDescription, fromElements.ElementType and
/// toElements.ElementType.
/// The valid values for methodDescription is obtained through use of the
/// GetAvailableMethods method.
/// </summary>
///
/// <remarks>
/// UpdateMappingMatrix is called during initialisation. UpdateMappingMatrix must be called prior
/// to Mapvalues.
/// </remarks>
///
/// <param name="methodIdentifier">String identification of mapping method</param>
/// <param name="fromElements">The IElementset to map from.</param>
/// <param name="toElements">The IElementset to map to</param>
///
/// <returns>
/// The method has no return value.
/// </returns>
private void UpdateMappingMatrix(ref IIdentifiable methodIdentifier, ref IElementSet fromElements, ref IElementSet toElements)
{
try
{
ElementSetChecker.CheckElementSet(fromElements);
ElementSetChecker.CheckElementSet(toElements);
_method = SpatialAdaptedOutputFactory.GetMethod(methodIdentifier);
_numberOfToRows = toElements.ElementCount;
_numberOfFromColumns = fromElements.ElementCount;
_mappingMatrix = new DoubleSparseMatrix(_numberOfToRows, _numberOfFromColumns);
if (fromElements.ElementType == ElementType.Point && toElements.ElementType == ElementType.Point)
{
#region
try
{
for (int i = 0; i < _numberOfToRows; i++)
{
XYPoint toPoint = CreateXYPoint(toElements, i);
for (int j = 0; j < _numberOfFromColumns; j++)
{
XYPoint fromPoint = CreateXYPoint(fromElements, j);
_mappingMatrix[i, j] = XYGeometryTools.CalculatePointToPointDistance(toPoint, fromPoint);
}
}
if (_method == ElementMapperMethod.Nearest)
{
for (int i = 0; i < _numberOfToRows; i++)
{
double minDist = _mappingMatrix[i, 0];
for (int j = 1; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] < minDist)
{
minDist = _mappingMatrix[i, j];
}
}
int denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] == minDist)
{
_mappingMatrix[i, j] = 1;
denominator++;
}
else
{
_mappingMatrix[i, j] = 0;
}
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
}
else if (_method == ElementMapperMethod.Inverse)
{
for (int i = 0; i < _numberOfToRows; i++)
{
double minDist = _mappingMatrix[i, 0];
for (int j = 1; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] < minDist)
{
minDist = _mappingMatrix[i, j];
}
}
if (minDist == 0)
{
int denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] == minDist)
{
_mappingMatrix[i, j] = 1;
denominator++;
}
else
{
_mappingMatrix[i, j] = 0;
}
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
else
{
double denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = 1 / _mappingMatrix[i, j];
denominator = denominator + _mappingMatrix[i, j];
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
}
}
else
{
throw new Exception("methodDescription unknown for point point mapping");
}
}
catch (Exception e)
{
throw new Exception("Point to point mapping failed", e);
}
#endregion
}
else if (fromElements.ElementType == ElementType.Point && toElements.ElementType == ElementType.PolyLine)
{
#region
try
{
for (int i = 0; i < _numberOfToRows; i++)
{
XYPolyline toPolyLine = CreateXYPolyline(toElements, i);
for (int j = 0; j < _numberOfFromColumns; j++)
{
XYPoint fromPoint = CreateXYPoint(fromElements, j);
_mappingMatrix[i, j] = XYGeometryTools.CalculatePolylineToPointDistance(toPolyLine,
fromPoint);
}
}
if (_method == ElementMapperMethod.Nearest)
{
for (int i = 0; i < _numberOfToRows; i++)
{
double minDist = _mappingMatrix[i, 0];
for (int j = 1; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] < minDist)
{
minDist = _mappingMatrix[i, j];
}
}
int denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] == minDist)
{
_mappingMatrix[i, j] = 1;
denominator++;
}
else
{
_mappingMatrix[i, j] = 0;
}
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
}
else if (_method == ElementMapperMethod.Inverse)
{
for (int i = 0; i < _numberOfToRows; i++)
{
double minDist = _mappingMatrix[i, 0];
for (int j = 1; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] < minDist)
{
minDist = _mappingMatrix[i, j];
}
}
if (minDist == 0)
{
int denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] == minDist)
{
_mappingMatrix[i, j] = 1;
denominator++;
}
else
{
_mappingMatrix[i, j] = 0;
}
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
else
{
double denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = 1 / _mappingMatrix[i, j];
denominator = denominator + _mappingMatrix[i, j];
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
}
}
else
{
throw new Exception("methodDescription unknown for point to polyline mapping");
}
}
catch (Exception e)
{
throw new Exception("Point to polyline mapping failed", e);
}
#endregion
}
else if (fromElements.ElementType == ElementType.Point &&
toElements.ElementType == ElementType.Polygon)
{
#region
try
{
for (int i = 0; i < _numberOfToRows; i++)
{
XYPolygon polygon = CreateXYPolygon(toElements, i);
int count = 0;
XYPoint point;
for (int n = 0; n < _numberOfFromColumns; n++)
{
point = CreateXYPoint(fromElements, n);
if (XYGeometryTools.IsPointInPolygon(point, polygon))
{
if (_method == ElementMapperMethod.Mean)
{
count = count + 1;
}
else if (_method == ElementMapperMethod.Sum)
{
count = 1;
}
else
{
throw new Exception(
"methodDescription unknown for point to polygon mapping");
}
}
}
for (int n = 0; n < _numberOfFromColumns; n++)
{
point = CreateXYPoint(fromElements, n);
if (XYGeometryTools.IsPointInPolygon(point, polygon))
{
_mappingMatrix[i, n] = 1.0 / count;
}
}
}
}
catch (Exception e)
{
throw new Exception("Point to polygon mapping failed", e);
}
#endregion
}
else if (fromElements.ElementType == ElementType.PolyLine &&
toElements.ElementType == ElementType.Point)
{
#region
try
{
for (int i = 0; i < _numberOfToRows; i++)
{
XYPoint toPoint = CreateXYPoint(toElements, i);
for (int j = 0; j < _numberOfFromColumns; j++)
{
XYPolyline fromPolyLine = CreateXYPolyline(fromElements, j);
_mappingMatrix[i, j] =
XYGeometryTools.CalculatePolylineToPointDistance(fromPolyLine, toPoint);
}
}
if (_method == ElementMapperMethod.Nearest)
{
for (int i = 0; i < _numberOfToRows; i++)
{
double minDist = _mappingMatrix[i, 0];
for (int j = 1; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] < minDist)
{
minDist = _mappingMatrix[i, j];
}
}
int denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] == minDist)
{
_mappingMatrix[i, j] = 1;
denominator++;
}
else
{
_mappingMatrix[i, j] = 0;
}
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
}
else if (_method == ElementMapperMethod.Inverse)
{
for (int i = 0; i < _numberOfToRows; i++)
{
double minDist = _mappingMatrix[i, 0];
for (int j = 1; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] < minDist)
{
minDist = _mappingMatrix[i, j];
}
}
if (minDist == 0)
{
int denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
if (_mappingMatrix[i, j] == minDist)
{
_mappingMatrix[i, j] = 1;
denominator++;
}
else
{
_mappingMatrix[i, j] = 0;
}
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
else
{
double denominator = 0;
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = 1 / _mappingMatrix[i, j];
denominator = denominator + _mappingMatrix[i, j];
}
for (int j = 0; j < _numberOfFromColumns; j++)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
}
}
else
{
throw new Exception("methodDescription unknown for polyline to point mapping");
}
}
catch (Exception e) // Catch for all of the Point to Polyline part
{
throw new Exception("Polyline to point mapping failed", e);
}
#endregion
}
else if (fromElements.ElementType == ElementType.PolyLine &&
toElements.ElementType == ElementType.Polygon)
{
#region
try
{
// For each polygon in target
for (int i = 0; i < _numberOfToRows; i++)
{
XYPolygon polygon = CreateXYPolygon(toElements, i);
if (_method == ElementMapperMethod.WeightedMean)
{
double totalLineLengthInPolygon = 0;
for (int n = 0; n < _numberOfFromColumns; n++)
{
XYPolyline polyline = CreateXYPolyline(fromElements, n);
_mappingMatrix[i, n] =
XYGeometryTools.CalculateLengthOfPolylineInsidePolygon(
polyline, polygon);
totalLineLengthInPolygon += _mappingMatrix[i, n];
}
if (totalLineLengthInPolygon > 0)
{
for (int n = 0; n < _numberOfFromColumns; n++)
{
_mappingMatrix[i, n] = _mappingMatrix[i, n] /
totalLineLengthInPolygon;
}
}
}
else if (_method == ElementMapperMethod.WeightedSum)
{
// For each line segment in PolyLine
for (int n = 0; n < _numberOfFromColumns; n++)
{
XYPolyline polyline = CreateXYPolyline(fromElements, n);
_mappingMatrix[i, n] =
XYGeometryTools.CalculateLengthOfPolylineInsidePolygon(
polyline, polygon) / polyline.GetLength();
}
}
else
{
throw new Exception(
"methodDescription unknown for polyline to polygon mapping");
}
}
}
catch (Exception e)
{
throw new Exception("Polyline to polygon mapping failed", e);
}
#endregion
}
else if (fromElements.ElementType == ElementType.Polygon &&
toElements.ElementType == ElementType.Point)
{
#region
try
{
if (_method != ElementMapperMethod.Value)
{
throw new Exception("methodDescription unknown for polygon to point mapping");
}
// Only create search tree if number of cols/rows is larger than say 10/10.
bool useSearchTree = _numberOfFromColumns > 10 && _numberOfToRows > 10;
XYElementSearchTree <int> fromSearchTree = null;
ICollection <int> fromCandidateElmts = null;
if (useSearchTree)
{
fromSearchTree = XYElementSearchTree <int> .BuildSearchTree(fromElements);
}
else
{
fromCandidateElmts = new IntSequence(0, _numberOfFromColumns - 1);
}
for (int n = 0; n < _numberOfToRows; n++)
{
XYPoint point = CreateXYPoint(toElements, n);
if (useSearchTree)
{
XYExtent toExtent = XYExtentUtil.GetExtent(point, XYGeometryTools.EPSILON);
fromCandidateElmts = fromSearchTree.FindElements(toExtent);
}
int count = 0;
// Check first for strict inclusion
foreach (int i in fromCandidateElmts)
{
XYPolygon polygon = CreateXYPolygon(fromElements, i);
if (XYGeometryTools.IsPointInPolygon(point, polygon))
{
_mappingMatrix[n, i] = 1.0;
count++;
}
}
if (count == 0)
{
// Not strictly inside any polygon, check also edges
foreach (int i in fromCandidateElmts)
{
XYPolygon polygon = CreateXYPolygon(fromElements, i);
if (XYGeometryTools.IsPointInPolygonOrOnEdge(point, polygon))
{
_mappingMatrix[n, i] = 1.0;
count++;
}
}
}
if (count > 1)
{
// In case of more than one hit, use average
foreach (int i in fromCandidateElmts)
{
if (_mappingMatrix[n, i] != 0.0)
{
_mappingMatrix[n, i] = 1.0 / count;
}
}
}
}
}
catch (Exception e)
{
throw new Exception("Polygon to point mapping failed", e);
}
#endregion
}
else if (fromElements.ElementType == ElementType.Polygon &&
toElements.ElementType == ElementType.PolyLine)
// Polygon to PolyLine
{
#region
try
{
for (int i = 0; i < _numberOfToRows; i++)
{
XYPolyline polyline = CreateXYPolyline(toElements, i);
if (_method == ElementMapperMethod.WeightedMean)
{
for (int n = 0; n < _numberOfFromColumns; n++)
{
XYPolygon polygon = CreateXYPolygon(fromElements, n);
_mappingMatrix[i, n] =
XYGeometryTools.CalculateLengthOfPolylineInsidePolygon(
polyline, polygon) / polyline.GetLength();
}
double sum = 0;
for (int n = 0; n < _numberOfFromColumns; n++)
{
sum += _mappingMatrix[i, n];
}
for (int n = 0; n < _numberOfFromColumns; n++)
{
_mappingMatrix[i, n] = _mappingMatrix[i, n] / sum;
}
}
else if (_method == ElementMapperMethod.WeightedSum)
{
for (int n = 0; n < _numberOfFromColumns; n++)
{
XYPolygon polygon = CreateXYPolygon(fromElements, n);
_mappingMatrix[i, n] =
XYGeometryTools.CalculateLengthOfPolylineInsidePolygon(
polyline, polygon) / polyline.GetLength();
}
}
else
{
throw new Exception(
"methodDescription unknown for polygon to polyline mapping");
}
}
}
catch (Exception e) // catch for all of Polygon to PolyLine
{
throw new Exception("Polygon to polyline mapping failed", e);
}
#endregion
}
else if (fromElements.ElementType == ElementType.Polygon &&
toElements.ElementType == ElementType.Polygon)
// Polygon to Polygon
{
#region
try
{
// Only create search tree if number of cols/rows is larger than say 100/10.
bool useSearchTree = _numberOfFromColumns > 10 && _numberOfToRows > 10;
XYElementSearchTree <int> fromSearchTree = null;
ICollection <int> fromCandidateElmts = null;
if (useSearchTree)
{
fromSearchTree = XYElementSearchTree <int> .BuildSearchTree(fromElements);
}
else
{
fromCandidateElmts = new IntSequence(0, _numberOfFromColumns - 1);
}
for (int i = 0; i < _numberOfToRows; i++)
{
XYPolygon toPolygon = CreateXYPolygon(toElements, i);
if (useSearchTree)
{
XYExtent toExtent = XYExtentUtil.GetExtent(toPolygon);
fromCandidateElmts = fromSearchTree.FindElements(toExtent);
}
foreach (int j in fromCandidateElmts)
{
XYPolygon fromPolygon = CreateXYPolygon(fromElements, j);
_mappingMatrix[i, j] = XYGeometryTools.CalculateSharedArea(
toPolygon, fromPolygon);
if (_method == ElementMapperMethod.Distribute)
{
_mappingMatrix[i, j] /= fromPolygon.GetArea();
}
}
if (_method == ElementMapperMethod.WeightedMean)
{
double denominator = 0;
foreach (int j in fromCandidateElmts)
{
denominator = denominator + _mappingMatrix[i, j];
}
foreach (int j in fromCandidateElmts)
{
if (denominator != 0)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / denominator;
}
}
}
else if (_method == ElementMapperMethod.WeightedSum)
{
foreach (int j in fromCandidateElmts)
{
_mappingMatrix[i, j] = _mappingMatrix[i, j] / toPolygon.GetArea();
}
}
else if (_method != ElementMapperMethod.Distribute)
{
throw new Exception(
"methodDescription unknown for polygon to polygon mapping");
}
}
}
catch (Exception e) // catch for all of Polygon to Polygon
{
throw new Exception("Polygon to polygon mapping failed", e);
}
#endregion
}
else // if the fromElementType, toElementType combination is no implemented
{
throw new Exception(
"Mapping of specified ElementTypes not included in ElementMapper");
}
}
catch (Exception e)
{
throw new Exception("UpdateMappingMatrix failed to update mapping matrix", 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)
{
// 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 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);
}
}
public void Protected_TriangleIntersectionArea()
{
XYPolygon t1 = new XYPolygon();
t1.Points.Add(new XYPoint(0.0, 0.5));
t1.Points.Add(new XYPoint(6.0, 0.5));
t1.Points.Add(new XYPoint(1.0, 7.0));
XYPolygon t2 = new XYPolygon();
t2.Points.Add(new XYPoint(1,1));
t2.Points.Add(new XYPoint(5,1));
t2.Points.Add(new XYPoint(1,5));
XYPolygon t3 = new XYPolygon();
t3.Points.Add(new XYPoint(1,1));
t3.Points.Add(new XYPoint(3,1));
t3.Points.Add(new XYPoint(1,3));
XYPolygon t4 = new XYPolygon();
t4.Points.Add(new XYPoint(1,2));
t4.Points.Add(new XYPoint(3,2));
t4.Points.Add(new XYPoint(3,4));
XYPolygon t5 = new XYPolygon();
t5.Points.Add(new XYPoint(6.5,3.5));
t5.Points.Add(new XYPoint(9.5,3.4));
t5.Points.Add(new XYPoint(7,5));
XYPolygon t6 = new XYPolygon();
t6.Points.Add(new XYPoint(-2,0));
t6.Points.Add(new XYPoint(3,0));
t6.Points.Add(new XYPoint(3,2));
//t2 is fully inside t1
Assert.AreEqual(8,AXYGeometryTools.ATriangleIntersectionArea(t2,t1),"t2, t1");
Assert.AreEqual(8,AXYGeometryTools.ATriangleIntersectionArea(t1,t2),"t1, t2");
// t4 is partly inside t2
Assert.AreEqual((double)7/ (double) 4, AXYGeometryTools.ATriangleIntersectionArea(t2,t4),"t2, t4");
Assert.AreEqual((double)7/ (double) 4, AXYGeometryTools.ATriangleIntersectionArea(t4,t2),"t4, t2");
// t3 is inside t2 but is sharing two edges
Assert.AreEqual(2, AXYGeometryTools.ATriangleIntersectionArea(t2,t3),"t2, t3");
Assert.AreEqual(2, AXYGeometryTools.ATriangleIntersectionArea(t3,t2),"t3, t2");
// t1 and t5 has no overlap
Assert.AreEqual(0, AXYGeometryTools.ATriangleIntersectionArea(t1,t5),"t1, t5");
Assert.AreEqual(0, AXYGeometryTools.ATriangleIntersectionArea(t5,t1),"t5, t1");
// two times t6
Assert.AreEqual(t6.GetArea(), AXYGeometryTools.ATriangleIntersectionArea(t6,t6),"t6, t6");
}
public void CalculateSharedArea()
{
XYPolygon p1 = new XYPolygon();
p1.Points.Add(new XYPoint(0, 3));
p1.Points.Add(new XYPoint(3, 0));
p1.Points.Add(new XYPoint(8, 0));
p1.Points.Add(new XYPoint(8, 2));
p1.Points.Add(new XYPoint(3, 1));
p1.Points.Add(new XYPoint(3, 3));
p1.Points.Add(new XYPoint(8, 3));
p1.Points.Add(new XYPoint(4, 7));
XYPolygon p2 = new XYPolygon();
p2.Points.Add(new XYPoint(3, 3));
p2.Points.Add(new XYPoint(4, 3));
p2.Points.Add(new XYPoint(4, 4));
p2.Points.Add(new XYPoint(3, 4));
XYPolygon p3 = new XYPolygon();
p3.Points.Add(new XYPoint(0, 0));
p3.Points.Add(new XYPoint(8, 0));
p3.Points.Add(new XYPoint(8, 8));
p3.Points.Add(new XYPoint(0, 8));
XYPolygon p4 = new XYPolygon();
p4.Points.Add(new XYPoint(-2, 0));
p4.Points.Add(new XYPoint(3, 0));
p4.Points.Add(new XYPoint(3, 2));
p4.Points.Add(new XYPoint(0, 2));
p4.Points.Add(new XYPoint(0, 5));
p4.Points.Add(new XYPoint(4, 5));
p4.Points.Add(new XYPoint(4, 7));
p4.Points.Add(new XYPoint(-2, 7));
Assert.AreEqual(p1.GetArea(),XYGeometryTools.CalculateSharedArea(p1,p1),1e-12,"Test1 - Polygon1 in Polygon1");
Assert.AreEqual(p2.GetArea(),XYGeometryTools.CalculateSharedArea(p2,p2),1e-12,"Test2 - Polygon1 in Polygon1");
Assert.AreEqual(p4.GetArea(),XYGeometryTools.CalculateSharedArea(p4,p4),1e-12,"Test3 - Polygon1 in Polygon1");
Assert.AreEqual(p2.GetArea(),XYGeometryTools.CalculateSharedArea(p1,p2),1e-12,"Test4 - Polygon2 in Polygon1");
Assert.AreEqual(p1.GetArea(),XYGeometryTools.CalculateSharedArea(p1,p3),1e-12,"Test5 - Polygon1 in Polygon2");
Assert.AreEqual(4,XYGeometryTools.CalculateSharedArea(p1,p4),1e-12,"Test6 - Polygon1 in Polygon3");
}
