/// <summary>
/// Set to be the minimum bounding circle for the 2 points.
/// </summary>
/// <param name="Point1">The first point to include.</param>
/// <param name="Point2">The second point to include.</param>
public void SetMinimum(C2DPoint Point1, C2DPoint Point2)
{
C2DVector Vec = new C2DVector(Point1, Point2);
Vec.Multiply( 0.5);
Radius = Vec.GetLength();
_Centre.Set(Point1.GetPointTo(Vec));
}
/// <summary>
/// Contructor.
/// </summary>
/// <param name="PtFrom">The point the arc is to go from.</param>
/// <param name="Vector">The vector defining the end point.</param>
/// <param name="dRadius">The corresponding circles radius.</param>
/// <param name="bCentreOnRight">Whether the centre is on the right.</param>
/// <param name="bArcOnRight">Whether the arc is to the right of the line.</param>
public C2DArc(C2DPoint PtFrom, C2DVector Vector, double dRadius,
bool bCentreOnRight, bool bArcOnRight)
{
Line.Set(PtFrom, Vector);
Radius = dRadius;
CentreOnRight = bCentreOnRight;
ArcOnRight = bArcOnRight;
}
/// <summary>
/// Distance to a line, returns the closest point on the circle and the line.
/// </summary>
/// <param name="Line">Line to calculate the distance to.</param>
/// <param name="ptOnThis">Closest point on the circle to recieve the result.</param>
/// <param name="ptOnOther">Closest point on the line to recieve the result.</param>
public double Distance(C2DLine Line, C2DPoint ptOnThis, C2DPoint ptOnOther)
{
var ProjInt = new CInterval();
Project(Line, ProjInt);
if (ProjInt.dMax < 0)
{
// This means that the circle projects entirely "below" the line so the nearest point
// To this is the first point on the line and there are no interections.
ptOnOther.Set(Line.point);
return(Distance(Line.point, ptOnThis));
}
var dLength = Line.GetLength();
if (ProjInt.dMin > dLength)
{
// This means that the circle projects entirely "above" the line so the nearest point
// To this is the second point on the line and there are no interections.
var ptClosest = new C2DPoint(Line.GetPointTo());
ptOnOther.Set(ptClosest);
return(Distance(ptClosest, ptOnThis));
}
// Now find out if there's an intersection.
var IntPts = new List <C2DPoint>();
if (Crosses(Line, IntPts))
{
ptOnThis.Set(IntPts[0]);
ptOnOther.Set(IntPts[0]);
return(0);
}
// Now find out if the line is entirely inside
if (ProjInt.dMin > 0 && ProjInt.dMax < dLength && this.Contains(Line.point))
{
var d1 = Distance(Line.point, ptOnThis);
var ptThisTemp = new C2DPoint();
var d2 = Distance(Line.GetPointTo(), ptThisTemp);
Debug.Assert(d1 < 0 && d2 < 0);
if (d2 > d1) // NOTE USE OF > AS d2 and d1 are -ve.
{
ptOnThis.Set(ptThisTemp);
ptOnOther.Set(Line.GetPointTo());
return(d2);
}
else
{
ptOnOther.Set(Line.point);
return(d1);
}
}
// We now know the line is entirely outside.
// Now find out if this is closest to a point on the line.
var dCenOnLine = (ProjInt.dMax + ProjInt.dMin) / 2.0;
if (dCenOnLine > 0)
{
if (dCenOnLine < dLength)
{
// The centre is projected on the line
var dFactor = dCenOnLine / dLength;
var vProj = new C2DVector(Line.vector);
vProj.Multiply(dFactor);
var ptOnLine = new C2DPoint(Line.point.GetPointTo(vProj));
ptOnOther.Set(ptOnLine);
return(Distance(ptOnLine, ptOnThis));
}
else
{
// The centre is projected above the line.
var ptClosest = new C2DPoint(Line.GetPointTo());
ptOnOther.Set(ptClosest);
return(Distance(ptClosest, ptOnThis));
}
}
else
{
// This means that the circle projects entirely "below" the line.
ptOnOther.Set(Line.point);
return(Distance(Line.point, ptOnThis));
}
}
/// <summary>
/// Gets the point on the line given by the factor. e.g. 0.5 = mid point.
/// </summary>
/// <param name="dFactorFromStart">The factor from the start.</param>
public C2DPoint GetPointOn(double dFactorFromStart)
{
C2DVector vNew = new C2DVector(vector);
vNew.Multiply( dFactorFromStart);
C2DPoint Result = new C2DPoint(point.x + vNew.i, point.y + vNew.j );
return Result;
}
/// <summary>
/// Returns the distance from this to the point with this as a ray.
/// </summary>
/// <param name="TestPoint"></param>
/// <param name="ptOnThis"></param>
/// <returns></returns>
public double DistanceAsRay(C2DPoint TestPoint, C2DPoint ptOnThis)
{
C2DVector vP1ToPoint = new C2DVector(point, TestPoint);
// The projection is on the line
double dFactorOnLine = vP1ToPoint.Dot(vector) / (vector.i * vector.i + vector.j * vector.j);
ptOnThis.Set(point.x + vector.i * dFactorOnLine,
point.y + vector.j * dFactorOnLine);
return TestPoint.Distance(ptOnThis);
}
/// <summary>
/// Equality test.
/// </summary>
public bool VectorEqualTo( C2DVector Other)
{
bool biClose;
bool bjClose;
if (i == 0)
biClose = Other.i == 0;
else
biClose = Math.Abs((Other.i - i) / i) < Constants.conEqualityTolerance;
if (j == 0)
bjClose = Other.j == 0;
else
bjClose = Math.Abs((Other.j - j) / j) < Constants.conEqualityTolerance;
return (biClose && bjClose);
}
/// <summary>
/// Returns the angle to the right to another vector.
/// </summary>
public double AngleToRight(C2DVector Other)
{
double Result = Other.AngleFromNorth() - AngleFromNorth();
if (Result < 0) Result += Constants.conTWOPI;
return Result;
}
/// <summary>
/// Moves this point by the vector given.
/// </summary>
/// <param name="Vector">The vector.</param>
public override void Move(C2DVector Vector)
{
P1.Move(Vector);
P2.Move(Vector);
P3.Move(Vector);
}
/// <summary>
/// Reflects this through the point given.
/// </summary>
/// <param name="Other">The point to reflect this through.</param>
public override void Reflect(C2DPoint Other)
{
// Set up a vector from this to the other
C2DVector vec = new C2DVector(this, Other);
// Now use the vector to find the reflection by continuing along it from the point given.
this.Set( Other.GetPointTo(vec) );
}
/// <summary>
/// Returns the point that the vector supplied would take this point to as a new object.
/// </summary>
/// <param name="v1">The vector from this to the new point.</param>
public C2DPoint GetPointTo(C2DVector v1)
{
return(new C2DPoint(x + v1.i, y + v1.j));
}
/// <summary>
/// Projects the point on the vector given returning a distance along the vector.
/// </summary>
/// <param name="vector">The vector to project this on.</param>
/// <param name="interval">The interval to recieve the result.
/// Both the min and max of the interval will be set to the result.</param>
public override void Project(C2DVector vector, CInterval interval)
{
interval.dMax = Project(vector);
interval.dMin = interval.dMax;
}
/// <summary>
/// Construction from a vector which can be thought of as a point (and vice versa).
/// </summary>
/// <param name="vector">Vector to assign to.</param>
public C2DPoint(C2DVector vector)
{
x = vector.i;
y = vector.j;
}
/// <summary>
/// Addition.
/// </summary>
public static C2DVector operator+(C2DVector V1, C2DVector V2)
{
var V3 = new C2DVector(V1.i + V2.i, V1.j + V2.j);
return(V3);
}
/// <summary>
/// Distance to a circle, returns the closest point on both circles.
/// </summary>
/// <param name="Other">Circle to calculate the distance to.</param>
/// <param name="ptOnThis">Closest point on this circle to recieve the result.</param>
/// <param name="ptOnOther">Closest point on the other circle to recieve the result.</param>
public double Distance(C2DCircle Other, C2DPoint ptOnThis, C2DPoint ptOnOther)
{
var dCenCenDist = _Centre.Distance(Other.Centre);
var dOtherRadius = Other.Radius;
// C2DPoint ptThis;
// C2DPoint ptOther;
var dDist = dCenCenDist - Radius - dOtherRadius;
if (dDist > 0)
{
// they do not interect and they are outside each other.
var Line = new C2DLine(_Centre, Other.Centre);
Line.vector.SetLength(Radius);
ptOnThis.Set(Line.GetPointTo());
Line.vector.Reverse();
Line.SetPointFrom(Other.Centre);
Line.vector.SetLength(Other.Radius);
ptOnOther.Set(Line.GetPointTo());
}
else
{
if ((dCenCenDist + Radius) < dOtherRadius)
{
// This is inside the other
dDist = dCenCenDist + Radius - dOtherRadius; // -ve if inside
var vec = new C2DVector(Other.Centre, Centre);
vec.Multiply(Radius / dCenCenDist); // set the vector to be the length of my radius.
ptOnThis.Set(_Centre.GetPointTo(vec));
vec.Multiply(dDist / Radius); // set the vector to be the distance.
ptOnOther.Set(ptOnThis.GetPointTo(vec));
}
else if ((dCenCenDist + dOtherRadius) < Radius)
{
// The other is inside this.
dDist = dCenCenDist + dOtherRadius - Radius; // -ve if inside
var vec = new C2DVector(_Centre, Other.Centre);
vec.Multiply(dOtherRadius / dCenCenDist); // set the vector to be the length of my radius.
ptOnOther.Set(Other.Centre.GetPointTo(vec));
vec.Multiply(dDist / dOtherRadius); // set the vector to be the distance.
ptOnThis.Set(ptOnOther.GetPointTo(vec));
}
else
{
// there is an intersection
dDist = 0;
var Ints = new List <C2DPoint>();
if (Crosses(Other, Ints))
{
ptOnThis.Set(Ints[0]);
ptOnOther.Set(ptOnThis);
}
else
{
Debug.Assert(false);
return(0);
}
}
}
// if (ptOnThis)
// *ptOnThis = ptThis;
// if (ptOnOther)
// *ptOnOther = ptOther;
return(dDist);
}
/// <summary>
/// Projects the point on the line given returning a distance along the line from the start.
/// </summary>
/// <param name="Line">The line to project this on.</param>
public double Project(C2DLine Line)
{
C2DVector vecthis = new C2DVector(Line.point, this );
return (vecthis.Dot(Line.vector)) / Line.vector.GetLength();
}
/// <summary>
/// Returns the boolean result (e.g. union) of 2 shapes. Boolean Operation defined by
/// the inside / outside flags.
/// </summary>
/// <param name="Other">Other polygon.</param>
/// <param name="HoledPolys">Set of polygons to recieve the result.</param>
/// <param name="bThisInside">Does the operation require elements of this INSIDE the other.</param>
/// <param name="bOtherInside">Does the operation require elements of the other INSIDE this.</param>
/// <param name="grid">The grid with the degenerate settings.</param>
public void GetBoolean(C2DHoledPolyBase Other, List <C2DHoledPolyBase> HoledPolys,
bool bThisInside, bool bOtherInside,
CGrid grid)
{
if (_Rim.Lines.Count == 0 || Other.Rim.Lines.Count == 0)
{
return;
}
if (_Rim.BoundingRect.Overlaps(Other.Rim.BoundingRect))
{
switch (grid.DegenerateHandling)
{
case CGrid.eDegenerateHandling.None:
{
var CompleteHoles1 = new List <C2DPolyBase>();
var CompleteHoles2 = new List <C2DPolyBase>();
var Routes1 = new C2DLineBaseSetSet();
var Routes2 = new C2DLineBaseSetSet();
GetRoutes(this, bThisInside, Other, bOtherInside, Routes1, Routes2,
CompleteHoles1, CompleteHoles2, grid);
Routes1.ExtractAllOf(Routes2);
if (Routes1.Count > 0)
{
Routes1.MergeJoining();
var Polygons = new List <C2DPolyBase>();
for (var i = Routes1.Count - 1; i >= 0; i--)
{
C2DLineBaseSet pRoute = Routes1[i];
if (pRoute.IsClosed(true))
{
Polygons.Add(new C2DPolyBase());
Polygons[Polygons.Count - 1].CreateDirect(pRoute);
}
else
{
// Debug.Assert(false);
grid.LogDegenerateError();
}
}
var NewComPolys = new C2DHoledPolyBaseSet();
PolygonsToHoledPolygons(NewComPolys, Polygons);
NewComPolys.AddKnownHoles(CompleteHoles1);
NewComPolys.AddKnownHoles(CompleteHoles2);
if (!bThisInside && !bOtherInside && NewComPolys.Count != 1)
{
// Debug.Assert(false);
grid.LogDegenerateError();
}
HoledPolys.AddRange(NewComPolys);
NewComPolys.Clear();
}
}
break;
case CGrid.eDegenerateHandling.RandomPerturbation:
{
var OtherCopy = new C2DHoledPolyBase(Other);
OtherCopy.RandomPerturb();
grid.DegenerateHandling = CGrid.eDegenerateHandling.None;
GetBoolean(OtherCopy, HoledPolys, bThisInside, bOtherInside, grid);
grid.DegenerateHandling = CGrid.eDegenerateHandling.RandomPerturbation;
}
break;
case CGrid.eDegenerateHandling.DynamicGrid:
{
var Rect = new C2DRect();
if (_Rim.BoundingRect.Overlaps(Other.Rim.BoundingRect, Rect))
{
//double dOldGrid = CGrid::GetGridSize();
grid.SetToMinGridSize(Rect, false);
grid.DegenerateHandling = CGrid.eDegenerateHandling.PreDefinedGrid;
GetBoolean(Other, HoledPolys, bThisInside, bOtherInside, grid);
grid.DegenerateHandling = CGrid.eDegenerateHandling.DynamicGrid;
}
}
break;
case CGrid.eDegenerateHandling.PreDefinedGrid:
{
var P1 = new C2DHoledPolyBase(this);
var P2 = new C2DHoledPolyBase(Other);
P1.SnapToGrid(grid);
P2.SnapToGrid(grid);
var V1 = new C2DVector(P1.Rim.BoundingRect.TopLeft, P2.Rim.BoundingRect.TopLeft);
var dPerturbation = grid.GridSize; // ensure it snaps back to original grid positions.
if (V1.i > 0)
{
V1.i = dPerturbation;
}
else
{
V1.i = -dPerturbation; // move away slightly if possible
}
if (V1.j > 0)
{
V1.j = dPerturbation;
}
else
{
V1.j = -dPerturbation; // move away slightly if possible
}
V1.i *= 0.411923; // ensure it snaps back to original grid positions.
V1.j *= 0.313131; // ensure it snaps back to original grid positions.
P2.Move(V1);
grid.DegenerateHandling = CGrid.eDegenerateHandling.None;
P1.GetBoolean(P2, HoledPolys, bThisInside, bOtherInside, grid);
for (var i = 0; i < HoledPolys.Count; i++)
{
HoledPolys[i].SnapToGrid(grid);
}
grid.DegenerateHandling = CGrid.eDegenerateHandling.PreDefinedGrid;
}
break;
case CGrid.eDegenerateHandling.PreDefinedGridPreSnapped:
{
var P2 = new C2DHoledPolyBase(Other);
var V1 = new C2DVector(_Rim.BoundingRect.TopLeft, P2.Rim.BoundingRect.TopLeft);
var dPerturbation = grid.GridSize;
if (V1.i > 0)
{
V1.i = dPerturbation;
}
else
{
V1.i = -dPerturbation; // move away slightly if possible
}
if (V1.j > 0)
{
V1.j = dPerturbation;
}
else
{
V1.j = -dPerturbation; // move away slightly if possible
}
V1.i *= 0.411923; // ensure it snaps back to original grid positions.
V1.j *= 0.313131; // ensure it snaps back to original grid positions.
P2.Move(V1);
grid.DegenerateHandling = CGrid.eDegenerateHandling.None;
GetBoolean(P2, HoledPolys, bThisInside, bOtherInside, grid);
for (var i = 0; i < HoledPolys.Count; i++)
{
HoledPolys[i].SnapToGrid(grid);
}
grid.DegenerateHandling = CGrid.eDegenerateHandling.PreDefinedGridPreSnapped;
}
break;
} // switch
}
}
/// <summary>
/// True if the point projects onto the line given and returns the
/// point on the line.
/// </summary>
/// <param name="Line"></param>
public void ProjectOnRay(C2DLine Line)
{
C2DVector vecthis = new C2DVector(Line.point, this );
double dProj = vecthis.Dot(Line.vector);
double dFactor = dProj / (Line.vector.i * Line.vector.i + Line.vector.j * Line.vector.j );
C2DVector vProj = new C2DVector(Line.vector);
vProj.i *= dFactor;
vProj.j *= dFactor;
this.Set(Line.point.x + vProj.i, Line.point.y + vProj.j);
}
/// <summary>
/// Projection onto the vector.
/// </summary>
/// <param name="Vector">Vector to project this on.</param>
/// <param name="Interval">Interval to recieve the result.</param>
public void Project(C2DVector Vector, CInterval Interval)
{
_Rim.Project(Vector, Interval);
}
/// <summary>
/// Rotates this to the right about the origin provided.
/// </summary>
/// <param name="dAng">The angle through which to rotate.</param>
/// <param name="Origin">The origin about which to rotate.</param>
public override void RotateToRight(double dAng, C2DPoint Origin)
{
C2DVector vector = new C2DVector(Origin, this);
vector.TurnRight(dAng);
x = Origin.x + vector.i;
y = Origin.y + vector.j;
}
/// <summary>
/// Subtraction.
/// </summary>
public static C2DVector operator-(C2DVector V1, C2DVector V2)
{
C2DVector V3 = new C2DVector(V1.i - V2.i, V1.j - V2.j);
return(V3);
}
/// <summary>
/// Returns the shortest angle between 2 vectors i.e. the dot product of the norms.
/// </summary>
public double AngleBetween(C2DVector Other)
{
double dDot = this.Dot(Other);
dDot /= (this.GetLength() * Other.GetLength());
return Math.Acos(dDot);
}
/// <summary>
/// Dot product.
/// </summary>
public double Dot(C2DVector Other)
{
return(i * Other.i + j * Other.j);
}
/// <summary>
/// Dot product.
/// </summary>
public double Dot(C2DVector Other)
{
return i * Other.i + j * Other.j;
}
/// <summary>
/// Cross product.
/// </summary>
public double Cross(C2DVector Other)
{
return(i * Other.i - j * Other.j);
}
/// <summary>
/// Subtraction.
/// </summary>
public static C2DVector operator -(C2DVector V1, C2DVector V2)
{
C2DVector V3 = new C2DVector(V1.i - V2.i, V1.j - V2.j);
return V3;
}
/// <summary>
/// Returns the angle to the left to another vector.
/// </summary>
public double AngleToLeft(C2DVector Other)
{
return(Constants.conTWOPI - AngleToRight(Other));
}
/// <summary>
/// Returns the distance from this to the other line.
/// </summary>
/// <param name="Other">The Other line.</param>
/// <param name="ptOnThis">Output. The closest point on this.</param>
/// <param name="ptOnOther">Output. The closest point on the other line.</param>
public double Distance(C2DLine Other, C2DPoint ptOnThis , C2DPoint ptOnOther)
{
// First, project the other line onto this and if it falls entirely below it or
// above it then 1. There is no intersection, 2. This is closest to one end on this line.
C2DPoint ptOtherP2 = new C2DPoint(Other.GetPointTo());
C2DVector vThisP1OtherP1 = new C2DVector(point, Other.point);
C2DVector vThisP1OtherP2 = new C2DVector(point, ptOtherP2);
C2DPoint ptThisP2 = new C2DPoint(GetPointTo());
double dOtherP1Proj = vThisP1OtherP1.Dot(vector);
double dOtherP2Proj = vThisP1OtherP2.Dot(vector);
// If they are both less than 0 then the projection falls below the line.
if (dOtherP1Proj <= 0 && dOtherP2Proj <= 0)
{
ptOnThis.Set(point);
return Other.Distance(point, ptOnOther);
}
// Now modify the projection so it is the length along this line.
double dThisLength = GetLength();
dOtherP1Proj = dOtherP1Proj / dThisLength;
dOtherP2Proj = dOtherP2Proj / dThisLength;
// If the projections are both above the line then the second point is closest
if (dOtherP1Proj >= dThisLength && dOtherP2Proj >= dThisLength)
{
ptOnThis.Set(ptThisP2);
return Other.Distance( ptThisP2, ptOnOther);
}
// This hasn't worked so try the same on the other line.
C2DVector vOtherP1ThisP1 = new C2DVector (Other.point, point);
C2DVector vOtherP1ThisP2 = new C2DVector(Other.point, ptThisP2);
double dThisP1Proj = vOtherP1ThisP1.Dot(Other.vector);
double dThisP2Proj = vOtherP1ThisP2.Dot(Other.vector);
// If they are both less than 0 then the projection falls below the line.
if (dThisP1Proj <= 0 && dThisP2Proj <= 0)
{
ptOnOther.Set( Other.point);
return Distance(Other.point, ptOnThis);
}
// Now modify the projection so it is the length along this line.
double dOtherLength = Other.GetLength();
dThisP1Proj = dThisP1Proj / dOtherLength;
dThisP2Proj = dThisP2Proj / dOtherLength;
// If the projections are both above the line then the second point is closest
if (dThisP1Proj >= dOtherLength && dThisP2Proj >= dOtherLength)
{
ptOnOther.Set(ptOtherP2);
return Distance( ptOtherP2, ptOnThis);
}
// Now test for an intersection.
List<C2DPoint> IntPoint = new List<C2DPoint>();
bool B1 = true, B2 = true;
if (this.Crosses(Other, IntPoint,ref B1, ref B2, false))
{
ptOnOther.Set(IntPoint[0]);
ptOnThis.Set(IntPoint[0]);
return 0;
}
// Otherwise, there MUST be a point projection on one of the lines otherwise both
// lines project on either side of each other which is impossible.
// So find the distances to all these projections and take the minimum.
double dDist = 0;
double dMinDist = 0;
bool bSet = false;
C2DPoint ptOnThisTemp = new C2DPoint();
C2DPoint ptOnOtherTemp = new C2DPoint();
// Is the other lines first point projected on this?
if (dOtherP1Proj >= 0 && dOtherP1Proj <= dThisLength)
{
// If so find the point on this line and get distance to it.
double dFactor = dOtherP1Proj / dThisLength;
ptOnThisTemp.Set(new C2DPoint(point.x + vector.i * dFactor,
point.y + vector.j * dFactor) );
dMinDist = Other.point.Distance(ptOnThisTemp);
bSet = true;
ptOnOther.Set(Other.point);
ptOnThis.Set(ptOnThisTemp);
}
// Is the other lines second point projected onto this?
if (dOtherP2Proj >= 0 && dOtherP2Proj <= dThisLength)
{
// If so find the point on this and then the distance. Is it less?
double dFactor = dOtherP2Proj / dThisLength;
ptOnThisTemp.Set( new C2DPoint(point.x + vector.i * dFactor,
point.y + vector.j * dFactor) );
dDist = ptOtherP2.Distance(ptOnThisTemp);
if (!bSet || dDist < dMinDist)
{
ptOnOther.Set(ptOtherP2);
ptOnThis.Set(ptOnThisTemp);
dMinDist = dDist;
bSet = true;
}
}
// Is the first point on this projected onto the other line?
if (dThisP1Proj >= 0 && dThisP1Proj <= dOtherLength)
{
// If so find the point and the distance. Is it less?
double dFactor = dThisP1Proj / dOtherLength;
ptOnOtherTemp.Set( new C2DPoint(Other.point.x + Other.vector.i * dFactor,
Other.point.y + Other.vector.j * dFactor));
dDist = point.Distance(ptOnOtherTemp);
if (!bSet || dDist < dMinDist)
{
ptOnThis.Set(point);
ptOnOther.Set(ptOnOtherTemp);
dMinDist = dDist;
bSet = true;
}
}
// Is the second point on this projected onto the other line?
if (dThisP2Proj >= 0 && dThisP2Proj <= dOtherLength)
{
// If so find the point and the distance. Is it less?
double dFactor = dThisP2Proj / dOtherLength;
ptOnOtherTemp.Set( new C2DPoint(Other.point.x + Other.vector.i * dFactor,
Other.point.y + Other.vector.j * dFactor));
dDist = ptThisP2.Distance(ptOnOtherTemp);
if (!bSet || dDist < dMinDist)
{
ptOnThis.Set(ptThisP2);
ptOnOther.Set(ptOnOtherTemp);
dMinDist = dDist;
bSet = true;
}
}
Debug.Assert( bSet );
// Now return the minimum distance
return dMinDist;
}
/// <summary>
/// Constructor with assignment.
/// </summary>
/// <param name="Other">other vector.</param>
public C2DVector(C2DVector Other)
{
i = Other.i;
j = Other.j;
}
/// <summary>
/// Projection onto a vector.
/// </summary>
/// <param name="Vector">The vector to project this on.</param>
/// <param name="Interval">Output. The interval.</param>
public override void Project(C2DVector Vector, CInterval Interval)
{
double dP1 = point.Project(Vector);
Interval.dMax = dP1;
Interval.dMin = dP1;
Interval.ExpandToInclude( GetPointTo().Project( Vector) );
}
/// <summary>
/// Assignment.
/// </summary>
/// <param name="Other">Other vector.</param>
public void Set(C2DVector Other)
{
i = Other.i;
j = Other.j;
}
/// <summary>
/// Moves this point by the vector given.
/// </summary>
/// <param name="Vector">The vector.</param>
public override void Move(C2DVector Vector)
{
P1.Move(Vector);
P2.Move(Vector);
P3.Move(Vector);
}
/// <summary>
/// This simply moves the real world rectangle.
/// </summary>
/// <param name="Vector">Vector to move / scroll by</param>
public void ScrollReal(C2DVector Vector)
{
RealRect.Move(Vector);
}
/// <summary>
/// Projects the point on the vector given returning a distance along the vector.
/// </summary>
/// <param name="Vector">The vector to project this on.</param>
/// <param name="Interval">The interval to recieve the result.
/// Both the min and max of the interval will be set to the result.</param>
public override void Project(C2DVector Vector, CInterval Interval)
{
Interval.dMax = Project(Vector);
Interval.dMin = Interval.dMax;
}
/// <summary>
/// This simply moves the real world rectangle but by a scaled, screen based
/// value e.g. 10 pixels to the right. The image is shown in the same place on
/// the screen but the image scrolls.
/// </summary>
/// <param name="Vector">Vector to scroll / move by.</param>
public void ScrollScreen(C2DVector Vector)
{
RealRect.Move(new C2DVector(Vector.i / Scale.x, Vector.j / Scale.y));
}
/// <summary>
/// True if the point projects onto the line given and returns the point on the line.
/// Also returns whether the line projects above or below the line if relevant.
/// </summary>
/// <param name="Line">The line to project this on.</param>
/// <param name="ptOnLine">The point to recieve the result.</param>
/// <param name="bAbove">The flag to indicate whether it projects above or below.</param>
public bool ProjectsOnLine(C2DLine Line, C2DPoint ptOnLine ,
ref bool bAbove)
{
C2DVector vecthis = new C2DVector(x - Line.point.x, y - Line.point.y);
double dProj = vecthis.Dot(Line.vector);
if (dProj < 0)
{
bAbove = false;
return false;
}
double dLength = Line.vector.GetLength();
dProj /= dLength;
if (dProj > dLength)
{
bAbove = true;
return false;
}
double dFactor = dProj / dLength;
C2DVector vProj = new C2DVector(Line.vector);
vProj.Multiply(dFactor);
ptOnLine.Set(Line.point.x + vProj.i, Line.point.y + vProj.j);
return true;
}
/// <summary>
/// Projects the point on the line given returning a distance along the line from the start.
/// </summary>
/// <param name="Line">The line to project this on.</param>
public double Project(C2DLine Line)
{
C2DVector vecthis = new C2DVector(Line.point, this);
return((vecthis.Dot(Line.vector)) / Line.vector.GetLength());
}
/// <summary>
/// Reflects this through the line given.
/// </summary>
/// <param name="Line">The line to reflect this through.</param>
public override void Reflect(C2DLine Line)
{
// First find the point along the line that this projects onto.
// Make a vector from the point on the line given to this point.
C2DVector vecthis = new C2DVector(Line.point, this );
// Find the length of the line given.
double dLength = Line.vector.GetLength();
// Now make the projection of this point on the line.
double dProj = vecthis.Dot(Line.vector);
dProj /= dLength;
// Find the factor along the line that the projection is.
double dFactor = dProj / dLength;
// Now set up a copy of the vector of the line given.
C2DVector vProj = new C2DVector(Line.vector);
// Multiply that by that factor calculated.
vProj.Multiply(dFactor);
// Use the vector to find the point on the line.
C2DPoint ptOnLine = new C2DPoint(Line.point.GetPointTo(vProj) );
// Noe simply reflect this in the point.
this.Reflect(ptOnLine);
}
/// <summary>
/// Projects the point on the vector given returning a distance along the vector.
/// </summary>
/// <param name="Vector">The vector to project this on.</param>
/// <param name="Interval">The interval to recieve the result.
/// Both the min and max of the interval will be set to the result.</param>
public override void Project(C2DVector Vector, CInterval Interval)
{
Interval.dMax = Project(Vector);
Interval.dMin = Interval.dMax;
}
/// <summary>
/// Construction from a vector which can be thought of as a point (and vice versa).
/// </summary>
/// <param name="Vector">Vector to assign to.</param>
public C2DPoint( C2DVector Vector)
{
x = Vector.i;
y = Vector.j;
}
/// <summary>
/// Returns the point that the vector supplied would take this point to as a new object.
/// </summary>
/// <param name="V1">The vector from this to the new point.</param>
public C2DPoint GetPointTo(C2DVector V1)
{
return(new C2DPoint(x + V1.i, y + V1.j));
}
/// <summary>
/// Projection onto the Vector.
/// </summary>
/// <param name="Vector">Vector to project on.</param>
/// <param name="Interval">Ouput. Projection.</param>
public override void Project(C2DVector Vector, CInterval Interval)
{
P1.Project(Vector, Interval);
Interval.ExpandToInclude(P2.Project(Vector));
Interval.ExpandToInclude(P3.Project(Vector));
}
/// <summary>
/// Moves this point by the vector given.
/// </summary>
/// <param name="vector">The vector.</param>
public override void Move(C2DVector vector)
{
x += vector.i;
y += vector.j;
}
/// <summary>
/// Returns the angle to the left to another vector.
/// </summary>
public double AngleToLeft(C2DVector Other)
{
return (Constants.conTWOPI - AngleToRight(Other));
}
/// <summary>
/// Construction from a vector which can be thought of as a point (and vice versa).
/// </summary>
/// <param name="Vector">Vector to assign to.</param>
public C2DPoint(C2DVector Vector)
{
x = Vector.i;
y = Vector.j;
}
/// <summary>
/// Cross product.
/// </summary>
public double Cross(C2DVector Other)
{
return i * Other.j - j * Other.i;
}
/// <summary>
/// Projects the point on the vector given returning a distance along the vector.
/// </summary>
/// <param name="Vector">The vector to project this on.</param>
public double Project(C2DVector Vector)
{
C2DVector vecthis = new C2DVector(x, y);
return((vecthis.Dot(Vector)) / Vector.GetLength());
}
/// <summary>
/// Assignment.
/// </summary>
/// <param name="Other">Other vector.</param>
public void Set(C2DVector Other)
{
i = Other.i;
j = Other.j;
}
/// <summary> /// Moves the entity by the vector provided. /// </summary> public abstract void Move(C2DVector Vector);
/// <summary>
/// Constructor with assignment.
/// </summary>
/// <param name="Other">other vector.</param>
public C2DVector(C2DVector Other)
{
i = Other.i;
j = Other.j;
}
/// <summary> /// Projects this onto the vector provided with the interval on the line returned. /// </summary> public abstract void Project(C2DVector Vector, CInterval Interval);
/// <summary>
/// Calculates the centroid of the polygon by moving it according to each holes
/// weighted centroid.
/// </summary>
public C2DPoint GetCentroid()
{
C2DPoint HoleCen = new C2DPoint(0, 0);
if (_Holes.Count == 0)
return Rim.GetCentroid();
C2DPoint PolyCen = Rim.GetCentroid();
double dPolyArea = Rim.GetArea();
double dHoleArea = 0;
for ( int i = 0 ; i < _Holes.Count; i++)
{
dHoleArea += GetHole(i).GetArea();
}
if (dHoleArea == 0 || dHoleArea == dPolyArea)
return Rim.GetCentroid();
else
{
for (int i = 0 ; i < _Holes.Count; i++)
{
C2DPoint pt = GetHole(i).GetCentroid();
pt.Multiply(GetHole(i).GetArea() / dHoleArea);
HoleCen += pt;
}
}
C2DVector Vec = new C2DVector(HoleCen, PolyCen);
Vec.Multiply( dHoleArea / (dPolyArea - dHoleArea));
PolyCen.Move(Vec);
return PolyCen;
}
/// <summary>
/// Returns the distance from this to the other line.
/// </summary>
/// <param name="Other">The Other line.</param>
/// <param name="ptOnThis">Output. The closest point on this.</param>
/// <param name="ptOnOther">Output. The closest point on the other line.</param>
public double Distance(C2DLine Other, C2DPoint ptOnThis, C2DPoint ptOnOther)
{
// First, project the other line onto this and if it falls entirely below it or
// above it then 1. There is no intersection, 2. This is closest to one end on this line.
var ptOtherP2 = new C2DPoint(Other.GetPointTo());
var vThisP1OtherP1 = new C2DVector(point, Other.point);
var vThisP1OtherP2 = new C2DVector(point, ptOtherP2);
var ptThisP2 = new C2DPoint(GetPointTo());
var dOtherP1Proj = vThisP1OtherP1.Dot(vector);
var dOtherP2Proj = vThisP1OtherP2.Dot(vector);
// If they are both less than 0 then the projection falls below the line.
if (dOtherP1Proj <= 0 && dOtherP2Proj <= 0)
{
ptOnThis.Set(point);
return(Other.Distance(point, ptOnOther));
}
// Now modify the projection so it is the length along this line.
var dThisLength = GetLength();
dOtherP1Proj = dOtherP1Proj / dThisLength;
dOtherP2Proj = dOtherP2Proj / dThisLength;
// If the projections are both above the line then the second point is closest
if (dOtherP1Proj >= dThisLength && dOtherP2Proj >= dThisLength)
{
ptOnThis.Set(ptThisP2);
return(Other.Distance(ptThisP2, ptOnOther));
}
// This hasn't worked so try the same on the other line.
var vOtherP1ThisP1 = new C2DVector(Other.point, point);
var vOtherP1ThisP2 = new C2DVector(Other.point, ptThisP2);
var dThisP1Proj = vOtherP1ThisP1.Dot(Other.vector);
var dThisP2Proj = vOtherP1ThisP2.Dot(Other.vector);
// If they are both less than 0 then the projection falls below the line.
if (dThisP1Proj <= 0 && dThisP2Proj <= 0)
{
ptOnOther.Set(Other.point);
return(Distance(Other.point, ptOnThis));
}
// Now modify the projection so it is the length along this line.
var dOtherLength = Other.GetLength();
dThisP1Proj = dThisP1Proj / dOtherLength;
dThisP2Proj = dThisP2Proj / dOtherLength;
// If the projections are both above the line then the second point is closest
if (dThisP1Proj >= dOtherLength && dThisP2Proj >= dOtherLength)
{
ptOnOther.Set(ptOtherP2);
return(Distance(ptOtherP2, ptOnThis));
}
// Now test for an intersection.
var IntPoint = new List <C2DPoint>();
bool B1 = true, B2 = true;
if (this.Crosses(Other, IntPoint, ref B1, ref B2, false))
{
ptOnOther.Set(IntPoint[0]);
ptOnThis.Set(IntPoint[0]);
return(0);
}
// Otherwise, there MUST be a point projection on one of the lines otherwise both
// lines project on either side of each other which is impossible.
// So find the distances to all these projections and take the minimum.
double dDist = 0;
double dMinDist = 0;
var bSet = false;
var ptOnThisTemp = new C2DPoint();
var ptOnOtherTemp = new C2DPoint();
// Is the other lines first point projected on this?
if (dOtherP1Proj >= 0 && dOtherP1Proj <= dThisLength)
{
// If so find the point on this line and get distance to it.
var dFactor = dOtherP1Proj / dThisLength;
ptOnThisTemp.Set(new C2DPoint(point.x + vector.i * dFactor,
point.y + vector.j * dFactor));
dMinDist = Other.point.Distance(ptOnThisTemp);
bSet = true;
ptOnOther.Set(Other.point);
ptOnThis.Set(ptOnThisTemp);
}
// Is the other lines second point projected onto this?
if (dOtherP2Proj >= 0 && dOtherP2Proj <= dThisLength)
{
// If so find the point on this and then the distance. Is it less?
var dFactor = dOtherP2Proj / dThisLength;
ptOnThisTemp.Set(new C2DPoint(point.x + vector.i * dFactor,
point.y + vector.j * dFactor));
dDist = ptOtherP2.Distance(ptOnThisTemp);
if (!bSet || dDist < dMinDist)
{
ptOnOther.Set(ptOtherP2);
ptOnThis.Set(ptOnThisTemp);
dMinDist = dDist;
bSet = true;
}
}
// Is the first point on this projected onto the other line?
if (dThisP1Proj >= 0 && dThisP1Proj <= dOtherLength)
{
// If so find the point and the distance. Is it less?
var dFactor = dThisP1Proj / dOtherLength;
ptOnOtherTemp.Set(new C2DPoint(Other.point.x + Other.vector.i * dFactor,
Other.point.y + Other.vector.j * dFactor));
dDist = point.Distance(ptOnOtherTemp);
if (!bSet || dDist < dMinDist)
{
ptOnThis.Set(point);
ptOnOther.Set(ptOnOtherTemp);
dMinDist = dDist;
bSet = true;
}
}
// Is the second point on this projected onto the other line?
if (dThisP2Proj >= 0 && dThisP2Proj <= dOtherLength)
{
// If so find the point and the distance. Is it less?
var dFactor = dThisP2Proj / dOtherLength;
ptOnOtherTemp.Set(new C2DPoint(Other.point.x + Other.vector.i * dFactor,
Other.point.y + Other.vector.j * dFactor));
dDist = ptThisP2.Distance(ptOnOtherTemp);
if (!bSet || dDist < dMinDist)
{
ptOnThis.Set(ptThisP2);
ptOnOther.Set(ptOnOtherTemp);
dMinDist = dDist;
bSet = true;
}
}
Debug.Assert(bSet);
// Now return the minimum distance
return(dMinDist);
}
/// <summary>
/// Returns the distance from this to the point.
/// </summary>
/// <param name="TestPoint">The test pointt.</param>
/// <param name="ptOnThis">Output. The closest point on this.</param>
public override double Distance(C2DPoint TestPoint, C2DPoint ptOnThis)
{
C2DVector vP1ToPoint = new C2DVector(point, TestPoint);
double dLength = GetLength();
double dProjLength = vP1ToPoint.Dot(vector);
if (dProjLength < 0)
{
ptOnThis.Set(point);
return TestPoint.Distance(point);
}
else
{
dProjLength = dProjLength / dLength;
if (dProjLength < dLength)
{
// The projection is on the line
double dFactorOnLine = dProjLength / dLength;
C2DPoint PtOnLine = new C2DPoint(point.x + vector.i * dFactorOnLine,
point.y + vector.j * dFactorOnLine);
ptOnThis.Set(PtOnLine);
return TestPoint.Distance(PtOnLine);
}
else
{
ptOnThis .Set(GetPointTo());
return TestPoint.Distance( GetPointTo() );
}
}
}
/// <summary>
/// Constructor.
/// </summary>
/// <param name="PointFrom">The point from.</param>
/// <param name="VectorTo">The vector defining the second point.</param>
public C2DLine(C2DPoint PointFrom, C2DVector VectorTo)
{
point.Set(PointFrom);
vector.Set(VectorTo);
}
/// <summary>
/// Constructor.
/// </summary>
/// <param name="PointFrom">The point from.</param>
/// <param name="VectorTo">The vector defining the second point.</param>
public C2DLine(C2DPoint PointFrom, C2DVector VectorTo)
{
point.Set(PointFrom);
vector.Set(VectorTo);
}
/// <summary>
/// Moves this point by the vector given.
/// </summary>
/// <param name="vector">The vector.</param>
public override void Move(C2DVector vector)
{
point.Move(vector);
}
/// <summary>
/// Moves this point by the vector given.
/// </summary>
/// <param name="vector">The vector.</param>
public override void Move(C2DVector vector)
{
point.Move(vector);
}
/// <summary>
/// Assignment.
/// </summary>
/// <param name="PointFrom">The point from.</param>
/// <param name="VectorTo">The vector defining the second point.</param>
public void Set(C2DPoint PointFrom, C2DVector VectorTo)
{
point.Set(PointFrom);
vector.Set(VectorTo);
}
/// <summary>
/// Assignment.
/// </summary>
/// <param name="PointFrom">The point from.</param>
/// <param name="VectorTo">The vector defining the second point.</param>
public void Set(C2DPoint PointFrom, C2DVector VectorTo)
{
point.Set(PointFrom);
vector.Set(VectorTo);
}
/// <summary>
/// Moves this point by the vector given.
/// </summary>
/// <param name="Vector">The vector.</param>
public override void Move(C2DVector Vector)
{
_Centre.Move(Vector);
}