private Point CalcVP(Vector a, Vector b, Vector c, Vector d)
{
Vector line1Cross = a.Cross(b);
Vector line2Cross = c.Cross(d);
Vector res = line1Cross.Cross(line2Cross);
return new Point(res.X / res.Z, res.Y / res.Z);
}
/// <summary>
/// Returns the Inner Product also known as the dot product of two vectors, U and V
/// </summary>
/// <param name="u">The input vector</param>
/// <param name="v">The vector to take the inner product against U</param>
/// <returns>a Double containing the dot product of U and V</returns>
public static double DotProduct(Vector u, Vector v)
{
return (u.X * v.X) + (u.Y * v.Y) + (u.Z * v.Z);
}
/// <summary>
/// Multiplies each component of vector U by the Scalar value
/// </summary>
/// <param name="u">A vector representing the vector to be multiplied</param>
/// <param name="scalar">Double, the scalar value to mulitiply the vector components by</param>
/// <returns>A Vector representing the vector product of vector U and the Scalar</returns>
public static Vector Divide(Vector u, double scalar)
{
if (scalar == 0) throw new ArgumentException("Divisor cannot be 0.");
return new Vector(u.X / scalar, u.Y / scalar, u.Z / scalar);
}
/// <summary>
/// Returns the Cross Product of two vectors U and V
/// </summary>
/// <param name="u">Vector, the first input vector</param>
/// <param name="v">Vector, the second input vector</param>
/// <returns>A Vector containing the cross product of U and V</returns>
public static Vector CrossProduct(Vector u, Vector v)
{
Vector result = new Vector();
result.X = (u.Y * v.Z - u.Z * v.Y);
result.Y = (u.Z * v.X - u.X * v.Z);
result.Z = (u.X * v.Y - u.Y * v.X);
return result;
}
/// <summary>
/// Adds the vectors U and V using vector addition, which adds the corresponding components
/// </summary>
/// <param name="u">One vector to be added</param>
/// <param name="v">A second vector to be added</param>
/// <returns></returns>
public static Vector Add(Vector u, Vector v)
{
return new Vector(u.X + v.X, u.Y + v.Y, u.Z + v.Z);
}
/// <summary>
/// Override for definition of equality for vectors
/// </summary>
/// <param name="v">A vector to compare with</param>
/// <returns>true if the X, Y, and Z coordinates are all equal</returns>
public bool Equals(Vector v)
{
if ((X == v.X) && (Y == v.Y) && (Z == v.Z)) return true;
return false;
}
/// <summary>
/// Returns the cross product of this vector with the specified vector V
/// </summary>
/// <param name="v">The vector to perform a cross product against</param>
/// <returns>A vector result from the inner product</returns>
public Vector Cross(Vector v)
{
Vector result = new Vector();
result.X = (Y * v.Z - Z * v.Y);
result.Y = (Z * v.X - X * v.Z);
result.Z = (X * v.Y - Y * v.X);
return result;
}
/// <summary>
/// Subtracts Vector V from Vector U
/// </summary>
/// <param name="u">A Vector to subtract from</param>
/// <param name="v">A Vector to subtract</param>
/// <returns>The Vector difference U - V</returns>
public static Vector Subtract(Vector u, Vector v)
{
return new Vector(u.X - v.X, u.Y - v.Y, u.Z - v.Z);
}
/// <summary>
/// Adds each of the elements of V to the elements of this vector
/// </summary>
/// <param name="v">Vector, the vector to add to this vector</param>
/// <returns>A vector result from the addition</returns>
public Vector Add(Vector v)
{
return new Vector(X + v.X, Y + v.Y, Z + v.Z);
}
/// <summary>
/// Subtracts each element of V from each element of this vector
/// </summary>
/// <param name="v">Vector, the vector to subtract from this vector</param>
/// <returns>A vector result from the subtraction</returns>
public Vector Subtract(Vector v)
{
return new Vector(X - v.X, Y - v.Y, Z - v.Z);
}
/// <summary>
/// Creates a new vector from a vector that can be longer or shorter than 3 ordinates.
/// If an X, Y or Z value is not specified, it will become 0. Values greater than
/// the Z ordinate are lost.
/// </summary>
/// <param name="vect"></param>
public Vector(Vector vect)
{
X = vect.X;
Y = vect.Y;
Z = vect.Z;
}
/// <summary>
/// Calculates the shortest distance to this line segment from the specified MapWinGIS.Point
/// </summary>
/// <param name="point">A MapWinGIS.Point specifing the location to find the distance to the line</param>
/// <returns>A double value that is the shortest distance from the given Point to this line segment</returns>
public double DistanceTo(Coordinate point)
{
Vertex p = new Vertex(point.X, point.Y);
Vertex pt = ClosestPointTo(p);
Vector dist = new Vector(new Coordinate(pt.X, pt.Y), point);
return dist.Length2D;
}
/// <summary>
/// Returns a vertex representing the closest point on this line segment from a given vertex
/// </summary>
/// <param name="point">The point we want to be close to</param>
/// <param name="isInfiniteLine">If true treat the line as infinitly long</param>
/// <param name="endPointFlag">Outputs 0 if the vertex is on the line segment, 1 if beyond P0, 2 if beyong P1 and -1 if P1=P2</param>
/// <returns>The point on this segment or infinite line that is closest to the given point</returns>
public Vertex ClosestPointTo(Vertex point, bool isInfiniteLine, out EndPointInteraction endPointFlag)
{
// If the points defining this segment are the same, we treat the segment as a point
// special handling to avoid 0 in denominator later
if (P2.X == P1.X && P2.Y == P1.Y)
{
endPointFlag = EndPointInteraction.P1equalsP2;
return P1;
}
//http://softsurfer.com/Archive/algorithm_0102/algorithm_0102.htm
Vector v = ToVector(); // vector from p1 to p2 in the segment
v.Z = 0;
Vector w = new Vector(P1.ToCoordinate(), point.ToCoordinate()); // vector from p1 to Point
w.Z = 0;
double c1 = w.Dot(v); // the dot product represents the projection onto the line
if (c1 < 0)
{
endPointFlag = EndPointInteraction.PastP1;
if (!isInfiniteLine) // The closest point on the segment to Point is p1
return P1;
}
double c2 = v.Dot(v);
if (c2 <= c1)
{
endPointFlag = EndPointInteraction.PastP2;
if (!isInfiniteLine) // The closest point on the segment to Point is p2
return P2;
}
// The closest point on the segment is perpendicular to the point,
// but somewhere on the segment between P1 and P2
endPointFlag = EndPointInteraction.OnLine;
double b = c1 / c2;
v = v.Multiply(b);
Vertex pb = new Vertex(P1.X + v.X, P1.Y + v.Y);
return pb;
}
/// <summary>
/// Non-static version of taking the square distance for a vector
/// </summary>
/// <param name="u">The vector to find the square of the distance of</param>
/// <returns>Double, the square of the distance</returns>
public static double Norm2(Vector u)
{
double n2 = u.X * u.X + u.Y * u.Y + u.Z * u.Z;
return n2;
}
/// <summary>
/// Returns the dot product of this vector with V2
/// </summary>
/// <param name="v">The vector to perform an inner product against</param>
/// <returns>A Double result from the inner product</returns>
public double Dot(Vector v)
{
return X * v.X + Y * v.Y + Z * v.Z;
}
/// <summary>
/// Multiplies each component of vector U by the Scalar value
/// </summary>
/// <param name="u">A vector representing the vector to be multiplied</param>
/// <param name="scalar">Double, the scalar value to mulitiply the vector components by</param>
/// <returns>A Vector representing the vector product of vector U and the Scalar</returns>
public static Vector Multiply(Vector u, double scalar)
{
return new Vector(u.X * scalar, u.Y * scalar, u.Z * scalar);
}
/// <summary>
/// Compares the values of each element, and if all the elements are equal, returns true.
/// </summary>
/// <param name="v">The vector to compare against this vector.</param>
/// <returns>Boolean, true if all the elements have the same value.</returns>
public bool Intersects(Vector v)
{
if ((X == v.X) && (Y == v.Y) && (Z == v.Z)) return true;
return false;
}
/// <summary>
/// Returns the Cross Product of two vectors U and V
/// </summary>
/// <param name="u">Vector, the first input vector</param>
/// <param name="v">Vector, the second input vector</param>
/// <returns>A Vector containing the cross product of U and V</returns>
public static Vector operator ^(Vector u, Vector v)
{
Vector result = new Vector();
result.X = (u.Y * v.Z - u.Z * v.Y);
result.Y = (u.Z * v.X - u.X * v.Z);
result.Z = (u.X * v.Y - u.Y * v.X);
return result;
}
/// <summary>
/// Returns the intersection of the specified segment with this bounding box. If there is no intersection,
/// then this returns null. If the intersection is a corner, then the LineSegment will be degenerate,
/// that is both the coordinates will be the same. Otherwise, the segment will be returned so that the
/// direction is the same as the original segment.
/// </summary>
/// <param name="self">The IEnvelope to use with this method</param>
/// <param name="segment">The LineSegment to intersect.</param>
/// <returns>An ILineSegment that is cropped to fit within the bounding box.</returns>
public static ILineSegment Intersection(this IEnvelope self, ILineSegment segment)
{
if (self == null) return null;
if (self.IsNull) return null;
if (segment == null) return null;
// If the line segment is completely contained by this envelope, simply return the original.
if (self.Contains(segment.P0) && self.Contains(segment.P1)) return segment;
int count = 0;
Coordinate[] borderPoints = new Coordinate[2];
ILineSegment[] border = self.BorderSegments();
for (int i = 0; i < 4; i++)
{
borderPoints[count] = border[i].Intersection(segment);
if (borderPoints[count] != null)
{
count++;
if (count > 1)
break;
}
}
// If there are two intersections, the line crosses this envelope
if (count == 2)
{
Vector v = new Vector(segment.P0, segment.P1);
Vector t = new Vector(borderPoints[0], borderPoints[1]);
return t.Dot(v) < 0 ? new LineSegment(borderPoints[1], borderPoints[0]) : new LineSegment(borderPoints[0], borderPoints[1]);
}
// if there is only one intersection, we probably have one point contained and one point not-contained
if (count == 1)
{
if (self.Contains(segment.P0))
{
// P1 got cropped, so make a line from p0 to the cropped point
return new LineSegment(segment.P0, borderPoints[0]);
}
return self.Contains(segment.P1) ? new LineSegment(borderPoints[0], segment.P1) : new LineSegment(borderPoints[0], borderPoints[0]);
}
return null;
}