/// <summary>
/// Calculates the cross product of this vector and the given one.
/// </summary>
/// <param name="other">The other vector.</param>
/// <returns>The cross product of the two vectors.</returns>
public CartesianVector CrossProduct(CartesianVector other)
{
return(new CartesianVector(
x: (Y * other.Z) - (other.Y * Z),
y: (other.X * Z) - (X * other.Z),
z: (X * other.Y) - (other.X * Y)));
}
/// <summary>
/// Returns the tangent vector of this <see cref="GreatCircle"/> in the given point, that points in the specified direction.
/// </summary>
/// <param name="point">The point on the <see cref="GreatCircle"/> that the tangent is wanted for.</param>
/// <param name="direction">The vector specifying in which direction the tangent vector will point.</param>
/// <returns>The tangent vector pointing in the right direction.</returns>
public CartesianVector GetTangentAt(CartesianVector point, CartesianVector direction)
{
var possibleTangent = GetTangentAt(point);
var otherPossibleTangent = -possibleTangent;
var intendedDirection = (direction - point).AsUnitVector;
// Don't need to divide by the length because the vectors are both unit vectors.
var possibleAngle = possibleTangent.DotProduct(intendedDirection);
var otherPossibleAngle = otherPossibleTangent.DotProduct(intendedDirection);
return(possibleAngle < otherPossibleAngle ? possibleTangent : otherPossibleTangent);
}
/// <summary>
/// Checks whether the given <see cref="GreatCircle"/> intersects with this one.
/// One point of intersection can then be found in the out-Parameter, the other is the antipodal point to it.
/// </summary>
/// <param name="other">The other <see cref="GreatCircle"/>.</param>
/// <param name="intersection">The point of intersection, if they intersect.</param>
/// <returns>Whether the two <see cref="GreatCircle"/>s intersect or not.</returns>
public bool Intersects(GreatCircle other, out CartesianVector intersection)
{
// http://www.boeing-727.com/Data/fly%20odds/distance.html
intersection = default(CartesianVector);
if (this == other)
{
return(false);
}
intersection = DefinitionVector.CrossProduct(other.DefinitionVector).AsUnitVector;
return(true);
}
public double DotProduct(CartesianVector other)
{
return((X * other.X) + (Y * other.Y) + (Z * other.Z));
}
/// <summary>
/// Returns one possible tangent vector of this <see cref="GreatCircle"/> in the given point, the other is antipodal to it.
/// </summary>
/// <param name="point">The point on the <see cref="GreatCircle"/> that the tangent is wanted for.</param>
/// <returns>One possible tangent vector.</returns>
public CartesianVector GetTangentAt(CartesianVector point)
{
return(DefinitionVector.CrossProduct(point).AsUnitVector);
}
/// <summary>
/// Creates a new instance of the <see cref="GreatCircle"/> struct with the given definition vector.
/// </summary>
/// <param name="definitionVector">The vector perpendicular to the plane that produces the great circle.</param>
public GreatCircle(CartesianVector definitionVector)
{
DefinitionVector = definitionVector.AsUnitVector;
}
/// <summary>
/// Creates a new instance of the <see cref="GreatCircle"/> struct given two points defining it.
/// </summary>
/// <param name="start">The start coordinate of the segment.</param>
/// <param name="end">The end coordinate of the segment.</param>
public GreatCircle(CartesianVector start, CartesianVector end)
: this(start.CrossProduct(end))
{
}
/// <summary>
/// Returns the tangent vector of this <see cref="GreatCircleSegement"/>'s underlaying <see cref="GreatCircle"/> in the given point, that points in the specified direction.
/// </summary>
/// <param name="point">The point on the underlaying <see cref="GreatCircle"/> that the tangent is wanted for.</param>
/// <param name="direction">The vector specifying in which direction the tangent vector will point.</param>
/// <returns>The tangent vector pointing in the right direction.</returns>
public CartesianVector GetTangentAt(SphereCoordinate point, CartesianVector direction)
{
return(BaseCircle.GetTangentAt(point, direction));
}
