/// <summary>
/// Checks whether the given <see cref="GreatCircleSegment"/> intersects with this <see cref="GreatCicle"/>.
/// The point of intersection can then be found in the out-Parameter.
/// </summary>
/// <param name="arc">The arc segment to be checked.</param>
/// <param name="intersection">The point of intersection, if they intersect.</param>
/// <returns>Whether the <see cref="GreatCircleSegment"/> intersects this <see cref="GreatCircle"/> or not.</returns>
public bool Intersects(GreatCircleSegment arc, out SphereCoordinate intersection)
{
intersection = default(SphereCoordinate);
CartesianVector possibleIntersection;
if (!Intersects(arc.BaseCircle, out possibleIntersection))
{
return(false);
}
if (arc.IsOnArc(possibleIntersection))
{
intersection = possibleIntersection;
return(true);
}
if (arc.IsOnArc(-possibleIntersection))
{
intersection = -possibleIntersection;
return(true);
}
return(false);
}
/// <summary>
/// Checks whether the given <see cref="GreatCircleSegment"/> intersects with this one.
/// The point of intersection can then be found in the out-Parameter.
/// </summary>
/// <param name="other">The arc segment to be checked.</param>
/// <param name="intersection">The point of intersection, if they intersect.</param>
/// <returns>Whether the two <see cref="GreatCircleSegment"/>s intersect or not.</returns>
public bool Intersects(GreatCircleSegment other, out SphereCoordinate intersection)
{
// http://www.boeing-727.com/Data/fly%20odds/distance.html
intersection = default(SphereCoordinate);
if (Length.IsAlmostEqualTo(0) || other.Length.IsAlmostEqualTo(0))
{
return(false);
}
CartesianVector possibleIntersection1;
if (!BaseCircle.Intersects(other.BaseCircle, out possibleIntersection1))
{
return(false);
}
var possibleIntersection2 = -possibleIntersection1;
if (IsOnArc(possibleIntersection1) && other.IsOnArc(possibleIntersection1))
{
intersection = possibleIntersection1;
return(true);
}
if (IsOnArc(possibleIntersection2) && other.IsOnArc(possibleIntersection2))
{
intersection = possibleIntersection2;
return(true);
}
return(false);
}
private static void Main(string[] args)
{
var start1 = new SphereCoordinate(0.5 * Math.PI, -0.25 * Math.PI);
Console.WriteLine((CartesianVector)start1);
var end1 = new SphereCoordinate(0.5 * Math.PI, 0.25 * Math.PI);
Console.WriteLine((CartesianVector)end1);
var start2 = new SphereCoordinate(0.25 * Math.PI, 0);
Console.WriteLine((CartesianVector)start2);
var end2 = new SphereCoordinate(0.75 * Math.PI, 0);
Console.WriteLine((CartesianVector)end2);
var arc1 = new GreatCircleSegment(start1, end1);
var arc2 = new GreatCircleSegment(start2, end2);
Console.WriteLine();
Console.WriteLine(arc1.Midpoint);
Console.WriteLine(new CartesianVector(0, 0, 1));
Console.WriteLine((SphereCoordinate)arc1.Midpoint);
Console.WriteLine((SphereCoordinate)new CartesianVector(0, 0, 1));
Console.WriteLine((CartesianVector)(SphereCoordinate)arc1.Midpoint);
Console.WriteLine();
SphereCoordinate intersection;
Console.WriteLine(arc1.Intersects(arc2, out intersection) + " " + intersection + " " + (CartesianVector)intersection);
Console.WriteLine();
var quarterSpherePoly = new VoronoiCell(new SphereCoordinate(0, 0), new SphereCoordinate(0.5 * Math.PI, 0), new SphereCoordinate(0.5 * Math.PI, 0.5 * Math.PI), new SphereCoordinate(0.5 * Math.PI, Math.PI));
Console.WriteLine("Area of quarter sphere Polygon: " + quarterSpherePoly.Area);
Console.WriteLine("Area of whole sphere: " + 4 * Math.PI);
Console.WriteLine("Area of quarter sphere: " + Math.PI);
Console.WriteLine();
Console.WriteLine(Math.Acos(new CartesianVector(0, 1, 0).DotProduct(new SphereCoordinate(Math.PI / 2, 0))));
Console.WriteLine(Math.Acos(new CartesianVector(0, 1, 0).DotProduct(new SphereCoordinate(Math.PI / 2, -Math.PI / 2))));
Console.WriteLine(Math.Acos(new CartesianVector(0, 1, 0).DotProduct(new SphereCoordinate(Math.PI / 2, 0))));
Console.WriteLine(Math.Acos(new CartesianVector(0, 1, 0).DotProduct(new SphereCoordinate(Math.PI / 2, -Math.PI / 2))));
Console.WriteLine();
Console.WriteLine(Math.Acos(new CartesianVector(1, 1, 0).AsUnitVector.DotProduct(new SphereCoordinate(Math.PI / 2, 0))));
Console.WriteLine(Math.Acos(new CartesianVector(1, 1, 0).AsUnitVector.DotProduct(new SphereCoordinate(Math.PI / 4, -Math.PI / 2))));
Console.WriteLine();
Console.WriteLine(Math.Acos(new CartesianVector(0, 1, 0).DotProduct(new CartesianVector(1, 1, 0).AsUnitVector)));
Console.WriteLine(Math.PI / 4);
Console.ReadLine();
}
/// <summary>
/// Checks whether the given <see cref="SphereCoordinate"/> is within this <see cref="VoronoiCell"/>.
/// </summary>
/// <param name="sphereCoordinate">The <see cref="SphereCoordinate"/> to check.</param>
/// <returns>Whether the given <see cref="SphereCoordinate"/> is within this <see cref="VoronoiCell"/>.</returns>
public bool IsInside(SphereCoordinate sphereCoordinate)
{
var centerToPoint = new GreatCircleSegment(Center, sphereCoordinate);
// Check if any sides intersect with the arc from Center to point.
SphereCoordinate _;
if (startCorner == null)
return FirstPart.Intersects(centerToPoint, out _);
else
foreach (var corner in Corners)
if (corner.ToNext.Intersects(centerToPoint, out _))
return false;
return true;
}
/// <summary>
/// Checks whether the given <see cref="GreatCircleSegment"/> intersects with this one.
/// The point of intersection can then be found in the out-Parameter.
/// </summary>
/// <param name="other">The arc segment to be checked.</param>
/// <param name="intersection">The point of intersection, if they intersect.</param>
/// <returns>Whether the two <see cref="GreatCircleSegment"/>s intersect or not.</returns>
public bool Intersects(GreatCircleSegment other, out SphereCoordinate intersection)
{
// http://www.boeing-727.com/Data/fly%20odds/distance.html
intersection = default(SphereCoordinate);
if (Length.IsAlmostEqualTo(0) || other.Length.IsAlmostEqualTo(0))
return false;
CartesianVector possibleIntersection1;
if (!BaseCircle.Intersects(other.BaseCircle, out possibleIntersection1))
return false;
var possibleIntersection2 = -possibleIntersection1;
if (IsOnArc(possibleIntersection1) && other.IsOnArc(possibleIntersection1))
{
intersection = possibleIntersection1;
return true;
}
if (IsOnArc(possibleIntersection2) && other.IsOnArc(possibleIntersection2))
{
intersection = possibleIntersection2;
return true;
}
return false;
}
/// <summary>
/// Creates a new instance of the <see cref="GreatCircle"/> struct given a segment of it.
/// </summary>
/// <param name="segment">A part of the great circle.</param>
public GreatCircle(GreatCircleSegment segment)
: this(segment.Start, segment.End)
{
}
/// <summary>
/// Checks whether the given <see cref="GreatCircleSegment"/> intersects with this <see cref="GreatCicle"/>.
/// The point of intersection can then be found in the out-Parameter.
/// </summary>
/// <param name="arc">The arc segment to be checked.</param>
/// <param name="intersection">The point of intersection, if they intersect.</param>
/// <returns>Whether the <see cref="GreatCircleSegment"/> intersects this <see cref="GreatCircle"/> or not.</returns>
public bool Intersects(GreatCircleSegment arc, out SphereCoordinate intersection)
{
intersection = default(SphereCoordinate);
CartesianVector possibleIntersection;
if (!Intersects(arc.BaseCircle, out possibleIntersection))
return false;
if (arc.IsOnArc(possibleIntersection))
{
intersection = possibleIntersection;
return true;
}
if (arc.IsOnArc(-possibleIntersection))
{
intersection = -possibleIntersection;
return true;
}
return false;
}
/// <summary>
/// Creates a new instance of the <see cref="GreatCircle"/> struct given a segment of it.
/// </summary>
/// <param name="segment">A part of the great circle.</param>
public GreatCircle(GreatCircleSegment segment)
: this(segment.Start, segment.End)
{
}