/// <summary>
/// Gets the intersection point of three planes.
/// </summary>
/// <param name="planeA">The first plane.</param>
/// <param name="planeB">The second plane.</param>
/// <param name="planeC">The third plane.</param>
/// <returns>
/// The point that touches all three planes. (<see cref="float.NaN"/>, <see cref="float.NaN"/>,
/// <see cref="float.NaN"/>) is returned if there is no unique intersection point, for example,
/// when two planes are parallel or the planes intersect in a line.
/// </returns>
public static Vector3F GetIntersection(Plane planeA, Plane planeB, Plane planeC)
{
// Get a point that meets this requirements: Dot(plane.Normal, point) == plane.DistanceFromOrigin
Matrix33F matrix = new Matrix33F(planeA.Normal.X, planeA.Normal.Y, planeA.Normal.Z,
planeB.Normal.X, planeB.Normal.Y, planeB.Normal.Z,
planeC.Normal.X, planeC.Normal.Y, planeC.Normal.Z);
Vector3F distances = new Vector3F(planeA.DistanceFromOrigin, planeB.DistanceFromOrigin, planeC.DistanceFromOrigin);
bool isInvertible = matrix.TryInvert();
if (isInvertible)
{
return(matrix * distances);
}
else
{
return(new Vector3F(float.NaN));
}
}
/// <summary>
/// Gets the intersection point of three planes.
/// </summary>
/// <param name="planeA">The first plane.</param>
/// <param name="planeB">The second plane.</param>
/// <param name="planeC">The third plane.</param>
/// <returns>
/// The point that touches all three planes. (<see cref="float.NaN"/>, <see cref="float.NaN"/>,
/// <see cref="float.NaN"/>) is returned if there is no unique intersection point, for example,
/// when two planes are parallel or the planes intersect in a line.
/// </returns>
public static Vector3F GetIntersection(Plane planeA, Plane planeB, Plane planeC)
{
// Get a point that meets this requirements: Dot(plane.Normal, point) == plane.DistanceFromOrigin
Matrix33F matrix = new Matrix33F(planeA.Normal.X, planeA.Normal.Y, planeA.Normal.Z,
planeB.Normal.X, planeB.Normal.Y, planeB.Normal.Z,
planeC.Normal.X, planeC.Normal.Y, planeC.Normal.Z);
Vector3F distances = new Vector3F(planeA.DistanceFromOrigin, planeB.DistanceFromOrigin, planeC.DistanceFromOrigin);
bool isInvertible = matrix.TryInvert();
if (isInvertible)
return matrix * distances;
else
return new Vector3F(float.NaN);
}