/// <summary>
/// Calculates the intersection point of two given lines in 3D space.
/// </summary>
/// <param name="plane">Fist line.</param>
/// <param name="line">Second line.</param>
/// <param name="intersection">Out parameter, true if intersection exists.</param>
/// <returns>The point of the intersection.</returns>
public static Point3D Intersection(Plane3D plane, Line3D line, out bool intersection)
{
Point3D point = new Point3D();
Matrix linearEquation = new Matrix(plane, line);
linearEquation.ToRREF();
int type = linearEquation.LinearEquationSolutionType();
intersection = false;
if (type == 1) //exactly one solution
{
if (plane.SupportVector.Z + linearEquation.Mtrx[0, 3] * plane.DirectionVectors[0].Z + linearEquation.Mtrx[1, 3] * plane.DirectionVectors[1].Z
== line.SupportVector.Z + linearEquation.Mtrx[2, 3] * line.DirectionVector.Z)
{
intersection = true;
point = plane.GetPointAt(linearEquation.Mtrx[0, 3], linearEquation.Mtrx[1, 3]);
}
}
else if (type == -1) //infinite soulutions
{
intersection = true;
point.X = double.NaN;
point.Y = double.NaN;
point.Z = double.NaN;
}
return(point);
}
/// <summary>
/// Checks if two planes are parallel to each other.
/// </summary>
/// <param name="plane1">First plane.</param>
/// <param name="plane2">Second plane.</param>
/// <returns></returns>
public static bool IsParallel(Plane3D plane1, Plane3D plane2)
{
return(IsParallel(plane1.NormalVector, plane2.NormalVector));
}
/// <summary>
/// Calculates the angle between a plane and a line in radians.
/// </summary>
/// <param name="plane">A plane.</param>
/// <param name="line">A line</param>
/// <returns></returns>
public static double AngleBetween(Plane3D plane, Line3D line)
{
return(Math.PI / 2 - AngleBetween(plane.NormalVector, line.DirectionVector));
}
/// <summary>
/// Calculates the angle between two planes in radians.
/// </summary>
/// <param name="plane1">First plane.</param>
/// <param name="plane2">Second plane.</param>
/// <returns></returns>
public static double AngleBetween(Plane3D plane1, Plane3D plane2)
{
return(AngleBetween(plane1.NormalVector, plane2.NormalVector));
}
/// <summary>
/// Calculates the angle between a plane and a vector in radians.
/// </summary>
/// <param name="plane">First line.</param>
/// <param name="vector">Second line.</param>
/// <returns></returns>
public static double AngleBetween(Plane3D plane, Vect3D vector)
{
return(Math.PI / 2 - AngleBetween(plane.NormalVector, vector));
}
