/// <summary>
/// Determines whether the specified matrix is a valid pose matrix.
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>
/// <see langword="true"/> if the specified matrix is a valid pose matrix; otherwise,
/// <see langword="false"/>.
/// </returns>
/// <remarks>
/// This method makes a simple, low-performance test.
/// </remarks>
public static bool IsValid(Matrix44D matrix)
{
Vector4D v1 = matrix * Vector4D.UnitX;
Vector4D v2 = matrix * Vector4D.UnitY;
Vector4D v3 = matrix * Vector4D.UnitZ;
return(Numeric.AreEqual(v1.LengthSquared(), 1) &&
Numeric.AreEqual(v2.LengthSquared(), 1) &&
Numeric.AreEqual(v3.LengthSquared(), 1) &&
Numeric.IsZero(Vector4D.Dot(v1, v2)) &&
Numeric.IsZero(Vector4D.Dot(v2, v3)) &&
Numeric.IsZero(Vector4D.Dot(v1, v3)) &&
Numeric.AreEqual(1.0, matrix.Determinant()) &&
Numeric.IsZero(matrix.M30) &&
Numeric.IsZero(matrix.M31) &&
Numeric.IsZero(matrix.M32) &&
Numeric.AreEqual(matrix.M33, 1));
}