public bool Equals(Vector2d obj)
{
return obj.x == this.x && obj.y == this.y;
}
/// <summary>
/// Obtains the square distance between two points.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <returns>Square distance.</returns>
public static double SquareDistance(Vector2d u, Vector2d v)
{
return (u.X - v.X)*(u.X - v.X) + (u.Y - v.Y)*(u.Y - v.Y);
}
/// </summary>
/// Check if the components of two vectors are approximate equals.
/// <param name="obj">Vector2d.</param>
/// <param name="threshold">Maximun tolerance.</param>
/// <returns>True if the three components are almost equal or false in anyother case.</returns>
public bool Equals(Vector2d obj, double threshold)
{
if (Math.Abs(obj.X - this.x) > threshold)
{
return false;
}
if (Math.Abs(obj.Y - this.y) > threshold)
{
return false;
}
return true;
}
/// <summary>
/// Obtains the counter clockwise perpendicular vector .
/// </summary>
/// <param name="u">Vector2d.</param>
/// <returns>Vector2d.</returns>
public static Vector2d Perpendicular(Vector2d u)
{
return new Vector2d(-u.Y, u.X);
}
/// <summary>
/// Rounds the components of a vector.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="numDigits">Number of significative defcimal digits.</param>
/// <returns>Vector2d.</returns>
public static Vector2d Round(Vector2d u, int numDigits)
{
return new Vector2d(Math.Round(u.X, numDigits), Math.Round(u.Y, numDigits));
}
/// <summary>
/// Obtains the dot product of two vectors.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <returns>The dot product.</returns>
public static double DotProduct(Vector2d u, Vector2d v)
{
return (u.X*v.X) + (u.Y*v.Y);
}
/// <summary>
/// Obtains the midpoint.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <returns>Vector2d.</returns>
public static Vector2d MidPoint(Vector2d u, Vector2d v)
{
return new Vector2d((v.X + u.X)*0.5F, (v.Y + u.Y)*0.5F);
}
/// <summary>
/// Obtains the distance between two points.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <returns>Distancie.</returns>
public static double Distance(Vector2d u, Vector2d v)
{
return (Math.Sqrt((u.X - v.X)*(u.X - v.X) + (u.Y - v.Y)*(u.Y - v.Y)));
}
/// <summary>
/// Obtains the cross product of two vectors.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <returns>Vector2d.</returns>
public static double CrossProduct(Vector2d u, Vector2d v)
{
return (u.X*v.Y) - (u.Y*v.X);
}
/// <summary>
/// Checks if two vectors are perpendicular.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <param name="threshold">Tolerance used.</param>
/// <returns>True if are penpendicular or false in anyother case.</returns>
public static bool ArePerpendicular(Vector2d u, Vector2d v, double threshold)
{
return MathHelper.IsZero(DotProduct(u, v), threshold);
}
/// <summary>
/// Checks if two vectors are parallel.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <param name="threshold">Tolerance used.</param>
/// <returns>True if are parallel or false in anyother case.</returns>
public static bool AreParallel(Vector2d u, Vector2d v, double threshold)
{
double a = u.X*v.Y - u.Y*v.X;
return MathHelper.IsZero(a, threshold);
}
/// <summary>
/// Obtains the angle between two vectors.
/// </summary>
/// <param name="u">Vector2d.</param>
/// <param name="v">Vector2d.</param>
/// <returns>Angle in radians.</returns>
public static double AngleBetween(Vector2d u, Vector2d v)
{
double cos = DotProduct(u, v)/(u.Modulus()*v.Modulus());
if (MathHelper.IsOne(cos))
{
return 0;
}
if (MathHelper.IsOne(-cos))
{
return Math.PI;
}
return Math.Acos(cos);
//if (AreParallel(u, v))
//{
// if (Math.Sign(u.X) == Math.Sign(v.X) && Math.Sign(u.Y) == Math.Sign(v.Y))
// {
// return 0;
// }
// return (double)Math.PI;
//}
//Vector3d normal = Vector3d.CrossProduct(new Vector3d(u.X, u.Y, 0), new Vector3d(v.X, v.Y, 0));
//if (normal.Z < 0)
//{
// return (double)(2 * Math.PI - Math.Acos(DotProduct(u, v) / (u.Modulus() * v.Modulus())));
//}
//return (double)(Math.Acos(DotProduct(u, v) / (u.Modulus() * v.Modulus())));
}
