public bool Equals(Vector3d obj)
{
return obj.x == this.x && obj.y == this.y && obj.z == this.z;
}
/// <summary>
/// Obtains the square distance between two points.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <returns>Square distance.</returns>
public static double SquareDistance(Vector3d u, Vector3d v)
{
return (u.X - v.X)*(u.X - v.X) + (u.Y - v.Y)*(u.Y - v.Y) + (u.Z - v.Z)*(u.Z - v.Z);
}
/// </summary>
/// Check if the components of two vectors are approximate equals.
/// <param name="obj">Vector3d.</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(Vector3d obj, double threshold)
{
if (Math.Abs(obj.X - this.x) > threshold)
{
return false;
}
if (Math.Abs(obj.Y - this.y) > threshold)
{
return false;
}
if (Math.Abs(obj.Z - this.z) > threshold)
{
return false;
}
return true;
}
/// <summary>
/// Obtains the midpoint.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <returns>Vector3d.</returns>
public static Vector3d MidPoint(Vector3d u, Vector3d v)
{
return new Vector3d((v.X + u.X)*0.5F, (v.Y + u.Y)*0.5F, (v.Z + u.Z)*0.5F);
}
/// <summary>
/// Rounds the components of a vector.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="numDigits">Number of significative defcimal digits.</param>
/// <returns>Vector3d.</returns>
public static Vector3d Round(Vector3d u, int numDigits)
{
return new Vector3d((Math.Round(u.X, numDigits)),
(Math.Round(u.Y, numDigits)),
(Math.Round(u.Z, numDigits)));
}
/// <summary>
/// Obtains the distance between two points.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <returns>Distancie.</returns>
public static double Distance(Vector3d u, Vector3d v)
{
return (Math.Sqrt((u.X - v.X)*(u.X - v.X) + (u.Y - v.Y)*(u.Y - v.Y) + (u.Z - v.Z)*(u.Z - v.Z)));
}
/// <summary>
/// Obtains the dot product of two vectors.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <returns>The dot product.</returns>
public static double DotProduct(Vector3d u, Vector3d v)
{
return (u.X*v.X) + (u.Y*v.Y) + (u.Z*v.Z);
}
/// <summary>
/// Checks if two vectors are perpendicular.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <param name="threshold">Tolerance used.</param>
/// <returns>True if are penpendicular or false in anyother case.</returns>
public static bool ArePerpendicular(Vector3d u, Vector3d v, double threshold)
{
return MathHelper.IsZero(DotProduct(u, v), threshold);
}
/// <summary>
/// Obtains the cross product of two vectors.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <returns>Vector3d.</returns>
public static Vector3d CrossProduct(Vector3d u, Vector3d v)
{
double a = u.Y*v.Z - u.Z*v.Y;
double b = u.Z*v.X - u.X*v.Z;
double c = u.X*v.Y - u.Y*v.X;
return new Vector3d(a, b, c);
}
/// <summary>
/// Checks if two vectors are parallel.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <param name="threshold">Tolerance used.</param>
/// <returns>True if are parallel or false in anyother case.</returns>
public static bool AreParallel(Vector3d u, Vector3d v, double threshold)
{
double a = u.Y*v.Z - u.Z*v.Y;
double b = u.Z*v.X - u.X*v.Z;
double c = u.X*v.Y - u.Y*v.X;
if (! MathHelper.IsZero(a, threshold))
{
return false;
}
if (!MathHelper.IsZero(b, threshold))
{
return false;
}
if (!MathHelper.IsZero(c, threshold))
{
return false;
}
return true;
}
/// <summary>
/// Obtains the angle between two vectors.
/// </summary>
/// <param name="u">Vector3d.</param>
/// <param name="v">Vector3d.</param>
/// <returns>Angle in radians.</returns>
public static double AngleBetween(Vector3d u, Vector3d 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);
}
/// <summary>
/// Gets the rotation matrix from the normal vector (extrusion direction) of an entity.
/// </summary>
/// <param name="zAxis">Normal vector.</param>
/// <returns>Rotation matriz.</returns>
public static Matrix3d ArbitraryAxis(Vector3d zAxis)
{
zAxis.Normalize();
Vector3d wY = Vector3d.UnitY;
Vector3d wZ = Vector3d.UnitZ;
Vector3d aX;
if ((Math.Abs(zAxis.X) < 1/64.0) && (Math.Abs(zAxis.Y) < 1/64.0))
aX = Vector3d.CrossProduct(wY, zAxis);
else
aX = Vector3d.CrossProduct(wZ, zAxis);
aX.Normalize();
Vector3d aY = Vector3d.CrossProduct(zAxis, aX);
aY.Normalize();
return new Matrix3d(aX.X, aY.X, zAxis.X, aX.Y, aY.Y, zAxis.Y, aX.Z, aY.Z, zAxis.Z);
}
/// <summary>
/// Transforms a point list between coordinate systems.
/// </summary>
/// <param name="points">Points to transform.</param>
/// <param name="zAxis">Object normal vector.</param>
/// <param name="from">Points coordinate system.</param>
/// <param name="to">Coordinate system of the transformed points.</param>
/// <returns>Transormed point list.</returns>
public static IList<Vector3d> Transform(IList<Vector3d> points, Vector3d zAxis, CoordinateSystem from, CoordinateSystem to)
{
Matrix3d trans = ArbitraryAxis(zAxis);
List<Vector3d> transPoints;
if (from == CoordinateSystem.World && to == CoordinateSystem.Object)
{
transPoints = new List<Vector3d>();
trans = trans.Traspose();
foreach (Vector3d p in points)
{
transPoints.Add(trans*p);
}
return transPoints;
}
if (from == CoordinateSystem.Object && to == CoordinateSystem.World)
{
transPoints = new List<Vector3d>();
foreach (Vector3d p in points)
{
transPoints.Add(trans*p);
}
return transPoints;
}
return points;
}
/// <summary>
/// Transforms a point between coordinate systems.
/// </summary>
/// <param name="point">Point to transform.</param>
/// <param name="zAxis">Object normal vector.</param>
/// <param name="from">Point coordinate system.</param>
/// <param name="to">Coordinate system of the transformed point.</param>
/// <returns>Transormed point.</returns>
public static Vector3d Transform(Vector3d point, Vector3d zAxis, CoordinateSystem from, CoordinateSystem to)
{
Matrix3d trans = ArbitraryAxis(zAxis);
if (from == CoordinateSystem.World && to == CoordinateSystem.Object)
{
trans = trans.Traspose();
return trans*point;
}
if (from == CoordinateSystem.Object && to == CoordinateSystem.World)
{
return trans*point;
}
return point;
}