/// <summary>
/// Returns the angle between two NetronVectors
/// </summary>
/// <param name="v1">a vector</param>
/// <param name="v2">a vector</param>
/// <returns></returns>
public static double Angle(NetronVector v1, NetronVector v2)
{
if ((v1.Length() > 0) && (v2.Length() > 0))
{
return(Math.Acos(v1.DotProduct(v2) / (v1.Length() * v2.Length())));
}
else
{
return(0);
}
}
/// <summary>
/// Return whether another vector is equal to this one
/// </summary>
/// <param name="v">a NetronVector vector</param>
/// <returns>true if the two are component-wise equal, otherwise false</returns>
public bool IsEqual(NetronVector v)
{
if (this.mX != v.X)
{
return(false);
}
if (this.mY != v.Y)
{
return(false);
}
if (this.mZ != v.Z)
{
return(false);
}
return(true);
}
/// <summary>
/// Rotates the vector
/// </summary>
/// <param name="phi">the angle around the x-axis</param>
/// <param name="theta">the angle around the y-axis</param>
/// <param name="psi">the angle around the z-axis</param>
public void RotateEquals(double phi, double theta, double psi)
{
NetronVector t = new NetronVector(); // Temporary variables for holding old values
double sX = Math.Sin(phi), cX = Math.Cos(phi), //to avoid reduntant calculations.
sY = Math.Sin(theta), cY = Math.Cos(theta),
sZ = Math.Sin(psi), cZ = Math.Cos(psi);
t.mY = mY * cX - mZ * sX; //rotate around the mX-axis
t.mZ = mY * sX + mZ * cX;
mY = t.mY; //update vars needed in algorithm
mZ = t.mZ;
t.mX = mX * cY - mZ * sY; //rotate around the mY-axis
t.mZ = mX * sY + mZ * cY;
mX = t.mX; //update vars needed in algorithm again
mZ = t.mZ;
t.mX = mX * cZ - mY * sZ; //rotate around the mZ-axis
t.mY = mX * sZ + mY * cZ;
mX = t.mX; //update vars for final storage
mY = t.mY;
mZ = t.mZ;
}
/// <summary>
/// Rotates a 3D point along the origin of its coordinate system
/// </summary>
/// <param name="phi">the angle around the x-axis</param>
/// <param name="theta">the angle around the y-axis</param>
/// <param name="psi">the angle around the z-axis</param>
/// <returns></returns>
public NetronVector Rotate(double phi, double theta, double psi)
{ //Euler angles
NetronVector t = new NetronVector(); // Temporary variables for holding old values
double sX = Math.Sin(phi), cX = Math.Cos(phi), //to avoid reduntant calculations.
sY = Math.Sin(theta), cY = Math.Cos(theta),
sZ = Math.Sin(psi), cZ = Math.Cos(psi);
NetronVector tmp = new NetronVector(this);
t.mY = tmp.mY * cX - tmp.mZ * sX; //rotate around the mX-axis
t.mZ = tmp.mY * sX + tmp.mZ * cX;
tmp.mY = t.mY; //update vars needed in algorithm
tmp.mZ = t.mZ;
t.mX = tmp.mX * cY - tmp.mZ * sY; //rotate around the mY-axis
t.mZ = tmp.mX * sY + tmp.mZ * cY;
tmp.mX = t.mX; //update vars needed in algorithm again
tmp.mZ = t.mZ;
t.mX = tmp.mX * cZ - tmp.mY * sZ; //rotate around the mZ-axis
t.mY = tmp.mX * sZ + tmp.mY * cZ;
tmp.mX = t.mX; //update vars for final storage
tmp.mY = t.mY;
return(t);
}
/// <summary>
/// Constructor; based on another NetronVector
/// </summary>
/// <param name="v">a vector</param>
public NetronVector(NetronVector v)
{
mX = v.mX; mY = v.mY; mZ = v.mZ;
}
/// <summary>
/// Returns the distance to the given vector
/// </summary>
/// <param name="v">a vector</param>
/// <returns>the distance to the given vector</returns>
public double Distance(NetronVector v)
{
return(Math.Sqrt((mX - v.X) * (mX - v.X) + (mY - v.Y) * (mY - v.Y) + (mZ - v.Z) * (mZ - v.Z)));
}
/// <summary>
/// The vector product and sets the result equal to this vector
/// </summary>
/// <param name="v">a vector</param>
public void CrossProductEquals(NetronVector v)
{
this.SetTo(new NetronVector(this.mY * v.mZ - v.mY * this.mZ, this.mZ * v.mX - v.mZ * this.mX, this.mX * v.mY - v.mX * this.mY));
}
/// <summary>
/// Sets this vector to the project of the original onto the given vector
/// </summary>
/// <param name="v">the vector onto which this vector is projected</param>
public void ProjectionEquals(NetronVector v)
{
this.SetTo(v.Multiply((this.DotProduct(v)) / (v.DotProduct(v))));
}
/// <summary>
/// The vector product with another vector
/// </summary>
/// <param name="v">the second vector of the product</param>
/// <returns>the resulting vector</returns>
public NetronVector CrossProduct(NetronVector v)
{
return(new NetronVector(this.mY * v.mZ - v.mY * this.mZ, this.mZ * v.mX - v.mZ * this.mX, this.mX * v.mY - v.mX * this.mY));
}
/// <summary>
/// Scalar product of this vector with another
/// </summary>
/// <param name="v">the second vector to make the scalar product with</param>
/// <returns>the result of the scalar product</returns>
public double DotProduct(NetronVector v)
{
return(mX * v.mX + mY * v.mY + mZ * v.mZ);
}
/// <summary>
/// Returns the projection of this vector on the given one
/// </summary>
/// <param name="v">the vector onto which this vector is projected</param>
/// <returns>the resulting vector</returns>
public NetronVector Projection(NetronVector v)
{
return(v.Multiply((this.DotProduct(v)) / (v.DotProduct(v))));
}
/// <summary>
/// Sets the coordinates of this vector to those of the given one
/// </summary>
/// <param name="v">a vector</param>
public void SetTo(NetronVector v)
{
mX = v.mX; mY = v.mY; mZ = v.mZ;
}
/// <summary>
/// Substract the vector with the given one
/// </summary>
/// <param name="v">a vector</param>
public void SubstractEquals(NetronVector v)
{
mX -= v.mX; mY -= v.mY; mZ -= v.mZ;
}
/// <summary>
/// Substract the vector with the given one
/// </summary>
/// <param name="v">a vector</param>
/// <returns>the result of the vector operation</returns>
public NetronVector Substract(NetronVector v)
{
return(new NetronVector(mX - v.mX, mY - v.mY, mZ - v.mZ));
}
/// <summary>
/// Adds a vector to the current one
/// </summary>
/// <param name="v">a vector</param>
public void AddEquals(NetronVector v)
{
mX += v.mX; mY += v.mY; mZ += v.mZ;
}
/// <summary>
/// Returns the addition of the vector with the given one
/// </summary>
/// <param name="v">a vector</param>
/// <returns></returns>
public NetronVector Add(NetronVector v)
{
return(new NetronVector(mX + v.mX, mY + v.mY, mZ + v.mZ));
}