}// end omothetia()
/// <summary>
/// scalar product between this and w.
/// </summary>
/// <param name="w">the second factor; the first factor is "this"</param>
/// <returns></returns>
public double scalarProduct(PointR3 w)
{
double scalar = this.getX * w.getX
+ this.getY * w.getY
+ this.getZ * w.getZ;
//
return(scalar);
}// end scalarscalarProduct()
}// end scalarProduct
/// <summary>
/// vector product between this and w, assuminig both in the x-y plane, i.e. z==0.
/// </summary>
/// <param name="w">the second factor; the first factor is "this"; the result will have the form (0,0,k) with k in R.</param>
/// <returns></returns>
public PointR3 vectorProduct(PointR2 w)
{
PointR3 v_inR3 = new PointR3(this.x, this.y, 0);
PointR3 w_inR3 = new PointR3(w.x, w.y, 0);
PointR3 external_inR3 = v_inR3.vectorProduct(w_inR3);
//ready
return(external_inR3);
} // end vectorProduct()
}// end getPointCoordinates
/// <summary>
/// product of a scalar for a vector, i.e. omothetia of a vector.
/// </summary>
public PointR3 omothetia(double theScalar)
{
LinearAlgebra.PointR3 stretchedVector = new PointR3(
this.getX * theScalar,
this.getY * theScalar,
this.getZ * theScalar
);
return(stretchedVector);
}// end omothetia()
}// getCoordinates
/// <summary>
/// scalar product between this and w.
/// </summary>
/// <param name="w">the second factor; the first factor is "this"</param>
/// <returns></returns>
public double scalarProduct(PointR2 w)
{
PointR3 v_inR3 = new PointR3(this.x, this.y, 0);
PointR3 w_inR3 = new PointR3(w.x, w.y, 0);
double scalar_inR3 = v_inR3.scalarProduct(w_inR3);
// ready.
return(scalar_inR3);
}// end scalarProduct
}// end NormaEuclidea
/// <summary>
/// vector product between this and w.
/// </summary>
/// <param name="w">the second factor; the first factor is "this"</param>
/// <returns></returns>
public PointR3 vectorProduct(PointR3 w)
{
double[,] externalProductTensor = new double[3, 3];
double imageX, imageY, imageZ;
// first row is dynamical: it will contain {e1, e2, e3}, once each.
// second row is {this.x, this.y, this.z}
// third row is {w.x, w.y, w.z}
//
externalProductTensor[0, 0] = 1.0;
externalProductTensor[0, 1] = 0.0;
externalProductTensor[0, 2] = 0.0;
//
externalProductTensor[1, 0] = this.x;
externalProductTensor[1, 1] = this.y;
externalProductTensor[1, 2] = this.z;
//
externalProductTensor[2, 0] = w.x;
externalProductTensor[2, 1] = w.y;
externalProductTensor[2, 2] = w.z;
//
LinearAlgebra.RealMatrix firstMatrix = new RealMatrix(externalProductTensor, 3, 3);
imageX = firstMatrix.det();
//
externalProductTensor[0, 0] = 0.0;
externalProductTensor[0, 1] = 1.0;
externalProductTensor[0, 2] = 0.0;
//
LinearAlgebra.RealMatrix secondMatrix = new RealMatrix(externalProductTensor, 3, 3);
imageY = secondMatrix.det();
//
externalProductTensor[0, 0] = 0.0;
externalProductTensor[0, 1] = 0.0;
externalProductTensor[0, 2] = 1.0;
//
LinearAlgebra.RealMatrix thirdMatrix = new RealMatrix(externalProductTensor, 3, 3);
imageZ = thirdMatrix.det();
//
PointR3 vectorProductImage = new PointR3(imageX, imageY, imageZ);
//ready
return(vectorProductImage);
} // end vectorProduct()
