An object of class "SpatPatterns".
Generates n_2 2D points associated with the given set of points (i.e., reference points) \(X_1\) in the
type=type fashion with the parameter=asc.par which specifies the level of association.
The generated points are intended to be from a different class, say class 2 (or \(X_2\) points)
than the reference (i.e., \(X_1\) points, say class 1 points, denoted as X1 as an argument
of the function), say class 1 points).
To generate \(n_2\) (denoted as n2 as an argument of the function)\(X_2\) points,
\(n_2\) of \(X_1\) points are randomly selected (possibly with replacement) and
for a selected X1 point, say \(x_{1ref}\),
a new point from the class 2, say \(x_{2new}\), is generated from a distribution specified
by the type argument.
In type I association, i.e., if type="I", first a \(Uniform(0,1)\) number, \(U\), is generated.
If \(U \le p\), \(x_{2new}\) is generated (uniform in the polar coordinates) within a
circle with radius equal to the distance to the closest \(X_1\) point,
else it is generated uniformly within the smallest bounding box containing \(X_1\) points.
In the type C association pattern
the new point from the class 2, \(x_{2new}\), is generated (uniform in the polar coordinates) within a circle
centered at \(x_{1ref}\) with radius equal to \(r_0\),
in type U association pattern \(x_{2new}\) is generated similarly except it is uniform in the circle.
In type G association, \(x_{2new}\) is generated from the bivariate normal distribution centered at \(x_{1ref}\) with covariance
\(\sigma I_2\) where \(I_2\) is \(2 \times 2\) identity matrix.
See ceyhan:serra-2014;textualnnspat for more detail.