Description Usage Arguments Details Value Author(s) Examples
Draws a sample of spatial locations within a spatially continuous polygonal sampling region.
1 | continuous.sample(poly, n, delta, k = 0, rho = NULL)
|
poly |
boundary of a polygon. |
n |
number of events. |
delta |
minimum permissible distance between any two events in preliminary sample. |
k |
number of locations in preliminary sample to be replaced by near neighbours of other preliminary sample locations in final sample (must be between 0 and |
rho |
maximum distance between close pairs of locations in final sample. |
To draw a sample of size n
from a spatially continuous region A, with the property that the distance between any two sampled locations is at least delta
, the following algorithm is used.
Step 1. Set i = 1 and generate a point x_{1} uniformly distributed on A.
Step 2. Increase i by 1, generate a point x_{i} uniformly distributed on A and calculate the minimum, d_{\min}, of the distances from x_{i} to all x_{j}: j < i .
Step 3. If d_{\min} ≥ δ, increase i by 1 and return to step 2 if i ≤ n, otherwise stop;
Step 4. If d_{\min} < δ, return to step 2 without increasing i.
Sampling close pairs of points. For some purposes, it is desirable that a spatial sampling scheme include pairs of closely spaced points. In this case, the above algorithm requires the following additional steps to be taken.
Let k
be the required number of close pairs. Choose a value rho
such that a close pair of points will be a pair of points separated by a distance of at most rho
.
Step 5. Set j = 1 and draw a random sample of size 2 from the integers 1,2,…,n, say (i_{1}; i_{2});
Step 6. Replace x_{i_{1}} by x_{i_{2}} + u , where u is uniformly distributed on the disc with centre x_{i_{2}} and radius rho
, increase i by 1 and return to step 5 if i ≤ k, otherwise stop.
A matrix of dimension n
by 2 containing event locations.
Emanuele Giorgi e.giorgi@lancaster.ac.uk
Peter J. Diggle p.diggle@lancaster.ac.uk
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