excerpt from pages 44-45:
The program selects sample points of x,y coordinates at random
within a rectangular area of any size. The points can be
increasingly uniformly distributed by not allowing the selection of
coordinates that are closer than a minimum distance to any
previously placed points. One enters the lengths of the X-axis
(100) and Y-axis (100), the number of points to select coordinates
for (6), and the minimum spacing between sample points (20). The
maximum hexagonal spacing that a certain number of points N in an
area (AREA) can be spaced is given by 1.0746/SQR(N/AREA) [12], and is 43.9 units for the parameters
above.
Usually, the minimum spacing distance used must be about 70%
or less of the maximum spacing distance theoretically possible in
order for the program to finish spacing points [13]. In addition to
the x,y coordinates, the polar coordinates are given by a distance
from the origin (lower left corner of the area) and an angle (from
the X-axis). The distance from the origin to each point is
calculated with the Pythagorean theorem and the angle is given from
BASIC by ATN(Y / X)) * 180 / 3.1415926#.
The spacing of sample
points may be desired if sampling disturbs the surrounding area
such that it is undesirable to sample nearby as could occur with a
truly random selection. Also, it is less likely that a clumped
sampling distribution could occur by chance and bias the
conclusions. These ideas are embodied in stratified sampling
methods [14].
selected references:
12. P. J. Clark and F. C. Evans, Distance to nearest neighbor as a
measure of spatial relationships in populations. Ecology 35,
445 (1954).
13. J. A. Byers, Dirichlet tessellation of bark beetle spatial attack
points. J. Anim. Ecol. 61, 759 (1992).
14. B. D. Ripley, Spatial Statistics. John Wiley & Sons, New York
(1981).
Other related references:
Byers, J.A. 1991. BASIC algorithms for random sampling and treatment
randomization. Computers in Biology and Medicine 21:69-77.
Byers, J.A. 1996. Random selection algorithms for spatial and
temporal sampling. Computers in Biology and Medicine
26:41-52.
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