Spaced point sampling
within retangular area
Byers, J.A. 1996. Random selection algorithms for spatial
    and temporal sampling. Computers in Biology and
    Medicine 26:41-52.
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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