A Mathematical Procedure to Transform a Mapped Circular Space into a Square Space.

Murray T. Williams
Multiresource Inventory Techniques
Rocky Mountain Forest and Range Experiment Station
USDA Forest Service
240 W. Prospect Road
Fort Collins, Colorado 80526-2098, U.S.A.
Phone: 303-498-1335

24pt

Abstract:

This paper describes a technique called morphing which transforms circular plots to square plots. This mathematical transformation is a bijective function which maps a circular space onto a square space of equal area. In one application, 835 mapped circular 0.2 acre plots of forest data were transformed into square plots and tiled together into a single population. This population was then used for statistical simulations studies, Use of the morphing technique saved 36.3% of the data compared with the technique of utilizing only the square inscribed in each 0.2 acre circle.

36pt