The geometry of the minimum radial separation functional: the planar case
Mark J. Kaiser · Measurement Science and Technology · 1995
The minimum radial separation measure associated with a planar simple polygon is computed using an exhaustive search strategy based on the definition of the measure. The algorithm is simple and direct, based on purely geometrical arguments, and provides an alternative and useful way to examine the minimum radial separation measure. The approach of considering the radial separation functional as the basic element of analysis complements rather than replaces existing numerical techniques to find the separation centre point, and because of its fundamental character, is also highly desirable in terms of standardization. Quantitative measures of tolerance specification that arise from this treatment include an intrinsic 'average' out-of-roundness and values for standard deviation. The concavity of the separation functional at the solution minimum is a useful means to quantify tolerance, and contour plots provide constant out-of-roundness regions. A minimum area difference measure is defined, along with its area difference functional, and the geometry of the separation functionals are illustrated by example.