Note that an alternative analysis (Figure S1) using the study site as the central point of the radius (rather than the mean center of the 40 observation points) for locating the random points gave similar results to those presented here.
We did not use the nest as the central point of the radius because the location of the natal nest was unknown and the young queen might not visit the natal nest anymore.
We will then describe the role of data transformation in this estimation and the interest in finding the point of minimum radius of curvature.
Our definition of the 'elbow' of a curve as the point of minimum radius of curvature is applicable to other problems in statistics, such as the choice of the number of principal components in a principal components analysis (Jolliffe, 2002).
More formally, the O-ring statistic O 12(r) for a bivariate pattern composed of type 1 and type 2 points yields the average density of type 2 point within rings of radius r and width dr around the points of pattern 1.
Let D be an arbitrary point on circle of radius 1 with center in C. Let (f: X to X ) be defined by f(A) = f(B) = f(D) = A,qquad f(C) = B. Let (varphi tau) = 1 - tau), (tauin[0, 1] ), and (M x, y, t) = frac{t}{t + d x, y)}), (t > 0), where by (d x, y) ) is denoted the Euclidean distance in (mathbb{R}^{2}).
In the rest of this paper, we will use to denote the neighboring points of within radius.
(2) By using the estimator described in Section 3, the estimate is calculated from the neighboring points of within radius.
That is, at each point x of void space, each point within a sphere of radius aEDT Σ (x) is visited.
Thus, the radius of the point-of-interest environment must be limited to the maximum radius that can be obtained for the object (in Figure 12 this limit was fixed at 120 mm). Figure 12 3D alignment in cluttered scenes (point-of-interest environment radius equal to 120 mm).
