In each function, r represents the distance between two random points, and D is the specimen edge length.
After 25 minutes, the distance between the centre of two successive pictures is smaller than the mean distance between two random points of a square corresponding to the nest area (after 25 minutes, one sample t test, t75 = 68, p<0.0001, n = 77).
For this reason, the "upper bound approach" has been proposed which relies on the fact that the Euclidean distance between two random points on a plane is necessarily less than (or equal to) the corresponding geodesics, which is known as inextensibility constraint.
In a simple continuous space, you'd need to write out infinitely many decimal places just to specify the exact distance between two random points, but physics titan John Wheeler showed that quantum effects probably make any digits after the 35th decimal place meaningless, because our whole classical notion of space breaks down on smaller scales, perhaps being replaced by a strange foamy structure.
Shape distribution by Osada et al. [21] is a global feature-based approach which utilize shape functions developed on distance, angle, area, and volumetric measurements between random points on the 3D model.
Hence, we obtain the distribution of distances between a sensor and the gateway, that is, the distance between a random point within the sphere and its center.
The Hop-F statistic compares the distance between vent I and its nearest neighbour vent (ri), and the distance between a random point and the nearest vent (di) (Fig. 3b).
The impulses reach the structure at random points on the surface and at random time intervals.
Ohbuchi et al. [56] investigate shape histograms that are discretely parametrized along the principal axes of inertia of the model and also extended D2 shape function by considering the angle between the surfaces on which two random points are located [57].
Differences in steepness between coral locations and random points were only visible in AUV derived slope, probably resulting from a tendency of the AUV to underestimate steepness of slope.
