Calculate sample variance of 3D point distance from centroid

Usage

point_3d_variance(point_matrix)

Arguments

point_matrix

An n-by-3 numerical matrix where each row corresponds to a single point in 3D space.

Value

A one-element numeric vector holding calculated variance

Details

The variance here is taken to mean the sum of variances for each dimension/axis: $$\frac{\sum_{i=1}^n (x_i-x_m)^2 + (y_i-y_m)^2 + (z-z_m)^2}{n-1}$$ Where $X/Y/Z$ represent one axis each, $a_m$ represents the mean of all points' coordinates on an axis, and $n$ represents the total number of points.

See also