Minimum Variance Analysis (MVA) is frequently used for the geometrical organization of a time series of vectors. The Coplanarity Variance Analysis (CVA) developed in this paper reproduces the layer geometry involving coplanar magnetosonic shocks or plane-polarized wave trains (including normals and coplanarity directions) 300 times more precisely (<0.1¿) than MVA using the same input data. The CVA technique exploits the eigenvalue degeneracy of the covariance matrix present at planar structures to find a consistent normal to the coplanarity plane of the fluctuations. Although Tangential Discontinuities (TDs) have a coplanarity plane, the eigenvalues of their covariance matrix are usually not degenerate; accordingly, CVA does not misdiagnose TDs as shocks or plane-polarized waves. Together CVA and MVA may be used to sort between the hypotheses that the time series is caused by a one-dimensional current layer that has magnetic disturbances that are (1) coplanar, linearly polarized (shocks/plane waves), (2) intrinsically helical (rotational/tangential discontinuities), or (3) neither 1 nor 2.