pystysuoruus

Pystysuoruus is a concept used to describe the degree of vertical alignment of a set of points, curves, or design elements relative to a chosen vertical reference axis. It is applicable in geometry, computer vision, and graphic design to assess how closely an object follows a vertical orientation.

For a discrete collection of points (x_i, y_i), pystysuoruus can be defined as the spread of the x-coordinates around their mean, sigma_x = sqrt( (1/n) sum (x_i - x_bar)^2 ). A smaller sigma_x indicates stronger verticality. For a curve described by x = f(y), an alternative measure is the L2 norm of the derivative dx/dy over the domain, or the maximum absolute slope max_y |dx/dy|, with smaller values corresponding to a more vertical shape.

To compute from an image or dataset, first align the data with a common vertical axis, extract relevant coordinates, sort by y if needed, and then compute the chosen metric. In practice, one may combine multiple components, such as weighting by point confidence or resampling to uniform y-intervals.

In computer vision, pystysuoruus can help evaluate the alignment of text columns, features in architectural plans, or detected lines in edge images. In typography and UI layout, it provides a measure of vertical rhythm and consistency across elements. In CAD and robotics, it can aid in alignment verification during assembly.

The measure depends on the chosen coordinate system, scale, and rotation; applying rotation changes verticality. Therefore, comparisons require a fixed reference frame and, when possible, normalization of units. It is a descriptive metric rather than a constraint by itself and should be used with other alignment indicators.