Linearscale

Linearscale is a concept used in data visualization and measurement to describe a scale that maps an input domain to an output range using a linear transformation. In this approach, equal changes in the input produce equal changes in the output, so distances on the visualization correspond directly to data differences. The relationship is typically an affine transformation of the form y = a x + b, where a sets the slope and b an offset.

Key properties include order preservation and uniform spacing: if the input values are evenly spaced, the resulting visual positions or values are also evenly spaced. A linearscale requires a defined domain (the input data minimum and maximum) and a range (the output interval, such as pixel coordinates or color values). It is commonly used for axes in graphs, charts, and dashboards, as well as for mapping data to color or size in a straightforward, interpretable way.

Common applications include plotting numerical data on linear axes, where a unit change in the data equals a consistent unit change on the display, and creating linear color ramps or size scales where data values map linearly to color intensity or marker size. Linearscale is often favored for its simplicity and interpretability but may be inappropriate for data that span several orders of magnitude or are highly skewed, where nonlinear scales (such as logarithmic or power scales) can provide more meaningful visual differentiation.

Implementation typically involves defining a domain [min, max] and a range [start, end], then computing a normalized value t = (x - min) / (max - min) and applying the output as start + t (end - start).