isolines

An isoline is a line that connects points of equal value for a given scalar field on a plane or surface. Isolines are used to represent spatial variation of a physical quantity and facilitate visualization of gradients and patterns. Common examples include contours (lines of equal elevation on maps), isotherms (temperature), isobars (atmospheric pressure), isohyets (precipitation), isochrones (time-to-travel) and isotachs (wind speed). The general concept applies to any continuous field, such as salinity (isohalines) or depth (depth contours).

Isolines reflect the smooth variation of the field; where the field changes rapidly, lines are spaced closely, and where the field changes slowly, lines are spaced farther apart. They are typically drawn so that lines never cross; they may form closed loops or terminate at the boundary of the data. The spacing and labeling convey magnitude and gradient, and the use of a contour interval standardizes interpretation across a map.

Construction usually starts with sample data points or a grid, followed by interpolation to generate a continuous surface and then contouring to extract lines at a chosen interval (contour interval) or at specific values. Common algorithms include raster-based marching squares and vector-based interpolation; in geographic information systems, isolines are stored as polyline features and may be smoothed or simplified.

Interpretation requires awareness of data resolution and measurement error: lines can be misleading if data are sparse, extrapolated beyond measured values, or tied to arbitrary intervals. Isolines are widely used in topography, meteorology, oceanography and other fields to study patterns, gradients and regional differences.