Vonalirány

Vonalirány is a term used in Hungarian to describe the direction or orientation of a straight line in a plane or space. It denotes how the line is pointed relative to a chosen reference direction, commonly the positive x-axis in mathematics or north in surveying and navigation. The concept is central to geometry, cartography, and engineering, where precise line orientation affects design, measurement, and interpretation.

In mathematics, if a line has direction vector (dx, dy), its direction angle with respect to the x-axis is θ = arctan2(dy, dx). The azimuth or bearing relative to north is α = (90° − θ) mod 360°. A line with slope m has θ = arctan(m). In three-dimensional space, a line’s direction is given by a direction vector (dx, dy, dz), and its orientation can be described by direction cosines or a pair of angles with respect to chosen axes.

Measurement of vonalirány can be done with instruments and software. Traditional methods use protractors or compass-based readings, while modern workflows rely on GIS, CAD, and surveying tools that compute direction from coordinate data. Sources of error include instrument precision, projection distortions, and data misalignment.

Applications of vonalirány span map making, route planning, land surveying, civil engineering, architecture, and robotics. The concept also underpins related notions such as azimuth, bearing, slope, and gradient, which describe orientation in different contexts. Etymologically, vonalirány is a compound of vonal (line) and irány (direction); in Hungarian technical literature it denotes the standard designation of a line’s orientation.