directiondependent

Directiondependent is an adjective used to describe quantities, effects, or measurements whose values vary with the direction of observation or measurement. It captures the idea of directional dependence, a form of anisotropy where properties are not the same in every direction. In many contexts, directiondependent is contrasted with isotropic behavior, where properties are identical in all directions.

Mathematically, direction dependence can be represented by functions defined on directions (for example on the unit sphere) or by tensors that encode how a quantity changes with orientation. Scalar fields may depend on direction, such as a refractive index n(θ, φ), while mechanical properties can be described by tensorial quantities like a stiffness or conductivity tensor. In surface science and computer graphics, direction-dependent quantities are often expressed as functions of incident and outgoing directions, as in a BRDF that describes how light reflects from a surface.

Common domains where directiondependent behavior is important include materials science, optics, acoustics, and imaging. In crystals, properties such as stiffness, thermal conductivity, or optical response vary with crystallographic direction. In optics, birefringent and anisotropic media exhibit direction-dependent refractive indices. In computer graphics, direction-dependent reflectance models capture how real surfaces reflect light differently depending on viewing and lighting directions. In astronomy and radio astronomy, direction-dependent effects arise from antenna beam patterns and propagation media, requiring specialized calibration.

Understanding directiondependent phenomena often involves angular representations, spherical harmonics, or tensor formalisms to quantify how a quantity changes with orientation.