Nonrectilinear

Nonrectilinear is an adjective describing forms, paths, or structures that do not conform to rectilinearity, the property of consisting entirely of straight-line segments aligned with a fixed set of directions (typically horizontal and vertical). Nonrectilinear objects may include curved edges, oblique angles, or mixtures of curved and straight elements.

In geometry and related fields, a rectilinear figure is one whose sides run only in a small set of directions, usually horizontal or vertical. A nonrectilinear figure therefore is not restricted to those directions; it may have curved edges, or straight edges at non-axis angles. For example, circles and ellipses are nonrectilinear; a polygon with sides inclined to the axes, or with curved boundaries, is also nonrectilinear. By contrast, a rectangle or an axis-aligned orthogonal polygon is rectilinear.

In design, architecture, and art, nonrectilinear forms are used to express curvature, organic contours, or dynamic movement, contrasting with rectilinear grids and orthogonal plans. In computer graphics and geometric modeling, rendering nonrectilinear shapes involves curves and non-axis-aligned edges, often requiring different algorithms for shading and tessellation.

In robotics and motion planning, nonrectilinear movement refers to paths that change direction in a continuous way rather than moving in a fixed set of axis-aligned directions, affecting strategies for navigation and obstacle avoidance.

See also rectilinearity; nonrectilinear tilings and architecture are common contexts in which the term appears.