Dlines

Dlines, short for dynamic lines, are a geometric primitive used in constraint-based drawing and parametric modeling. Unlike ordinary line segments defined by fixed endpoints, a Dline is governed by a set of constraints that determine its position, length, and orientation. When related elements change, the Dline recalculates to satisfy its constraints, allowing for responsive and adaptive diagrams.

A Dline is typically defined by two or more anchor points and a constraint set. Common constraints include fixed length, specified direction or angle, parallelism or perpendicularity to other lines, tangency to curves, and attachment to specific points on other shapes. Some systems also support soft constraints, which permit small deviations to preserve aesthetic or practical tolerances. The coordinates of a Dline are thus the solution to a constraint system, often updated incrementally as the user edits the diagram or as dependent elements move.

In practice, Dlines are used in computer-aided design, technical illustration, graph drawing, and user interface layout where elements must maintain relationships under dynamic changes. They enable designers to adjust a single element while maintaining consistent structure and alignment across a composition, reducing manual repositioning and ensuring geometric integrity.

Historically, Dlines emerged from research in constraint-based geometry and constraint solving in the early 2010s, and have since been implemented in various CAD and vector-graphics toolkits. They are commonly presented alongside other parametric primitives such as constrainted curves and Bezier segments. See also: constraint-based drawing, parametric modeling, and automated diagram layout.