Cornercutting

Cornercutting is the practice of taking shortcuts that bypass steps in a process to save time or effort. In everyday usage, it can refer to skipping quality checks, using lower-grade materials, or rushing tasks. While it can improve efficiency, corner-cutting often reduces reliability, safety, or accuracy and may violate standards or contracts. Critics describe it as unethical or imprudent when it undermines outcomes.

In mathematics and computer graphics, corner-cutting denotes a family of algorithms that transform a polygonal chain into a smoother curve by repeatedly cutting corners at the joints. The coefficients specify where new points are placed along each edge, and the original vertices are progressively removed. The process creates more, smoother vertices and, in the limit, produces curves with higher continuity. The best-known example is Chaikin's corner-cutting algorithm, which inserts two points on each edge of a polyline at fixed fractions and replaces the edge with two segments. Repeating the operation yields a curve that converges to a quadratic B-spline. Other schemes, such as the Lane-Riesenfeld algorithm, generalize corner-cutting by repeated averaging to generate higher-degree splines.

Applications include generating smooth curves from control polygons in computer graphics, geometric modeling, and animation. In planning and robotics, corner-cutting concepts appear as path simplification techniques that shorten travel distance or duration, sometimes trading off path optimality for safety or feasibility. The term remains informal outside mathematical contexts, where it broadly implies any shortcut that may compromise completeness or quality.