endpointsdistinct

Endointsdistinct is a term used in geometry and related disciplines to describe a property of one-dimensional objects, such as segments or arcs, where the two endpoints are distinct. In this sense, an object has endpointsdistinct if its endpoint set contains two different points, rather than a single repeated point.

Formal characterization of endpointsdistinct often relies on the underlying space. In a metric or topological space with a distance function d, two points A and B are distinct when d(A,B) > 0 or equivalently when A ≠ B. For a geometric segment or arc with endpoints A and B, endpointsdistinct means A ≠ B, which implies the object has nonzero length and is not degenerate.

Applications and implications of endpointsdistinct appear in both theory and computation. In proofs, ensuring endpoints are distinct avoids degeneracy and clarifies length, parameterization, and boundary conditions. In computational geometry and computer graphics, a check for endpointsdistinct may be performed before performing length calculations, collision checks, or path integrations to prevent division by zero or undefined behavior. In programming, endpointsdistinct can be implemented as a boolean predicate endpointsDistinct(p, q) that returns true if p and q are different points.

Related concepts include nondegenerate segments, simple curves, and the notion of endpoint, as well as distance and metric properties that quantify how far apart endpoints lie. See also non-degeneracy, endpoint, and distance. While not a standardized term across all disciplines, endpointsdistinct serves as a concise descriptor for the non-degeneration condition of one-dimensional geometric objects.