sideorigin

Sideorigin is a concept encountered in geometry and related computational methods. It refers to a point or set of points designated as origins associated with the sides of a polygon or polyhedron, used to define local coordinate systems, offsets, or parameterizations along the sides.

In typical formulations, a sideorigin for a side AB of a polygon is a point O chosen on or near the perpendicular to AB, so that O serves as a reference for linear measurements, local barycentric coordinates, or side-based interpolation. Different sideorigins can be chosen to satisfy global consistency: for adjacent sides, constraints may require O for AB and BC to align along vertex B.

Common choices include the midpoint of AB, the orthogonal projection of the polygon centroid onto AB, or a point defined by a user-specified rule. In convex polygons, midpoints provide symmetry; other choices can optimize particular criteria such as smoothness in morphing or stability in mesh generation.

Applications include computer graphics for rendering offset curves, mesh generation and refinement, morphing between shapes, and path-planning algorithms that rely on side-based coordinate frames. In literature, sideorigin is often described as a flexible construction rather than a fixed standard.

Because the term is not universally standardized, definitions and properties of sideorigin vary between sources. It is primarily a descriptive tool rather than a fundamental mathematical object, and its utility depends on the surrounding algorithmic context.