outwardoffset

Outward offset is a geometric operation that constructs a parallel curve, boundary, or region at a fixed distance away from an original feature, moving outward from its interior. In continuous geometry, the outward offset of a smooth plane curve C by distance d is the set {x + d n(x) | x in C}, where n(x) is the unit outward normal. For polygons and other non-smooth shapes, the operation is often implemented by offsetting each edge outward and recomputing the vertices, commonly modeled as the Minkowski sum of the shape with a disk of radius d.

Outward offsets are used in CAD/CAM, GIS, computer graphics, and computational geometry to create buffers, toolpaths, or margins around features. When d is small, area increases roughly by the original perimeter times d, with an additional term related to boundary curvature; for convex shapes the exact area gain is A_out = A + P d + pi d^2; for non-convex shapes, the relationship is more complex due to holes and concavities.

Corner handling: joins can be rounded, beveled, or mitered; large d can cause self-intersections or topology changes, requiring cleanup and possibly recomputation of interior boundaries. Robust implementations rely on Minkowski-sum approaches, straight-skeleton methods, or buffering operations in software libraries.

Applications include creating safety margins, manufacturing toolpaths, collision avoidance in robotics, and digital imaging operations like morphological dilation. Limitations include sensitivity to sharp features, numerical precision issues, and potential self-intersections that require post-processing.

See also: inward offset, buffering, Minkowski sum, dilation, offset curve.