An Accurate Scaling Algorithm for Convex and Non-convex Polygons Based on the Angle Bisector Method

This paper proposes an accurate offset algorithm for convex and non-convex polygons based on angular bisectors, termed the ABO (Angular Bisector Offset) algorithm. By calculating the unit vectors of adjacent edges and their cross products to determine vertex convexity, and positioning new vertices along the angle bisector direction based on scaling orientation (inward or outward), the algorithm achieves equidistant scaling of complex polygon contours. To address potential edge self-intersections during outward scaling, the algorithm incorporates a topology repair mechanism based on planar graph and outer boundary search. This ensures the simplicity and topological consistency of the output polygon through intersection detection and vertex replacement. For graphics with curved boundaries, an equal-error line approximation method is employed for discretization, expanding the algorithm's applicability. Experimental results demonstrate that the ABO algorithm outperforms traditional methods in preserving geometric accuracy and topological structure. It is applicable in fields such as CAD/CAM, GIS buffer zone analysis, and robotic path planning, providing a unified, efficient, and robust solution for the precise scaling of both convex and non-convex polygons.