A Constructive Method for Filling Irregular Shapes Using Recursive Self-Similar Packing скачать в хорошем качестве

A Constructive Method for Filling Irregular Shapes Using Recursive Self-Similar Packing

Abstract We present a novel approach to filling irregular planar regions with scaled copies of a template shape. Rather than using circles as the packing primitive, we generalize the boundary-driven recursive packing method to arbitrary irregular shapes, creating a self-similar tiling system. Given an irregular shape A with preserved boundary topology, we construct scaled versions B, B', B'', ... and recursively fill A with these copies at decreasing scales. The method provides theoretical convergence guarantees, establishes packing density bounds, and demonstrates practical advantages for complex domains including non-convex regions and fractal boundaries. Experimental results achieve 82-91% area coverage across diverse shape classes with computational complexity O(n log n) per iteration.