Nestar Polygons

by Simon Whitechapel

To create a nest-of-stars polygon, or nestar, take a polygon with v vertices and find each point (x, y) that is a/b of the distance between vertices Vn and Vn+1, where n = 1..v and n+1 = 2..v+1 (Vv+1 = V1). Use these points to create a new polygon and repeat r times to create a set of points (x1, y1)..(xr·v, yr·v). Now find the points that are c/d of the distance between all pairs in this set of points (if c/d ≠ 1/2 there are two possible points, so one is chosen by ordering the pair chronologically). The process is illustrated here:

vertices = 4; a/b = 1/2; c/d = 1/2

v = 4; a/b = 1/3; c/d = 1/2

v = 5; a/b = 1/2; c/d = 1/2

v = 5; a/b = 1/3; c/d = 1/6

v = 4; a/b = 1/3 > 2/3 > 1/3...; c/d = 1/5

v = 4; a/b = 1/8; c/d = 1/2

© 2008 Simon Whitechapel

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