iterated_circle_inversions

Command line tool for generating images of iterated circle inversions.

The code is C++23 with a dependency on Boost for boost::hash_combine and the R-tree implementation in Boost.Geometry, but no other dependencies e.g. I currently serialize to raster files using only stb-image-write.h.

The basic idea is the following:

• Let S be a set of seed circles
• Repeat n times:
  • Let S2 be an empty set of circles
  • For each combination [a,b] of circes in S:
    • Add a and b to S2 if they are not already in S2
    • Let c be a inverted about b, and let d be b inverted about a.
    • Add c and d to S2 if they are not already in S2.
  • Let S := S2

The above was generated via the following JSON input:

{
    "circles": [
        [ 0.7071067811865476, 0, 1 ],
        [ 0, 0.7071067811865476, 1 ],
        [ -0.7071067811865476, 0, 1 ],
        [ 0, -0.7071067811865476, 1 ],
        [ 0, 0, 1.7071067811865475 ]
    ],
    "iterations": 3,
    "out-file": "square_3iters.png",
    "resolution" : 3000,
    "antialiasing-level": 3,
    "colors": [ "#000000", "#444444", "#AAAAAA", "#FFD700" ],
    "view": [ -10, -10, 10, 10 ]
}

• circles: The circles array items are the [center_x, center_y, radius] of seed circles.
• iterations: Number of passes of performing circle inversion over all pairs of circles.
• out-file: Pathname of the output file. The extension determines whether we are outputting a raster file or exporting SVG.
• resolution: (raster output only) size in pixels of the longest dimension of the raster image that will be created i.e. if the logical image is 5.0 units wide by 2.5 units high and resolution is 1000 then the width of the generated image will be 1000 pixels and the height will be 500 pixels.
• antialiasing_level: (raster output only) must be [0..4]. Zero means don't antialias. Four means AA alot, each channel of an anti-aliased pixel will be accurate to the full 256 value range, but will cause rasterization to be slower.
• colors: (raster output only) color table. The color of a given segment is the kth color, where k is the number of circles that contain that segment modulo the number of colors.
• view: (raster output only) region in unscaled logical units, i.e. in the same units as the seeds, of the region to rasterize.

more output below