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Geometric patterns: polygon algorithms, sampling distributions, phyllotaxis, tilings, symmetry groups, packings, space-filling curves, polyhedra, aperiodic tilings, and knots.
Modules§
- aperiodic
- Aperiodic tilings: Penrose P2 (kite/dart) and P3 (rhombs) by Robinson-triangle deflation, de Bruijn multigrid projection, Ammann-Beenker, the hat and spectre monotiles (ported from the reference implementations accompanying Smith, Myers, Kaplan & Goodman-Strauss 2023), the pinwheel tiling, and 1-D quasiperiodic sequences.
- knots
- Knots and space curves: parametric knot families, Frenet and rotation-minimizing frames, curvature/torsion estimates, and the classical knot invariants computable from a curve in space — writhe and linking number by the Gauss integral, crossing numbers of projections, and the Alexander polynomial from a knot diagram.
- packing
- Circle and sphere packings: Descartes/Apollonian circles, lattice packings, random sequential adsorption, Doyle spirals, Ford circles, Steiner chains, and the problem of Apollonius.
- phyllotaxis
- Phyllotactic patterns and spirals: Vogel sunflowers, Fibonacci point sets, the classical spiral family, and parastichy analysis.
- polygon_
ops - 2-D polygon algorithms: triangulation, simplification, offsetting, Minkowski sums, boolean operations, clipping, decomposition, hulls, skeletons, enclosing/inscribed shapes, and fill patterns.
- polyhedra
- Polyhedra: Platonic/Archimedean/Catalan/Johnson solids, Goldberg and geodesic polyhedra, and Conway polyhedron operators.
- sampling
- Random and low-discrepancy sampling: Poisson disk (Bridson), blue-noise ranking, stratified jitter, uniform samplers over shapes, random polygons (Valtr), random rotations (Shoemake), and Lloyd relaxation.
- space_
filling - Space-filling curves and locality-preserving orders: Hilbert (2-D and 3-D), Peano, Morton/Z-order, Gray codes, and L-system curves (Sierpiński arrowhead, Moore, Gosper).
- symmetry
- Plane symmetry groups (the 17 wallpaper groups and 7 frieze groups), lattices, 3-D point groups, symmetry detection, and Hankin-style Islamic star patterns.
- tilings
- Plane tilings: regular and Archimedean (uniform) tilings, their Laves duals, hex-grid coordinate algebra, and a few classic non-edge-to-edge patterns (brick, herringbone).