652 lines
15 KiB
C++
652 lines
15 KiB
C++
// Hyperbolic Rogue -- Kite-and-dart tiling
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// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
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/** \file apeirodic-hat.cpp
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* \brief Apeirodic Hat tiling, based on https://arxiv.org/pdf/2303.10798.pdf
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*/
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#include "hyper.h"
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namespace hr {
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EX namespace hat {
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EX bool in() { return cgflags & qHAT; }
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struct rule_base {
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int id0, edge0, id1, edge1, master_connection;
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};
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struct rule_recursive {
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int id0, id1, child, parent, rev_child;
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};
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vector<rule_base> rules_base = {
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rule_base{0, 0, 4, 6, -1},
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{0, 10, 2, 6, -1},
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{0, 11, 2, 5, -1},
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{0, 12, 4, 8, -1},
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{0, 13, 4, 7, -1},
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{0, 1, 4, 5, -1},
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{0, 2, 5, 6, -1},
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{0, 3, 5, 5, -1},
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{0, 4, 1, 0, -1},
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{0, 5, 1, 13, -1},
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{0, 6, 1, 12, -1},
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{0, 7, 1, 11, -1},
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{0, 8, 2, 8, -1},
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{0, 9, 2, 7, -1},
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{1, 0, 0, 4, -1},
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{1, 10, 2, 9, -1},
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{1, 11, 0, 7, -1},
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{1, 12, 0, 6, -1},
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{1, 13, 0, 5, -1},
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{1, 1, 6, 6, -1},
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{1, 2, 6, 5, -1},
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{1, 3, 6, 4, -1},
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{1, 4, 2, 13, 24},
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{1, 4, 3, 13, 33},
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{1, 4, 4, 13, 8},
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{1, 4, 5, 13, 13},
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{1, 4, 6, 13, 18},
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{1, 4, 7, 13, 10},
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{1, 5, 2, 12, 24},
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{1, 5, 3, 12, 33},
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{1, 5, 4, 12, 8},
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{1, 5, 5, 12, 13},
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{1, 5, 6, 12, 18},
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{1, 5, 7, 12, 10},
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{1, 6, 2, 11, 24},
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{1, 6, 3, 11, 33},
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{1, 6, 4, 11, 8},
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{1, 6, 5, 11, 13},
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{1, 6, 6, 11, 18},
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{1, 6, 7, 11, 10},
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{1, 7, 3, 0, 28},
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{1, 7, 3, 4, 8},
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{1, 7, 6, 0, 17},
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{1, 7, 7, 0, 32},
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{1, 8, 3, 13, 28},
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{1, 8, 3, 3, 8},
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{1, 8, 6, 13, 17},
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{1, 8, 7, 13, 32},
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{1, 9, 3, 12, 28},
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{1, 9, 3, 2, 8},
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{1, 9, 6, 12, 17},
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{1, 9, 7, 12, 32},
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{2, 0, 2, 13, 21},
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{2, 0, 3, 13, 23},
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{2, 0, 5, 13, 31},
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{2, 0, 6, 3, 22},
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{2, 10, 3, 11, 28},
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{2, 10, 3, 1, 8},
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{2, 10, 6, 11, 17},
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{2, 10, 7, 11, 32},
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{2, 11, 1, 6, 22},
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{2, 11, 3, 10, 28},
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{2, 11, 6, 10, 17},
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{2, 11, 7, 10, 32},
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{2, 1, 2, 12, 21},
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{2, 12, 1, 5, 22},
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{2, 12, 2, 1, 28},
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{2, 12, 3, 1, 32},
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{2, 12, 5, 1, 17},
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{2, 1, 3, 12, 23},
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{2, 13, 1, 4, 22},
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{2, 13, 2, 0, 28},
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{2, 13, 3, 0, 32},
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{2, 13, 5, 0, 17},
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{2, 1, 5, 12, 31},
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{2, 1, 6, 2, 22},
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{2, 2, 3, 9, -1},
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{2, 3, 3, 8, -1},
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{2, 4, 3, 7, -1},
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{2, 5, 0, 11, -1},
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{2, 6, 0, 10, -1},
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{2, 7, 0, 9, -1},
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{2, 8, 0, 8, -1},
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{2, 9, 1, 10, -1},
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{3, 0, 1, 7, 21},
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{3, 0, 2, 13, 15},
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{3, 0, 5, 13, 27},
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{3, 0, 6, 3, 16},
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{3, 0, 7, 3, 31},
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{3, 10, 2, 11, 21},
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{3, 10, 3, 11, 23},
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{3, 10, 5, 11, 31},
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{3, 10, 6, 1, 22},
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{3, 11, 1, 6, 16},
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{3, 11, 2, 10, 21},
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{3, 11, 3, 10, 23},
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{3, 11, 5, 10, 31},
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{3, 1, 2, 10, 11},
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{3, 1, 2, 12, 15},
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{3, 12, 1, 5, 16},
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{3, 12, 1, 9, 21},
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{3, 12, 2, 1, 23},
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{3, 12, 4, 1, 31},
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{3, 13, 1, 4, 16},
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{3, 13, 1, 8, 21},
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{3, 13, 2, 0, 23},
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{3, 13, 4, 0, 31},
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{3, 1, 5, 12, 27},
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{3, 1, 6, 2, 16},
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{3, 1, 7, 2, 31},
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{3, 2, 1, 9, 11},
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{3, 2, 7, 9, -1},
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{3, 3, 1, 8, 11},
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{3, 3, 7, 8, -1},
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{3, 4, 1, 7, 11},
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{3, 4, 7, 7, -1},
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{3, 5, 4, 10, -1},
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{3, 6, 4, 9, -1},
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{3, 7, 2, 4, -1},
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{3, 8, 2, 3, -1},
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{3, 9, 2, 2, -1},
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{4, 0, 3, 13, 14},
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{4, 0, 6, 13, 26},
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{4, 0, 6, 3, 11},
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{4, 0, 7, 13, 20},
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{4, 10, 3, 5, -1},
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{4, 11, 1, 6, 11},
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{4, 11, 7, 6, -1},
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{4, 12, 1, 5, 11},
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{4, 12, 7, 5, -1},
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{4, 1, 3, 12, 14},
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{4, 13, 1, 4, 11},
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{4, 13, 7, 4, -1},
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{4, 1, 6, 12, 26},
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{4, 1, 6, 2, 11},
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{4, 1, 7, 12, 20},
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{4, 2, 5, 9, -1},
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{4, 3, 5, 8, -1},
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{4, 4, 5, 7, -1},
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{4, 5, 0, 1, -1},
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{4, 6, 0, 0, -1},
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{4, 7, 0, 13, -1},
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{4, 8, 0, 12, -1},
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{4, 9, 3, 6, -1},
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{5, 0, 2, 13, 29},
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{5, 0, 5, 13, 19},
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{5, 0, 6, 3, 30},
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{5, 10, 3, 11, 14},
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{5, 10, 6, 1, 11},
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{5, 10, 6, 11, 26},
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{5, 10, 7, 11, 20},
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{5, 11, 1, 6, 30},
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{5, 11, 3, 10, 14},
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{5, 11, 6, 10, 26},
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{5, 11, 7, 10, 20},
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{5, 1, 2, 12, 29},
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{5, 12, 1, 5, 30},
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{5, 12, 2, 1, 14},
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{5, 12, 3, 1, 20},
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{5, 12, 5, 1, 26},
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{5, 13, 1, 4, 30},
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{5, 13, 2, 0, 14},
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{5, 13, 3, 0, 20},
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{5, 13, 5, 0, 26},
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{5, 1, 5, 12, 19},
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{5, 1, 6, 2, 30},
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{5, 2, 6, 9, -1},
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{5, 3, 6, 8, -1},
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{5, 4, 6, 7, -1},
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{5, 5, 0, 3, -1},
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{5, 6, 0, 2, -1},
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{5, 7, 4, 4, -1},
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{5, 8, 4, 3, -1},
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{5, 9, 4, 2, -1},
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{6, 0, 1, 7, 29},
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{6, 0, 6, 3, 25},
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{6, 0, 7, 3, 19},
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{6, 10, 2, 11, 29},
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{6, 10, 5, 11, 19},
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{6, 10, 6, 1, 30},
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{6, 11, 1, 6, 25},
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{6, 11, 2, 10, 29},
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{6, 11, 5, 10, 19},
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{6, 12, 1, 5, 25},
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{6, 12, 1, 9, 29},
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{6, 12, 4, 1, 19},
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{6, 1, 3, 10, 24},
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{6, 13, 1, 4, 25},
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{6, 13, 1, 8, 29},
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{6, 13, 4, 0, 19},
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{6, 1, 5, 10, 8},
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{6, 1, 6, 10, 13},
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{6, 1, 6, 2, 25},
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{6, 1, 7, 10, 33},
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{6, 1, 7, 2, 19},
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{6, 2, 2, 1, 24},
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{6, 2, 3, 1, 33},
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{6, 2, 4, 1, 8},
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{6, 2, 5, 1, 13},
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{6, 2, 6, 1, 18},
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{6, 2, 7, 1, 10},
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{6, 3, 2, 0, 24},
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{6, 3, 3, 0, 33},
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{6, 3, 4, 0, 8},
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{6, 3, 5, 0, 13},
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{6, 3, 6, 0, 18},
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{6, 3, 7, 0, 10},
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{6, 4, 1, 3, -1},
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{6, 5, 1, 2, -1},
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{6, 6, 1, 1, -1},
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{6, 7, 5, 4, -1},
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{6, 8, 5, 3, -1},
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{6, 9, 5, 2, -1},
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{7, 0, 1, 7, 15},
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{7, 0, 6, 3, 12},
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{7, 0, 7, 3, 27},
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{7, 10, 2, 11, 15},
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{7, 10, 5, 11, 27},
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{7, 10, 6, 1, 16},
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{7, 10, 7, 1, 31},
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{7, 11, 1, 6, 12},
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{7, 11, 2, 10, 15},
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{7, 11, 5, 10, 27},
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{7, 12, 1, 5, 12},
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{7, 12, 1, 9, 15},
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{7, 12, 4, 1, 27},
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{7, 13, 1, 4, 12},
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{7, 13, 1, 8, 15},
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{7, 13, 4, 0, 27},
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{7, 1, 6, 2, 12},
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{7, 1, 7, 10, 14},
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{7, 1, 7, 2, 27},
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{7, 2, 3, 1, 14},
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{7, 2, 6, 1, 26},
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{7, 2, 7, 1, 20},
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{7, 3, 3, 0, 14},
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{7, 3, 6, 0, 26},
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{7, 3, 7, 0, 20},
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{7, 4, 4, 13, -1},
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{7, 5, 4, 12, -1},
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{7, 6, 4, 11, -1},
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{7, 7, 3, 4, -1},
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{7, 8, 3, 3, -1},
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{7, 9, 3, 2, -1},
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};
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vector<rule_recursive> rules_recursive = {
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rule_recursive{0, 0, -1, -1, -1},
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{0, 1, 10, 18, 12},
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{0, 1, 25, -1, 18},
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{0, 1, 32, 17, 15},
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{0, 2, 10, 13, 12},
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{0, 2, 30, -1, 13},
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{0, 3, 10, 8, 12},
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{0, 3, 11, -1, 8},
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{0, 4, 10, 24, 12},
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{0, 4, 21, -1, 28},
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{0, 5, 10, 33, 12},
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{0, 5, 17, 8, 29},
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{0, 5, 32, 28, 15},
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{0, 6, 10, 10, 12},
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{0, 6, 32, 32, 15},
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{1, 0, 12, 25, 10},
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{1, 0, 15, 29, 32},
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{1, 0, 18, -1, 25},
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{1, 1, -1, -1, -1},
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{1, 1, 14, 13, 31},
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{1, 1, 19, 18, 26},
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{1, 1, 26, 25, 19},
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{1, 1, 31, 30, 14},
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{1, 2, 14, 8, 31},
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{1, 2, 17, -1, 29},
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{1, 2, 19, 13, 26},
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{1, 2, 23, 19, 23},
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{1, 3, 19, 8, 26},
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{1, 3, 27, 19, 20},
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{1, 4, 19, 24, 26},
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{1, 4, 23, 29, 23},
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{1, 5, 14, 24, 31},
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{1, 5, 19, 33, 26},
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{1, 6, 14, 33, 31},
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{1, 6, 19, 10, 26},
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{1, 6, 26, 19, 19},
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{2, 0, 12, 30, 10},
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{2, 0, 13, -1, 30},
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{2, 1, 23, 26, 23},
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{2, 1, 26, 30, 19},
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{2, 1, 29, -1, 17},
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{2, 1, 31, 11, 14},
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{2, 2, -1, -1, -1},
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{2, 2, 20, 19, 27},
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{2, 2, 27, 26, 20},
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{2, 3, 17, -1, 29},
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{2, 4, 20, 29, 27},
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{2, 4, 27, 14, 20},
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{2, 5, 23, 14, 23},
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{2, 5, 27, 20, 20},
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{2, 6, 23, 20, 23},
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{3, 0, 12, 11, 10},
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{3, 0, 8, -1, 11},
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{3, 1, 20, 26, 27},
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{3, 1, 26, 11, 19},
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{3, 2, 29, -1, 17},
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{3, 3, -1, -1, -1},
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{3, 4, 22, -1, 24},
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{3, 5, 16, -1, 33},
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{3, 5, 20, 14, 27},
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{3, 6, 12, -1, 10},
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{3, 6, 20, 20, 27},
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{4, 0, 12, 22, 10},
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{4, 0, 28, -1, 21},
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{4, 1, 23, 17, 23},
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{4, 1, 26, 22, 19},
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{4, 2, 20, 31, 27},
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{4, 2, 27, 17, 20},
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{4, 3, 24, -1, 22},
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{4, 4, -1, -1, -1},
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{4, 4, 20, 21, 27},
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{4, 4, 27, 28, 20},
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{4, 5, 20, 23, 27},
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{4, 5, 23, 28, 23},
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{4, 5, 27, 32, 20},
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{4, 5, 29, -1, 17},
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{4, 5, 31, 8, 14},
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{4, 6, 23, 32, 23},
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{5, 0, 12, 16, 10},
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{5, 0, 15, 21, 32},
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{5, 0, 29, 11, 17},
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{5, 1, 26, 16, 19},
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{5, 1, 31, 22, 14},
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{5, 2, 20, 27, 27},
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{5, 2, 23, 31, 23},
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{5, 3, 27, 31, 20},
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{5, 3, 33, -1, 16},
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{5, 4, 14, 11, 31},
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{5, 4, 17, -1, 29},
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{5, 4, 20, 15, 27},
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{5, 4, 23, 21, 23},
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{5, 4, 27, 23, 20},
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{5, 5, -1, -1, -1},
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{5, 5, 23, 23, 23},
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{5, 6, 26, 31, 19},
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{5, 6, 29, -1, 17},
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{6, 0, 12, 12, 10},
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{6, 0, 15, 15, 32},
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{6, 1, 19, 26, 26},
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{6, 1, 26, 12, 19},
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{6, 1, 31, 16, 14},
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{6, 2, 23, 27, 23},
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{6, 3, 10, -1, 12},
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{6, 3, 27, 27, 20},
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{6, 4, 23, 15, 23},
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{6, 5, 17, -1, 29},
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{6, 5, 19, 14, 26},
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{6, 6, -1, -1, -1},
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{6, 6, 14, 14, 31},
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{6, 6, 19, 20, 26},
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{6, 6, 26, 27, 19},
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{6, 6, 31, 31, 14},
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};
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EX ld hat_param = 1;
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struct hrmap_hat : hrmap {
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// always generate the same way
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std::mt19937 hatrng;
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int hatrand(int i) {
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return hatrng() % i;
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}
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// cluster centers are of type 1, all the rest are of type 0 (they are mirror images)
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int shvid(cell *c) override {
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return c->master->c7 == c ? 1 : 0;
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}
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// vertices of each type of hat
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vector<hyperpoint> hatcorners[2];
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void init() {
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transmatrix T = Id;
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auto& hc = hatcorners[0];
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hc.clear();
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hatcorners[1].clear();
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auto move = [&] (ld angle, ld dist) {
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hc.push_back(T * C0);
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T = T * spin(angle * degree);
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T = T * xpush(dist);
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};
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ld q = 6;
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ld eshort = 0.3;
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ld elong = sqrt(3) * eshort;
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if(fake::in()) q = fake::around;
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if(q != 6) {
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eshort = edge_of_triangle_with_angles(M_PI / q, 60._deg, 90._deg);
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elong = edge_of_triangle_with_angles(60._deg, M_PI / q, 90._deg);
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}
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else {
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eshort *= hat_param;
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elong *= 2 - hat_param;
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// 0-length edges cause problems...
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if(eshort == 0) eshort = .0001;
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if(elong == 0) elong = .0001;
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}
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ld i60 = (M_PI - TAU*2/q)/degree;
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ld n60 = (M_PI - TAU*4/q)/degree;
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move(-90, eshort); move( 60, eshort); move( 0, eshort);
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move( 60, eshort); move( 90, elong); move(n60, elong);
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move( 90, eshort); move(-60, eshort); move( 90, elong);
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move(i60, elong); move(-90, eshort); move( 60, eshort);
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move( 90, elong); move(i60, elong);
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|
|
|
if(q == 6) {
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|
ld area = 0;
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for(int i=0; i<14; i++) area += (hc[(i+1)%14] ^ hc[i]) [2];
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println(hlog, "area = ", area);
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|
area = abs(area);
|
|
ld scale = sqrt(2.5 / area);
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|
for(auto& h: hc) h = h * scale + (C0) * (1-scale);
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|
}
|
|
|
|
hyperpoint ctr = Hypc;
|
|
for(auto h: hc) ctr += h;
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|
ctr /= isize(hc);
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|
ctr = normalize(ctr);
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|
for(auto& h: hc) h = gpushxto0(ctr) * h;
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|
|
|
hatcorners[1] = hc;
|
|
for(auto& h: hatcorners[1]) h = MirrorX * h;
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|
reverse(hatcorners[1].begin(), hatcorners[1].end());
|
|
}
|
|
|
|
constexpr static int relations = 34;
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|
|
|
// heptagons represent clusters
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|
// heptagon->distance is 0 for clusters of hats, d+1 for supercluster of heptagon d
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|
// heptagon->zebraval is 1 for central, 0 for non-central
|
|
// 0 is supercluster, 1..(7-zebraval) are child clusters, 8..(relations-1) are nearby clusters on the same level
|
|
|
|
/** for 0-level, the list of hats*/
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|
map<heptagon*, vector<cell*>> hats;
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|
|
|
heptagon *origin;
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|
|
|
heptagon *getOrigin() override { return origin; }
|
|
|
|
hyperpoint get_corner(cell *c, int cid, ld cf) override {
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|
cid = gmod(cid, isize(hatcorners[0]));
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|
int t = c->master->c7 == c;
|
|
auto& h = hatcorners[t][cid];
|
|
|
|
return C0 * (1-3./cf) + h * (3./cf);
|
|
}
|
|
|
|
heptagon *create_step(heptagon *h, int dir) override {
|
|
auto h1 = get_step(h, dir);
|
|
if(!h1) throw hr_exception("create_step");
|
|
return h1;
|
|
}
|
|
|
|
heptagon *get_step(heptagon *h, int dir) {
|
|
if(dir == -1) return h;
|
|
if(h->move(dir)) return h->move(dir);
|
|
if(dir == 0) {
|
|
// create parent
|
|
auto h1 = init_heptagon(relations);
|
|
h1->distance = h->distance + 1;
|
|
if(h->distance >= 1000) throw hr_exception("too much recursion");
|
|
h1->zebraval = hatrand(2);
|
|
if(h->zebraval == 1) {
|
|
h->c.connect(dir, h1, 1, false);
|
|
}
|
|
else {
|
|
h->c.connect(dir, h1, 2 + hatrand(5-h->zebraval), false);
|
|
}
|
|
return h1;
|
|
}
|
|
if(dir <= 7 - h->zebraval) {
|
|
// create child
|
|
auto h1 = init_heptagon(relations);
|
|
h1->distance = h->distance - 1;
|
|
h1->zebraval = dir == 1;
|
|
h->c.connect(dir, h1, 0, false);
|
|
if(h1->distance == 0) build_cells(h1);
|
|
return h1;
|
|
}
|
|
// create side connection
|
|
createStep(h, 0);
|
|
int id = h->c.spin(0)-1;
|
|
indenter ind(2);
|
|
for(auto& ru: rules_recursive) {
|
|
if(ru.id0 == id && ru.child == dir) {
|
|
heptagon *h1 = get_step(h->move(0), ru.parent);
|
|
if(!h1) continue;
|
|
heptagon *h2 = get_step(h1, ru.id1+1);
|
|
if(!h2) continue;
|
|
h->c.connect(dir, h2, ru.rev_child, false);
|
|
return h2;
|
|
}
|
|
}
|
|
return nullptr;
|
|
}
|
|
|
|
int fix(int d) {
|
|
int n = isize(hatcorners[0]);
|
|
return gmod(n-2-d, n);
|
|
}
|
|
|
|
int hat_id(cell *c) {
|
|
auto& gha = hats[c->master];
|
|
for(int i=0; i<isize(gha); i++) if(gha[i] == c) return i;
|
|
throw hr_exception("not in hats");
|
|
}
|
|
|
|
void find_cell_connection(cell *c, int d) {
|
|
int id = hat_id(c);
|
|
indenter ind(2);
|
|
for(auto& ru: rules_base) {
|
|
if(ru.id0 == id && ru.edge0 == fix(d)) {
|
|
heptagon *h = get_step(c->master, ru.master_connection);
|
|
if(!h) continue;
|
|
build_cells(h);
|
|
auto& ha = hats[h];
|
|
if(ru.id1 >= isize(ha)) continue;
|
|
auto& c1 = ha[ru.id1];
|
|
c->c.connect(d, c1, fix(ru.edge1), false);
|
|
return;
|
|
}
|
|
}
|
|
throw hr_exception("cell connection not found");
|
|
}
|
|
|
|
transmatrix adj(cell *c0, int d0) override {
|
|
cell *c1 = c0->cmove(d0);
|
|
int t0 = c0 == c0->master->c7;
|
|
int t1 = c1 == c1->master->c7;
|
|
int n = isize(hatcorners[0]);
|
|
int d1 = c0->c.spin(d0);
|
|
|
|
hyperpoint vl = hatcorners[t0][d0];
|
|
hyperpoint vr = hatcorners[t0][(d0+1)%n];
|
|
|
|
hyperpoint vm = mid(vl, vr);
|
|
|
|
transmatrix rm = gpushxto0(vm);
|
|
|
|
hyperpoint xvl = hatcorners[t1][d1];
|
|
hyperpoint xvr = hatcorners[t1][(d1+1)%n];
|
|
hyperpoint xvm = mid(xvl, xvr);
|
|
|
|
transmatrix xrm = gpushxto0(xvm);
|
|
|
|
if(abs(hdist(vl, vr) - hdist(xvl, xvr)) > 1e-3)
|
|
throw hr_exception("wrong length connection");
|
|
|
|
transmatrix T = rgpushxto0(vm) * rspintox(rm*vr) * spintox(xrm*xvl) * xrm;
|
|
|
|
return T;
|
|
}
|
|
|
|
void build_cells(heptagon *h) {
|
|
if(h->c7) return;
|
|
auto& ha = hats[h];
|
|
ha.resize(8 - h->zebraval);
|
|
for(auto& hac: ha) hac = newCell(isize(hatcorners[0]), h);
|
|
h->c7 = ha[0];
|
|
}
|
|
|
|
hrmap_hat() {
|
|
hatrng.seed(37);
|
|
init();
|
|
origin = init_heptagon(relations);
|
|
origin->distance = 0;
|
|
origin->zebraval = 1;
|
|
build_cells(origin);
|
|
}
|
|
|
|
~hrmap_hat() {
|
|
clearfrom(origin);
|
|
}
|
|
|
|
};
|
|
|
|
EX hrmap *new_map() { return new hrmap_hat; }
|
|
|
|
hrmap_hat* hat_map() { return dynamic_cast<hrmap_hat*>(currentmap); }
|
|
|
|
EX bool pseudohept(cell *c) {
|
|
int id = hat_map()->hat_id(c);
|
|
return id == 0 || id == 6;
|
|
}
|
|
|
|
EX int get_hat_id(cell *c) {
|
|
return hat_map()->hat_id(c);
|
|
}
|
|
|
|
EX void reshape() {
|
|
hrmap_hat *hatmap;
|
|
hatmap = FPIU( hat_map() );
|
|
if(!hatmap) return;
|
|
hatmap->init();
|
|
}
|
|
|
|
EX color_t hatcolor(cell *c, int mode) {
|
|
vector<int> cols;
|
|
auto *m = (hrmap_hat*) (currentmap);
|
|
cols.push_back(m->hat_id(c));
|
|
heptagon *h = c->master;
|
|
for(int i=0; i<6; i++) { h->cmove(0); cols.push_back(h->c.spin(0)-1); h = h->cmove(0); }
|
|
color_t col = 0xFFFFFF;
|
|
if(cols[0] == 0) col |= 0x1000000;
|
|
vector<int> ads = {0, 0x1, 0x100, 0x101, 0x10000, 0x10001, 0x10100, 0x10101 };
|
|
for(int a=0; a<7; a++) {
|
|
col -= ads[cols[a]] << (mode - a) % 7;
|
|
}
|
|
return col;
|
|
}
|
|
|
|
}}
|
|
|
|
|