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361 lines
10 KiB
C++
361 lines
10 KiB
C++
// non-Euclidean sunflower spirals (aka golden spirals or Fibonacci spirals)
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// Copyright (C) 2018 Zeno and Tehora Rogue, see 'hyper.cpp' for details
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// use: commandline parameter -sunflower <quantity> <density>
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// e.g.: hyper -sunflower-qd 10000 1
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// e.g.: hyper -sunflower-dr 1 4.5
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// Commandlines for https://twitter.com/ZenoRogue/status/1247900522905886723 :
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// Part 1:
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// -geo 1 -sunflower-node 1 -sunflower-qd "1..10..20..60..100..140..180..220..|1000..1040..|2000..2040..|5000..5040..|10000..10040" 1 -zoom "sqrt(1000/(100+sunq))" -animperiod 20000 -shott 0 -back A0E0A0 -lw 16 -shotxy 1000 1000 -shotaa 2
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// Part 2:
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// -rugtsize 8192 -rugon -run -rugv 4000000 -run -sunflower-dr "0.001..0.002..0.005..0.01..0.02..0.04..0.06..0.07..0.08..0.09" 3..4.1..4.5..4.5..4.5..4.5..4.5..4.5..4.5 -lw 4 -sunflower-out 1 -shott 0 -back A0E0A0 -shotxy 1000 1000 -shotaa 2 -sunflower-adj 16 -animrec 600 curv%04d.png
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// rotate the rug; press F10; wait until rug has millions of vertices; press F10; animation will be recorded
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// Part 3:
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// -rugtsize 8192 -rugon -rugv 1000000 -sunflower-dr .5 4.5 -lw 16 -shott 0 -back A0E0A0 -shotxy 1000 1000 -shotaa 2 -sunflower-adj 6
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// (rotation animation set manually)
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// Part 4:
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// -geo 2 -sunflower-dr .1 pi -shott 0 -back A0E0A0 -shotxy 1000 1000 -shotaa 2 -animmove "2*pi" 0 0
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#include "rogueviz.h"
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namespace rogueviz {
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namespace sunflower {
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bool nodes;
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ld qty = 100;
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ld density = 1, zdensity;
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ld range;
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ld yshift;
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ld distance_per_rug;
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bool adjust_rug;
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/* which property to infer from the other two: 'd'ensity, 'q'ty or 'r'ange */
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char infer;
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vector<hyperpoint> ps;
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int iqty;
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ld qfrac;
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bool outward = false;
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ld step_angle = M_PI * (3 - sqrt(5));
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hyperpoint p(int i) {
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ld step = step_angle;
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return spin((outward ? i : i-iqty) * step) * xpush(sphere ? (acos(1 - (i+.5+qfrac) * density)) : euclid ? sqrt((i+.5+qfrac) * density) : acosh(1 + (i+.5+qfrac) * density)) * C0;
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}
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vector<int> inext, inext2;
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vector<int> fibs;
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color_t sunflower1 = 0xC04000FF;
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color_t sunflower2 = 0xFFD500FF;
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color_t sunflower3 = 0x000000FF;
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bool overlay = false;
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bool sunflower_cell(cell *c, shiftmatrix V) {
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density = zdensity / 100;
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ld qd;
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if(sphere) {
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if(infer == 'r')
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range = qty * density * 90._deg;
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else qd = range / 90._deg;
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}
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else if(euclid) {
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if(infer == 'r')
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range = sqrt(qty * density);
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else qd = range * range;
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}
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else {
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if(infer == 'r')
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range = acosh(1 + qty * density);
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else
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qd = (cosh(range) - 1);
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}
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if(infer == 'q') qty = qd / density;
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if(infer == 'd') density = qd / qty;
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if(adjust_rug) {
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using namespace rug;
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model_distance = sqrt(zdensity) * distance_per_rug;
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}
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iqty = qty;
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qfrac = qty - iqty;
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if(outward) qfrac = 0;
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if(iqty < 0 || iqty > 2000000) return false;
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if(fibs.empty()) {
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ld best_error = 1;
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vector<int> sgns;
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for(int i=1; i<iqty; i++) {
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ld v = i * step_angle / TAU;
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v = frac(v);
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auto sgn = v > .5;
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if(sgn) v = 1-v;
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if(v < best_error) fibs.push_back(i), sgns.push_back(sgn), best_error = v;
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}
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println(hlog, "fibs = ", fibs);
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println(hlog, "sgns = ", sgns);
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}
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ps.resize(iqty);
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inext.resize(iqty);
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inext2.resize(iqty);
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while(fibs.back() < iqty) {
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/* to do: might not work correctly if step_angle is changed */
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auto add = fibs.back() + *(fibs.end()-2);
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fibs.push_back(add);
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}
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if(c == cwt.at) {
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for(int i=0; i<iqty; i++) ps[i] = p(i);
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for(int i=0; i<iqty; i++) {
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ld ba = 99;
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ld bb = 99;
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int bi = 0, bj = 0;
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for(int a: fibs) {
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if(a>i) break;
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if(hdist(ps[i], ps[i-a]) < ba)
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bb = ba, bj = bi, ba = hdist(ps[i], ps[i-a]), bi = i-a;
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else if(hdist(ps[i], ps[i-a]) < bb)
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bb = hdist(ps[i], ps[i-a]), bj = i-a;
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}
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inext[i] = bi;
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inext2[i] = bj;
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}
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if(sunflower1 || sunflower2 || sunflower3) for(int i=0; i<iqty; i++) {
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if(inext[inext[i]] == inext2[i] || inext2[inext[i]] == inext2[i] || inext[inext2[i]] == inext[i] || inext2[inext2[i]] == inext[i]) {
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curvepoint(ps[i]);
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curvepoint(ps[inext2[i]]);
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curvepoint(ps[inext[i]]);
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// queuecurve(0xFFFFFFFF, 0x00C000FF, PPR::LINE);
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queuecurve(V * ypush(yshift), sunflower3, sunflower1, PPR::LINE);
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}
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else {
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curvepoint(ps[i]);
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curvepoint(ps[inext[i]]);
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curvepoint(ps[inext[i] + inext2[i] - i]);
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curvepoint(ps[inext2[i]]);
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queuecurve(V * ypush(yshift), sunflower3, sunflower2, PPR::LINE);
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}
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if(nodes) queuepolyat(V * ypush(yshift) * rgpushxto0(ps[i]), cgi.shSnowball, 0xFF, PPR::SUPERLINE);
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}
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}
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return !overlay;
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}
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void insert_param() {
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param_f(zdensity, "sund");
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param_f(qty, "sunq");
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param_f(range, "sunr");
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param_f(distance_per_rug, "sunf");
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param_f(yshift, "sunyshift");
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}
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void show();
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void enable() {
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rv_hook(hooks_o_key, 80, [] (o_funcs& v) { v.push_back(named_dialog("sunflowers", show)); });
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rv_hook(hooks_drawcell, 100, sunflower_cell);
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}
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int readArgs() {
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using namespace arg;
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if(0) ;
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else if(argis("-sunflower-qd")) {
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enable();
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infer = 'r';
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shift_arg_formula(qty);
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shift_arg_formula(zdensity);
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patterns::whichShape = '9';
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insert_param();
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nohud = true;
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}
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else if(argis("-sunflower-qr")) {
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enable();
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infer = 'd';
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shift_arg_formula(qty);
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shift_arg_formula(range);
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patterns::whichShape = '9';
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insert_param();
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nohud = true;
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}
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else if(argis("-sunflower-dr")) {
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infer = 'q';
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shift_arg_formula(zdensity);
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shift_arg_formula(range);
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enable();
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/*
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patterns::whichShape = '9';
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*/
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insert_param();
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nohud = true;
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}
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else if(argis("-sunflower-node")) {
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shift(); nodes = argi();
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}
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else if(argis("-sunflower-out")) {
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shift(); outward = argi();
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}
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else if(argis("-sunflower-angle")) {
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shift_arg_formula(step_angle, [] { fibs.clear(); });
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}
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else if(argis("-sunflower-adj")) {
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adjust_rug = true;
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shift_arg_formula(distance_per_rug);
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}
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else if(argis("-sunflower-colors")) {
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PHASEFROM(2);
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shift(); sunflower1 = argcolor(32);
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shift(); sunflower2 = argcolor(32);
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shift(); sunflower3 = argcolor(32);
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}
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else if(argis("-sunflower-overlay")) {
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PHASEFROM(2);
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shift(); overlay = argi();
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}
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else return 1;
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return 0;
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}
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void show() {
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cmode = sm::SIDE | sm::MAYDARK;
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gamescreen();
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dialog::init(XLAT("sunflower spirals"), 0xFFFFFFFF, 150, 0);
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dialog::addSelItem("density", fts(zdensity), 'd');
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dialog::add_action([] {
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if(infer == 'd') infer = 'q';
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dialog::editNumber(zdensity, 0, 2, .1, 1, "density", "density");
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});
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dialog::addSelItem("quantity", fts(qty), 'q');
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dialog::add_action([] {
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if(infer == 'q') infer = 'r';
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dialog::editNumber(qty, 1, 100000, .1, 1000, "quantity", "quantity");
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dialog::scaleLog();
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});
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dialog::addSelItem("radius", fts(range), 'q');
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dialog::add_action([] {
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if(infer == 'r') infer = 'd';
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dialog::editNumber(range, 0, 10, .1, TAU, "range", "range");
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dialog::scaleLog();
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});
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dialog::addSelItem("infer", infer == 'd' ? "density" : infer == 'q' ? "quantity" : "range", 'i');
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dialog::add_action([] {
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if(infer == 'r') infer = 'd';
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else if(infer == 'd') infer = 'q';
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else infer = 'r';
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});
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if(rug::rugged) {
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dialog::addBoolItem("adjust Rug curvature", adjust_rug, 'a');
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dialog::add_action([] {
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adjust_rug = !adjust_rug;
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distance_per_rug = rug::model_distance / sqrt(zdensity);
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});
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if(adjust_rug) {
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dialog::addSelItem("factor", fts(distance_per_rug), 'f');
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dialog::add_action([] {
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dialog::editNumber(distance_per_rug, 0, 10, .1, 4,
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"factor", "factor");
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});
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}
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else {
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dialog::addItem("disable the Hypersian Rug", 'f');
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dialog::add_action(rug::close);
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}
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}
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else {
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dialog::addItem("enable the Hypersian Rug", 'a');
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dialog::add_action(rug::init);
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}
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dialog::addBoolItem("draw the seeds", nodes, 's');
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dialog::addBoolItem("grow at the edge", outward, 'o');
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dialog::addBack();
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dialog::display();
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}
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auto hook = 0
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#if CAP_COMMANDLINE
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+ addHook(hooks_args, 100, readArgs)
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#endif
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+ addHook_rvslides(144, [] (string s, vector<tour::slide>& v) {
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if(s != "mixed") return;
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using namespace tour;
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v.push_back(
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tour::slide{"sunflower spirals", 18, LEGAL::ANY | QUICKGEO,
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"A sunflower sends out its n-th seed at angle 180° (3-sqrt(5)). "
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"As new seeds are created, older seeds are pushed out. Therefore. "
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"the distance d(n) of the n-th seed from the center will be such that "
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"the area of a circle of radius d(n) changes linearly with n.\n\n"
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"In the Euclidean plane, this process creates an interesting "
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"phenomenon: if we try to compute the number of spirals at a given "
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"distance from the center, we usually obtain a Fibonacci number. "
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"The further from the start we are, the larger Fibonacci number we "
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"get.\n\n"
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"Because of the exponential growth in the hyperbolic plane, we "
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"get to larger Fibonacci numbers faster.\n\n"
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"Press 123 to change the geometry, 5 to see this in the Hypersian Rug model. "
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"Press o to change the density.",
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[] (presmode mode) {
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slide_url(mode, 'y', "YouTube link", "https://www.youtube.com/watch?v=bKzibaNqEog");
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slide_url(mode, 't', "Twitter link", "https://twitter.com/ZenoRogue/status/1247900522905886723");
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setPlainCanvas(mode);
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if((mode == pmStop || mode == pmGeometry) && rug::rugged) rug::close();
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if(mode == pmKey) {
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if(rug::rugged) rug::close();
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else rug::init();
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}
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if(mode == pmStart) {
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stop_game();
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enable();
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tour::slide_backup(range, sphere ? 2 : euclid ? 10 : 4.3);
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tour::slide_backup<ld>(zdensity, 1);
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tour::slide_backup(infer, 'q');
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insert_param();
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start_game();
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}
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}}
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);
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});
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}
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} |