hyperrogue/rogueviz/hypocycloid.cpp

// compile with mymake rogueviz/hypocycloid

// for https://twitter.com/ZenoRogue/status/1358464890978127875 :
// -hypocyc -shot-1000 -noscr -canvas i -noplayer -geo 1 circ1=1 circ2=2 show=.05 lw=20 -zoom .9 -animvideo 360 cycloid-2-euc.mp4
// for https://twitter.com/ZenoRogue/status/1358464962088337410 :
// -hypocyc -shot-1000 -noscr -canvas i -noplayer -geo 0 "circ1=0../0..4../0..|4../0..0../0" "circ2=0../0..8../0..|8../0..0../0" show=.05 lw=3 loops=10 -zoom .9 -animvideo 3600 cycloid-2-hyp.mp4
// for https://twitter.com/ZenoRogue/status/1358465029876690948 :
// -hypocyc -shot-1000 -noscr -canvas i -noplayer -geo 0 "circ1=0../0..8../0..|8../0..0../0" "circ2=0../0..32../0..|32../0..0../0" prec=3600 show=.05 lw=3 loops=10 -zoom .9 -animvideo 3600 cycloid-4-hyp.mp4

// for https://twitter.com/ZenoRogue/status/1358506225990828033 :
// -hypocyc -shot-1000 -noscr -canvas i -noplayer -geo 2 "circ1=0../0...5../0..|.5../0..0../0" "circ2=0../0..1../0..|1../0..0../0" show=.05 lw=3 loops=10 -zoom .9 -animvideo 1200 cycloid-2-sph.mp4

// for https://twitter.com/ZenoRogue/status/1358505146553159682 :
// -hypocyc -shot-1000 -noscr -canvas i -noplayer -geo 0 circ1=1 circ2=2 show=.1 lw=5 -zoom .9 "ratio=2../0..8../0..|8../0..2../0" prec=3600 -animvideo 3600 half-radius.mp4

#include "../hyper.h"

namespace hr {

namespace hypocyc {

/* what to roll on: 0 = circle, 1 = horocycle, 2 = straight line, 3 = equidistant */
int shape = 0;

ld circ1 = 0.5; /* circumference of the small circle (actually, circumference divided by 2pi) */
ld circ2 = 1;   /* circumference of the large circle (actually, circumference divided by 2pi); for shape=3, this determines the radius */

ld show = 0.02; /* radius of the blue circle which shows the moving point */

ld lw = 3;      /* linewidth multiplier */

ld loops = 1;   /* with loops=k, the circle goes around k times during the full animation; the unit is the rotation of the large circle for shape=0 and the rotation of the small circle for shape>0 */

ld ratio = 0;   /* if set to non-zero, circ1 and circ2 are assigned so that the ratio of radii is ratio */

ld xdist = 0;   /* by how much shift the image */

int prec = 360; /* precision */

ld cshift = 0;  /* cshift=0 means that we start at the center point, cshift=.5 means it is in the middle of the route */

ld draw_loops = 1; /* how many loops to draw */

void circ_frame() {
  ld t = (frac((1. * ticks) / anims::period) - cshift) * prec * loops;
  
  if(ratio) {
    ld min = 0;
    ld max = 10;
    for(int it=0; it<100; it++) {
      ld x = (min + max) / 2;
      ld f = sin_auto(2*x) - ratio * sin_auto(x);
      if((f > 0) ^ sphere) max = x;
      else min = x;
      }
    circ1 = sin_auto(min);
    circ2 = sin_auto(2*min);
    }
  
  
  ld rad1 = asin_auto(circ1);
  ld rad2 = asin_auto(circ2);
  
  dynamicval<ld> d(circ2);  
  if(circ2 > 1) {
    /* circumference between 1 and 2 means the other hemisphere */
    circ2 = 2 - circ2;
    rad2 = M_PI - asin_auto(circ2);
    }
  
  vid.linewidth *= lw;
  
  shiftmatrix at = ggmatrix(cwt.at) * xpush(xdist);
  
  ld kdegree = TAU / prec;

  ld cs = TAU * cshift;

  if(shape) {
    auto shapefun = [&] (ld x) {
      if(shape == 1)
        return parabolic1(x);
      if(shape == 2)
        return ypush(x);
      if(shape == 3)
        return xpush(-rad2) * ypush(x / cosh(rad2)) * xpush(rad2);
      return Id;
      };
    
    for(int i=0; i<=prec*draw_loops; i++) {
      ld t = i*kdegree-cs*draw_loops;
      curvepoint(shapefun(circ1*t) * C0);
      }
    queuecurve(at, 0xFF0000FF, 0x200000FF, PPR::LINE);

    for(int i=0; i<=prec; i++)
      curvepoint(shapefun(circ1*t*kdegree) * xpush(rad1) * spin(i*kdegree) * xpush(rad1) * C0);
    queuecurve(at, 0x00FF00FF, 0x002000FF, PPR::LINE);

    for(int q=0; q<360; q+=36) queueline(
      at * shapefun(circ1*t*kdegree) * xpush(rad1) * C0,
      at * shapefun(circ1*t*kdegree) * xpush(rad1) * spin(q*degree-t*kdegree) * xpush(rad1) * C0,
      0xFFD500FF, 4);
    
    for(int i=0; i<=prec; i++)
      curvepoint(shapefun(circ1*t*kdegree) * xpush(rad1) * spin(M_PI-t*kdegree) * xpush(rad1) * spin(i*kdegree) * xpush(show) * C0);
    queuecurve(at, 0xFFFFFFFF, 0xFFFF, PPR::LINE);

    for(int i=0; i<=prec*draw_loops; i++) {
      ld t = i*kdegree-cs*draw_loops;
      curvepoint(shapefun(circ1*t) * xpush(rad1) * spin(M_PI-t) * xpush(rad1) * C0);  
      }
    queuecurve(at, 0xFFFFFFFF, 0, PPR::LINE);
    }
  
  else {
  
    if(1) {
      for(int i=0; i<=prec; i++)
        curvepoint(spin(i*kdegree) * xpush(rad2) * C0);      
      queuecurve(at, 0xFF0000FF, 0x200000FF, PPR::LINE);
      }
  
    for(int i=0; i<=prec; i++)
      curvepoint(spin(t*kdegree) * xpush(rad2-rad1) * spin(i*kdegree) * xpush(rad1) * C0);
    queuecurve(at, 0x00FF00FF, 0x002000FF, PPR::LINE);
    
    for(int q=0; q<360; q+=36) queueline(
      at * spin(t*kdegree) * xpush(rad2-rad1) * C0, 
      at * spin(t*kdegree) * xpush(rad2-rad1) * spin(q*degree-t*kdegree*circ2/circ1) * xpush(rad1) * C0,
      0xFFD500FF, 4);
    
    for(int i=0; i<=prec*draw_loops; i++) {
      ld t = i*kdegree-cs*draw_loops;
      curvepoint(spin(t) * xpush(rad2-rad1) * spin(-t*circ2/circ1) * xpush(rad1) * C0);
      }
  
    queuecurve(at, 0xFFFFFFFF, 0, PPR::LINE);
  
    for(int i=0; i<=prec; i++)
      curvepoint(spin(t*kdegree) * xpush(rad2-rad1) * spin(-t*kdegree*circ2/circ1) * xpush(rad1) * spin(i*kdegree) * xpush(show) * C0);
    queuecurve(at, 0xFFFFFFFF, 0xFFFF, PPR::LINE);
    }

  vid.linewidth /= lw;
  }

void enable() {
  addHook(hooks_frame, 100, circ_frame);
  }

auto shot_hooks = arg::add2("-hypocyc", enable)
  + addHook(hooks_configfile, 100, [] {
    param_f(circ1, "circ1");
    param_f(circ2, "circ2");
    param_f(show, "show");
    param_f(loops, "loops");
    param_f(ratio, "ratio");
    param_i(prec, "prec");
    param_f(xdist, "xdist");
    param_f(lw, "lw");
    param_f(cshift, "cshift");
    param_i(shape, "shape");
    param_f(draw_loops, "draw_loops");
    });

}
}