// 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 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"); }); } }