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// compile with mymake rogueviz/hypocycloid
// for https://twitter.com/ZenoRogue/status/1358464890978127875 :
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// -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
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// for https://twitter.com/ZenoRogue/status/1358464962088337410 :
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// -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
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// for https://twitter.com/ZenoRogue/status/1358465029876690948 :
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// -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
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// for https://twitter.com/ZenoRogue/status/1358506225990828033 :
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// -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
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// for https://twitter.com/ZenoRogue/status/1358505146553159682 :
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// -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
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# include "../hyper.h"
namespace hr {
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namespace hypocyc {
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/* what to roll on: 0 = circle, 1 = horocycle, 2 = straight line, 3 = equidistant */
int shape = 0 ;
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ld circ1 = 0.5 ; /* circumference of the small circle (actually, circumference divided by 2pi) */
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ld circ2 = 1 ; /* circumference of the large circle (actually, circumference divided by 2pi); for shape=3, this determines the radius */
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ld show = 0.02 ; /* radius of the blue circle which shows the moving point */
ld lw = 3 ; /* linewidth multiplier */
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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 */
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ld ratio = 0 ; /* if set to non-zero, circ1 and circ2 are assigned so that the ratio of radii is ratio */
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ld xdist = 0 ; /* by how much shift the image */
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int prec = 360 ; /* precision */
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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 */
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void circ_frame ( ) {
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ld t = ( frac ( ( 1. * ticks ) / anims : : period ) - cshift ) * prec * loops ;
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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 ) ;
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if ( ( f > 0 ) ^ sphere ) max = x ;
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else min = x ;
}
circ1 = sin_auto ( min ) ;
circ2 = sin_auto ( 2 * min ) ;
}
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ld rad1 = asin_auto ( circ1 ) ;
ld rad2 = asin_auto ( circ2 ) ;
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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 ) ;
}
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vid . linewidth * = lw ;
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shiftmatrix at = ggmatrix ( cwt . at ) * xpush ( xdist ) ;
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ld kdegree = 2 * M_PI / prec ;
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ld cs = 2 * M_PI * 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 ) ;
}
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queuecurve ( at , 0xFF0000FF , 0x200000FF , PPR : : LINE ) ;
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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 ) ;
}
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else {
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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 ) ;
}
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vid . linewidth / = lw ;
}
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void enable ( ) {
addHook ( hooks_frame , 100 , circ_frame ) ;
}
auto shot_hooks = arg : : add2 ( " -hypocyc " , enable )
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+ 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 " ) ;
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param_f ( xdist , " xdist " ) ;
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param_f ( lw , " lw " ) ;
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param_f ( cshift , " cshift " ) ;
param_i ( shape , " shape " ) ;
param_f ( draw_loops , " draw_loops " ) ;
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} ) ;
}
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}