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rogueviz::hypocycloid:: generalized

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Zeno Rogue 2021-02-08 23:07:25 +01:00
parent 90f3c562eb
commit cb394e9ea0
1 changed files with 81 additions and 24 deletions
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105
rogueviz/hypocycloid.cpp
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@ -17,21 +17,30 @@
namespace hr {
/* 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) */
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 */
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 = (1. * prec * ticks) / anims::period * loops;
ld t = (frac((1. * ticks) / anims::period) - cshift) * prec * loops;
if(ratio) {
ld min = 0;
@ -51,33 +60,77 @@ void circ_frame() {
vid.linewidth *= lw;
shiftmatrix at = shiftless(Id); // * xpush(rad2);
shiftmatrix at = shiftless(Id) * xpush(xdist);
ld kdegree = 2 * M_PI / prec;
if(1) {
for(int i=0; i<=prec; i++)
curvepoint(spin(i*kdegree) * xpush(rad2) * C0);
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);
}
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);
}
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);
else {
for(int i=0; i<=prec; i++)
curvepoint(spin(i*kdegree) * xpush(rad2-rad1) * spin(-i*kdegree*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);
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;
}
@ -90,7 +143,11 @@ auto shot_hooks = addHook(hooks_frame, 100, circ_frame)
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");
});
}