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fixed draw_boundary in hyperbolic geometry in mdHemisphere and mdHyperboloid

This commit is contained in:
Zeno Rogue 2023-08-15 10:56:39 +02:00
parent 63fc2c9c92
commit ccb5068964
1 changed files with 43 additions and 16 deletions
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59
hypgraph.cpp
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@ -1027,9 +1027,8 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
if(sphere) ret[2] = -ret[2];
}
ret[0] = ret[0] / 3;
tie(ret[1], ret[2]) = make_pair(((sphere?0:1) - ret[2]) / 3, ret[1] / 3);
ret = cspin90(2, 1) * ret / 3;
if(hyperbolic) ret[1] += 1/3.;
ret = pconf.ball() * ret;
break;
}
@ -2687,6 +2686,33 @@ void queuestraight(hyperpoint X, int style, color_t lc, color_t fc, PPR p) {
} */
}
/** ball is written as cspin(0, 1, alpha) * cspin(2, 1, beta) * cspin(0, 2, gamma) */
struct ball_deconstruct {
ld alpha, beta, gamma;
transmatrix talpha, tbeta, tgamma, igamma;
ld cos_beta, sin_beta;
};
/** create a ball_deconstruct object */
ball_deconstruct deconstruct_ball() {
// (0,1,0) -> (0, cos beta, sin beta) -> (sin alpha, cos beta * cos alpha, sin beta)
hyperpoint h = pconf.ball() * point3(0, 1, 0);
ball_deconstruct d;
if(h[0] == 0 && h[1] == 0) { println(hlog, "gimbal lock"); return d; }
d.alpha = atan2(h[0], h[1]);
d.beta = atan2(h[2], hypot(h[0], h[1]));
d.cos_beta = cos(d.beta);
d.sin_beta = sin(d.beta);
d.talpha = cspin(0, 1, d.alpha);
d.tbeta = cspin(2, 1, d.beta);
d.tgamma = rot_inverse(d.tbeta) * rot_inverse(d.talpha) * pconf.ball();
h = d.tgamma * point3(0, 0, 1);
d.gamma = atan2(h[0], h[2]);
if(!eqmatrix(d.tgamma, cspin(0, 2, d.gamma))) println(hlog, "deconstruction failed");
d.igamma = cspin(1, 0, d.gamma);
return d;
}
EX void draw_boundary(int w) {
if((nonisotropic || gproduct) && pmodel == mdDisk) {
@ -2808,24 +2834,26 @@ EX void draw_boundary(int w) {
break;
case mdHemisphere: {
ld cb = pconf.ball() [1][1];
ld sb = pconf.ball() [2][1];
auto d = deconstruct_ball();
if(hyperbolic) {
queuereset(mdPixel, p);
for(int i=0; i<=360; i++) {
ld s = sin(i * degree);
curvepoint(point3(current_display->radius * cos(i * degree), current_display->radius * s * (cb * s >= 0 - 1e-6 ? 1 : abs(sb)), 0));
ld c1 = cos(i * degree - d.gamma);
ld s1 = sin(i * degree - d.gamma);
curvepoint(point3(current_display->radius * c1, current_display->radius * s1 * (d.cos_beta * s1 >= 0 - 1e-6 ? 1 : abs(d.sin_beta)), 0));
}
queuecurve(shiftless(Id), lc, fc, p);
queuecurve(shiftless(d.talpha), lc, fc, p);
queuereset(pmodel, p);
p = PPR::CIRCLE; fc = 0;
queuereset(mdPixel, p);
for(int i=0; i<=360; i++) {
ld c = cos(i * degree);
ld s = sin(i * degree);
curvepoint(point3(current_display->radius * cos(i * degree), current_display->radius * s * sb, 0));
curvepoint(point3(current_display->radius * c, current_display->radius * s * d.sin_beta, 0));
}
queuecurve(shiftless(Id), lc, fc, p);
queuecurve(shiftless(d.talpha), lc, fc, p);
queuereset(pmodel, p);
}
if(euclid) {
@ -2843,12 +2871,11 @@ EX void draw_boundary(int w) {
case mdHyperboloid: {
if(hyperbolic) {
as_hyperboloid:
auto d = deconstruct_ball();
ld& tz = pconf.top_z;
ld mz = sphere ? atan(sqrt(tz*tz-1)) : acosh(tz);
ld cb = pconf.ball() [1][1];
ld sb = pconf.ball() [2][1];
if(abs(sb) <= abs(cb) + 1e-5) {
if(abs(d.sin_beta) <= abs(d.cos_beta) + 1e-5) {
ld step = .01 / (1 << vid.linequality);
hyperpoint a;
@ -2858,7 +2885,7 @@ EX void draw_boundary(int w) {
a = xpush0(t * mz);
if(t != 0) {
a[1] = sb * a[2] / -cb;
a[1] = d.sin_beta * a[2] / -d.cos_beta;
ld v = -1 + a[2] * a[2] - a[1] * a[1];
if(v < 0) continue;
a[0] = sqrt(v);
@ -2868,7 +2895,7 @@ EX void draw_boundary(int w) {
curvepoint(a);
}
if((sb > 0) ^ (cb < 0)) {
if((d.sin_beta > 0) ^ (d.cos_beta < 0)) {
ld alpha = M_PI - atan2(a[0], -a[1]);
for(ld t=-1; t<=1; t += step)
@ -2881,7 +2908,7 @@ EX void draw_boundary(int w) {
curvepoint(xspinpush0(+90._deg - t * alpha, mz));
}
queuecurve(shiftless(Id), lc, fc, p);
queuecurve(shiftless(d.igamma), lc, fc, p);
fc = 0; p = PPR::CIRCLE;
}